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Distinguishing quantum states becomes exponentially difficult as their fidelity approaches unity, with diminishing success probabilities. This study revisits chaotic dynamics, leveraging their extreme sensitivity to initial conditions for rapid amplification of state discrimination measures. The discrete-time chaotic evolution of qubit states is generated via iterative application of a nonlinear conformal map on the Julia set. The "quantum microscope" is characterized by a magnification power quantified through a temporal Bell-type inequality. Fixed points of the conformal map are shown to dictate optimal measurement operators, enabling (a) well-defined magnification power and (b) bounded Bell-type inequality values, providing a device-independent framework for self-testing the microscopes performance., Comment: 12 pages, 9 figures

In [Phys. Rev. A 77, 060304(R),(2008)], Facchi et al. introduced absolutely maximally entangled (AME) states and also suggested ``majority-agreed key distribution"(MAKD) as a possible application for such states. In MAKD, the qubits of an AME state are distributed one each to many spatially separated parties. AME property makes it necessary that quantum key distribution(QKD) between any two parties can only be performed with the cooperation of a majority of parties. Our contributions to MAKD are, $(1)$ We recognize that stabilizer structure of the shared state is a useful addition to MAKD and prove that the cooperation of any majority of parties(including the two communicants) is necessary and sufficient for QKD between any two parties sharing AME stabilizer states. Considering the rarity of qubit AME states, we extended this result to the qudit case. $(2)$ We generalize to shared graph states that are not necessarily AME. We show that the stabilizer structure of graph states allows for QKD between any inseparable bipartition of qubits. Inseparability in graph states is visually apparent in the connectivity of its underlying mathematical graph. We exploit this connectivity to demonstrate conference keys and multiple independent keys per shared state. Recent experimental and theoretical progress in graph state preparation and self-testing make these protocols feasible in the near future., Comment: 14 pages, 8 figures, 2 tables

Edge reconstruction of gate-tunable compressible quantum Hall fluids in the filling fraction range 1/3 to 2/3 is studied by measuring transmitted conductance of two individually excited fractional $e^2/3h$ edge modes of bulk 2/3 fractional quantum Hall fluid. Our findings reveal that the measured transmitted conductance deviates from the fully equilibrated value for the filling fraction range 1/3 to 2/3 of the gate-tunable compressible quantum Hall fluids at higher magnetic fields. This observation suggests that at the boundary of the compressible fluid a reconstructed $e^2/3h$ fractional edge mode is present and the mode does not completely equilibrate with the inner dissipative bulk region. Consequently, this outer reconstructed edge mode supports adiabatic charge transport, allowing non-equilibrated current transport through the compressible region. These studies open new avenues for achieving robust fractional edge modes even in compressible quantum Hall fluids under strong magnetic fields, enhancing our understanding of edge state dynamics in these complex systems., Comment: 9 pages, 5 figures

An m-uniform quantum state on n qubits is an entangled state in which every m-qubit subsystem is maximally mixed. Such a state spans a pure [[n,0,m+1]] quantum error correcting code (QECC). Starting with an m-uniform state realized as the graph state associated with an m-regular graph, and a classical [n,k,d \ge m+1] binary linear code with certain additional properties, we construct codeword stabilized (CWS) codes that are pure [[n,k,m+1]] QECCs. We propose measurement-based protocols for encoding into code states and recovery of logical qubits from code states. Our proposed protocols support sequential encoding and partial recovery of logical qubits, which can be useful for quantum memory applications., Comment: A shorter version of this manuscript is available in the Proceedings of the 2024 International Symposium on Information Theory (ISIT 2024)

We studied longitudinal and Hall photothermal voltages under a planar magnetic field scan in epitaxial thin films of the Topological Insulator (TI) Sb2Te3, grown using pulsed laser deposition (PLD). Unlike prior research that utilised polarised light-induced photocurrent to investigate the TI, our study introduces advancements based on unpolarized light-induced local heating. This method yields a thermoelectric response exhibiting a direct signature of strong spin-orbit coupling. Our analysis reveals three distinct contributions when fitting the photothermal voltage data to the angular dependence of the planar magnetic field. The interaction between the applied magnetic field and the thermal gradient on the bulk band orbitals enables the differentiation between the ordinary Nernst effect from the out-of-plane thermal gradient and an extraordinary magneto-thermal contribution from the planar thermal gradient. The fitting of our data to theoretical models indicates that these effects primarily arise from the bulk states of the TI rather than the surface states. These findings highlight PLD-grown epitaxial topological insulator thin films as promising candidates for optoelectronic devices, including sensors and actuators. Such devices offer controllable responses through position-dependent, non-invasive local heating via focused incident light and variations in the applied magnetic field direction.

We investigate helical edge states (HES) emerging at the composite domain wall of spin and pseudo-spin degrees of freedom in a 2-D bulk governed by the Bernevig-Hughes-Zhang Hamiltonian which underwent quantum spin Hall to anomalous Hall transition. We numerically study the stability of Majorana bound state (MBS) formed due to proximity induced superconductivity in these helical edge states. We establish exceptional robustness of MBS against moderate chemical potential or magnetic disorder owing to the existence of the simultaneous orthogonality between the right and the left moving modes both in spin and pseudo-spin space. Hence our proposal could pave the way to realizing robust Majorana bound state on 2D platforms., Comment: 7 pages, 5 figures

Any pure state of a qubit can be geometrically represented as a point on the extended complex plane through stereographic projection. By employing successive conformal maps on the extended complex plane, we can generate an effective discrete-time evolution of the pure states of the qubit. This work focuses on a subset of analytic maps known as fractional linear conformal maps. We show that these maps serve as a unifying framework for a diverse range of quantum-inspired conceivable dynamics, including (i) unitary dynamics,(ii) non-unitary but linear dynamics and (iii) non-unitary and non-linear dynamics where linearity (non-linearity) refers to the action of the discrete time evolution operator on the Hilbert space. We provide a characterization of these maps in terms of Leggett-Garg Inequality complemented with No-signaling in Time (NSIT) and Arrow of Time (AoT) conditions., Comment: 9 pages, 1 figure

Optimal choice of spin polarization enables electron injection into the helical edge state at a precise position, despite the uncertainty principle, permitting access to specific nonlocal Green's functions. We show, within 1D effective description, that this fact facilitates a direct identification of odd-frequency pairing through parity measurement (under frequency reversal) of the nonlocal differential conductance in a setup comprising the Josephson junction on the helical edge state of a 2D topological insulator with two spin-polarized probes tunnel-coupled to the junction region. A 2D numerical simulation has also been conducted to confirm theoretical predictions as well as to demonstrate the experimental feasibility of the proposal., Comment: 11 pages, 3 figures

Despite its non-Hermitian nature, the transverse optical beam shift exhibits both real eigenvalues and non-orthogonal eigenstates. To explore this unexpected similarity to typical PT (parity-time)-symmetric systems, we first categorize the entire parametric regime of optical beam shifts into Hermitian, PT-unbroken, and PT-broken phases. Besides experimentally unveiling the PT-broken regime, crucially, we illustrate that the observed PT-transition is rooted in the momentum-domain inhomogeneous polarization transformation of the beam. The correspondence with a typical non-Hermitian photonic system is further established. Our work not only resolves a longstanding fundamental issue in the field of optical beam shift but also puts forward the notion of novel non-Hermitian spin-orbit photonics: a new direction to study non-Hermitian physics through the optical beam shifts.

Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can be assigned a synthetic band topology owing to their periodic dependence on the Josephson phase bias. We demonstrate that the BdG symmetry adds a twist to this topological character, i.e., gap closing points may or \textit{may not} correspond to change of Chern number, hence extending the standard paradigm for topological bands. We further show that the topology of Andreev bands depends only on the scattering matrix of the junction and is independent of the topological nature of superconductors forming the JJ hence indicating a universal behaviour of multi-terminal JJ. We also show that the chiral junction, supported by quantum Hall state at the junction region, leads to flat Andreev bands (implying absence of DC Josephson effects) that are devoid of Berry curvature ( implying absence of AC Josephson effects). Such electrically inert JJ may be useful for storage of quantum information in future quantum devices.

Parafermion zero modes can be trapped in the domain walls of quantum Hall edges proximitized by superconductors and ferromagnets. The $\nu = 1/3$ fractional quantum Hall side strip arising due to edge reconstruction of a $\nu = 1$ edge doubles the number of topological sectors such that each of them is $Z_{2} \times Z_{2}$ degenerate. The many-body spectrum displays a $4\pi$ Josephson periodicity, with the states in each $Z_{2}$ being energetically decoupled. Signatures of the new states appear in the fractional Josephson current when the edge velocities are taken to be different.

AC transformer action of a quantum point contact separating quantum Hall states with distinct filling fractions $(\nu_{1},\nu_{2})$ is studied theoretically. The AC gain ($g_{\nu_{1},\nu_{2}}(\omega)$) of this setup is shown to exceed its DC bound ($g^{max}_{\nu_{1},\nu_{2}}(\omega=0) = 2\,\mathrm{max}\lbrace\nu_{1},\nu_{2}\rbrace/(\nu_{1}+\nu_{2})$) for a certain range of frequency in the presence of appropriate inter-electron interactions owing to displacement current induced by the ambient gate electrodes. This setup is also endowed with the unique possibility of having frequency tunable resonances and anti-resonances across the QPC., Comment: 10 pages, 4 figures

We investigate the effects of introducing a boost (a Zeeman field parallel to the spin quantization axis) at the proximitized helical edge of a two-dimensional (2D) quantum spin Hall insulator. Our self-consistent analysis finds that a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting phase may emerge at the edge when the boost is larger than a critical value tied to the induced pairing gap. A non-trivial consequence of retaining the 2D bulk in the model is that this boundary FFLO state supports a finite magnetization as well as finite current (flowing along the edge). This has implications for a proper treatment of the ultra-violet cutoff in analyses employing the effective one-dimensional (1D) helical edge model. Our results may be contrasted with previous studies of such 1D models, which found that the FFLO phase either does not appear for any value of the boost (in non-self-consistent calculations), or that it self-consistently appears even for infinitesimal boost, but carries no current and magnetization., Comment: 7 pages, 5 figures

Quantum theory provides rules governing much of the microscopic world, and among its counter-intuitive consequences are correlations that exceed the bounds from local, classical theories. In two-level quantum systems - qubits - unitary dynamics theoretically limit these spatiotemporal quantum correlations, called Bell/Clauser-Horn-Shimony-Holt or Leggett-Garg inequalities, to $2\sqrt{2}$ or 1.5 respectively. Experiments with state-of-the-art qubits have approached the spatial, Bell and temporal, Leggett-Garg quantum correlation bounds. Here, using a dissipative, trapped $^{40}$Ca$^+$ ion governed by a two-level, non-Hermitian Hamiltonian, we observe temporal correlation values up to 1.703(4) for the Leggett-Garg parameter $K_3$, clearly exceeding the hitherto inviolable L\"{u}der's bound of 1.5. These excesses occur across the exceptional point of the parity-time symmetric Hamiltonian responsible for the qubit's non-unitary, coherent dynamics. Distinct evolution speeds for antipodal qubit states, which violate the unified (Mendelstam-Tamm or Margolus-Levitin) bound $\tau_{\textrm{QSL}}$ for the transit time based on quantum speed limit, result in the super-quantum $K_3$ values observed over a wide parameter range. Our results demonstrate that post-selected, coherent dynamics of non-Hermitian Hamiltonians pave the way for enhanced quantum correlations that exceed protocols based on unitary or dissipative dynamics., Comment: 9 pages, 4 figures

An entangled state is said to be $m$-uniform if the reduced density matrix of any $m$ qubits is maximally mixed. This is intimately linked to pure quantum error correction codes (QECCs), which allow not only to correct errors, but also to identify their precise nature and location. Here, we show how to create $m$-uniform states using local gates or interactions and elucidate several QECC applications. We first show that $D$-dimensional cluster states are $m$-uniform with $m=2D$. This zero-correlation length cluster state does not have finite size corrections to its $m=2D$ uniformity, which is exact both for infinite and for large enough but finite lattices. Yet at some finite value of the lattice extension in each of the $D$ dimensions, which we bound, the uniformity is degraded due to finite support operators which wind around the system. We also outline how to achieve larger $m$ values using quasi-$D$ dimensional cluster states. This opens the possibility to use cluster states to benchmark errors on quantum computers. We demonstrate this ability on a superconducting quantum computer, focusing on the 1D cluster state which, we show, allows to detect and identify 1-qubit errors, distinguishing $X$, $Y$ and $Z$ errors., Comment: Published version

We examine Berry phase pertaining to purely quadrupolar state ($\langle \psi | \vec{S} | \psi \rangle = 0$) of a spin-$1$ system. Using the Majorana stellar representation of these states, we provide a visualization for the topological (zero or $\pi$) nature of such quadrupolar Berry phase. We demonstrates that the $\pi$ Berry phase of quadrupolar state is induced by the Majorana stars collectively tracing out a closed path (a great circle) by exchanging their respective positions on the Bloch sphere. We also analyse the problem from the perspective of dynamics where a state from the quadrupolar subspace is subjected to a static magnetic field. We show that time evolution generated by such Hamiltonian restricts the states to the quadrupolar subspace itself thereby producing a geometric phase (of the Aharonov-Anandan type) quantized to zero or $\pi$. A global unitary transformation which maps the quadrupolar subspace to the subspace of purely real states proves a natural way of understanding the topological character of this subspace and its connection to the anti-unitary symmetries., Comment: 10 pages, 3 figures

Volkov-Pankratov (VP) states are a family of sub-gap states which appear at the smooth interface/domain wall between topologically distinct gapped states. We study the emergence of such states in the edge spectrum of a quantum spin Hall system subjected to a smoothly varying mass term (Zeeman field) that switches sign at a given spatial point. Both the VP states at non-zero energy and the zero energy Jackiw-Rebbi mode stay localized at the interfacial region, however, the former feature several distinctive signatures compared to the latter such as non-trivial spin textures that can be characterized by a winding number in real space. On applying an electric field, the texture deforms leaving its winding number unaltered. Moreover, the VP states exhibit an intriguing interplay between the electric and the magnetic field with a collapse of the spectrum onto the zero mode when they are equal in magnitude. Quantum transport simulations on a 2D lattice model are performed to undergird our theoretical prediction., Comment: 10 pages, 5 figures

We study a parafermion Josephson junction (JJ) comprising a pair of counter-propagating edge modes of two quantum Hall (QH) systems, proximitized by an s-wave superconductor. We show that the difference between the lengths (which can be controlled by external gates) of the two counter-propagating chiral edges at the Josephson junction, can act as a source of spontaneous phase bias. For the Laughlin filling fractions, $\nu = 1/m,~ m \in 2\mathbb{Z}+1$, this leads to an electrical control of either Majorana $(m=1)$ or parafermion $(m\neq 1)$ zero modes., Comment: 10 pages, 4 figures

An effective two-spin density matrix (TSDM) for a pair of spin-$1/2$ degree of freedom, residing at a distance of $R$ in a spinful Fermi sea, can be obtained from the two-electron density matrix following the framework prescribed in Phys. Rev. A 69, 054305 (2004). We note that the single spin density matrix (SSDM) obtained from this TSDM for generic spin-degenerate systems of free fermions is always pinned to the maximally mixed state $i.e.$ $(1/2) \ \mathbb{I}$, independent of the distance $R$ while the TSDM confirms to the form for the set of maximally entangled mixed state (the so called "X-state") at finite $R$. The X-state reduces to a pure state (a singlet) in the $R\rightarrow 0$ limit while it saturates to an X-state with largest allowed value of von-Neumann entropy of $2 \ln2$ as $R \rightarrow \infty$ independent of the value of chemical potential. However, once an external magnetic field is applied to lift the spin-degeneracy, we find that the von-Neumann entropy of SSDM becomes a function of the distance $R$ between the two spins. We also show that the von-Neumann entropy of TSDM in the $R\rightarrow \infty$ limit becomes a function of the chemical potential and it saturate to $2 \ln2$ only when the band in completely filled unlike the spin-degenerate case. Finally we extend our study to include spin-orbit coupling and show that it does effect these asymptotic results. Our findings are in sharp contrast with previous works which were based on continuum models owing to physics which stem from the lattice model., Comment: 7 pages, 5 figures

We study Leggett-Garg inequality (LGI) of a two level system (TLS) undergoing non-Hermitian dynamics governed by a non-linear Bloch equation (derived in J. Phys. A: Math. Theor. 54, 115301 (2021)) across a PT-transition. We present an algebraic identification of the parameter space for the maximum violation of LGI (in particular $K_{3}$). In the PT-symmetric regime the maximum allowed value for $K_{3}$ is always found to be greater than the quantum bound (L\"{u}ders bound) of $3/2$ but it does not reach the algebraic maximum of $K_{3}=3$ in general. However, in the limit where PT-symmetry breaking parameter approaches the exceptional point from the PT-symmetric side, $K_{3}$ is found to asymptotically approach its algebraic maximum of 3. In contrast, the maximum value of $K_{3}$ always reaches its algebraic maximum in the PT-broken phase $i.e.$ $K_{3}\rightarrow 3$. We find that (i) the speed of evolution (SOE) must reach its maximum value (in the parameter space of initial state and the time interval between successive measurements) to facilitate the value of $K_{3} \rightarrow 3$, (ii) together with the constraint that its minimum value must run into SOE equals to zero during the evolution of the state. In fact we show that the minimum speed of evolution can serve as an order parameter which is finite on the PT-symmetric side and identically zero on the PT-broken side. Finally, we discuss a possible experimental realization of this dynamics by quantum measurement followed by post-selection procedure in a three level atom coupled to cavity mode undergoing a Lindbladian dynamics., Comment: 9 pages, 5 figures

A recent study have shown that it is possible to have enhancement, in contrast to an expected suppression, in tunneling density of states (TDOS) in a Luttinger liquid (LL) which is solely driven by the non-local density-density interactions. Also, it is well known that a LL in proximity to a superconductor (SC) shows enhancement in TDOS in the vicinity of the junction in the zero energy limit. In this paper, we study the interplay of nonlocal density-density interaction and superconducting correlations in the TDOS in the vicinity of the SC-LL junction, where the LL maybe realized on the edge of an integer or a fractional quantum Hall state. We show that the TDOS enhancement in a LL quantum wire (QW) due to superconducting correlation at the junction can be farther amplified in presence of appropriate choice of non-local interaction parameters, which is demonstrated through a neat algebraic expression in the weak interaction limit. We also show that, in the full parameter regime comprising both the local and the non-local interaction, the region of enhanced TDOS for LL junction with "superconducting" boundary condition and that of "non-superconducting charge conserving" boundary condition (discussed in Phys. Rev. B 104, 045402 (2021)) are mutually exclusive. We show that this fact can be understood in terms of symmetry relation established between the superconducting and non-superconducting sectors of the theory. We compare the dependence of the proximity induced pair potential and TDOS as a function of distance $x$ from the junction. We demonstrate that the dependence of the spatial power law exponent for the `TDOS(x)/TDOS(x -> 0)' and the `pair-potential(x)/pair-potential(x -> 0)' are distinct function of the various local and non-local interaction parameters, which implies that the TDOS enhancement can not be directly attributed to the proximity induced pair potential in the LL.

We discuss the construction of $n$-qubit pure states with maximum bipartite entanglement across all possible choices of $k$ vs $n-k$ bi-partitioning, which implies that the Von Neumann entropy of every $k$-qubit reduced density matrix corresponding to this state should be $k \ln 2 $. Such states have been referred to as $k$-uniform, $k$-MM states. We show that a subset of the 'graph states' satisfy this condition, hence providing a recipe for constructing $k$-uniform states. Finding recipes for construction of $k$-uniform states using graph states is useful since every graph state can be constructed starting from a product state using only controlled-$Z$ gates. Though, a priori it is not clear how to construct a graph which corresponds to an arbitrary $k$-uniform state, but in particular, we show that graphs with no isolated vertices are $1$-uniform. Graphs organized as a circular linear chain corresponds to the case of $2$-uniform state, where we show that the minimum number of qubits required to host such a state is $n=5$. $3$-uniform states can be constructed by forming bi-layer graphs with $n/2$ qubits ($n=2\mathbb{Z}$) in each layer, such that each layer forms a fully connected graph while inter-layer connections are such that the vertices in one layer has a one to one connectivity to the other layer. $4$-uniform states can be formed by taking 2D lattice graphs( also referred elsewhere as a 2D cluster Ising state ) with periodic boundary conditions along both dimensions and both dimensions having at least $5$ vertices., Comment: 8 pages, 4 tikz figures and 1 figure

It is known that Josephson junction (JJ) hosting scattering centers with energy-dependent scattering amplitudes which breaks the $\omega\rightarrow-\omega$ symmetry (where $\omega$ is the excitation energy of electron about the Fermi level) exhibits finite thermoelectric response. In contrast, here we show that even in a ballistic JJ this symmetry is broken and it leads to a non-zero thermoelectric response when the junction length is of the order of coherence length of the superconductor and the corresponding thermoelectric coefficient confirms to the universal sinusoidal dependence on $\phi_{12}$, where $\phi_{12}$ is the superconducting phase bias. In presence of multiple scatterers in the junction region, we have numerically shown that the sign of the even-in-$\phi_{12}$ part of the thermoelectric coefficient fluctuates violently from one disorder configuration to another hence averaging to vanishingly small values while the odd part tends towards the universal sinusoidal dependence on $\phi_{12}$ as we approach the large disorder limit under disorder averaging., Comment: 11 pages, 6 figures

We study Leggett-Garg inequalities (LGIs) for a two level system (TLS) undergoing Markovian dynamics described by unital maps. We find analytic expression of LG parameter $K_{3}$ (simplest variant of LGIs) in terms of the parameters of two distinct unital maps representing time evolution for intervals: $t_{1}$ to $t_{2}$ and $t_{2}$ to $t_{3}$. We show that the maximum violation of LGI for these maps can never exceed well known L\"{u}ders bound of $K_{3}^{L\ddot{u}ders}=3/2$ over the full parameter space. We further show that if the map for the time interval $t_{1}$ to $t_{2}$ is non-unitary unital then irrespective of the choice of the map for interval $t_{2}$ to $t_{3}$ we can never reach L\"{u}ders bound. On the other hand, if the measurement operator eigenstates remain pure upon evolution from $t_{1}$ to $t_{2}$, then depending on the degree of decoherence induced by the unital map for the interval $t_{2}$ to $t_{3}$ we may or may not obtain L\"{u}ders bound. Specifically, we find that if the unital map for interval $t_{2}$ to $t_{3}$ leads to the shrinking of the Bloch vector beyond half of its unit length, then achieving the bound $K_{3}^{L\ddot{u}ders}$ is not possible. Hence our findings not only establish a threshold for decoherence which will allow for $K_{3} = K_{3}^{L\ddot{u}ders}$, but also demonstrate the importance of temporal sequencing of the exposure of a TLS to Markovian baths in obtaining L\"{u}ders bound., Comment: 9 pages, 2 figures

Conductance of the edge modes as well as conductance across the co-propagating edge modes around the \nu = 4/3, 5/3 and 2 quantum Hall states are measured by individually exciting the modes. Temperature dependent equilibration rates of the outer unity conductance edge mode are presented for different filling fractions. We find that the equilibration rate of the outer unity conductance mode at \nu = 2 is higher and more temperature sensitive compared to the mode at fractional filling 5/3 and 4/3. At lowest temperature, equilibration length of the outer unity conductance mode tends to saturate with lowering filling fraction \nu by increasing magnetic field B. We speculate this saturating nature of equilibration length is arising from an interplay of Coulomb correlation and spin orthogonality., Comment: 7 pages

A hybrid setup consisting of a superconductivity-proximitized quantum spin Hall (QSH) insulator and a quantum anomalous Hall (QAH) insulator is proposed for chiral injection of electrons into the Majorana bound state (MBS). An unexplored region of the phase space involving the exchange field induced boost of the helical edge state is then proposed for the detection of the MBS. 2-D transport simulations of our proposed setup is compared with the corresponding setup in the absence of the QAH region, when moderate disorder and a small but finite bulk out-of-plane magnetic field and a Rashba field are included. The remarkable contrast between the two results demonstrates the possibility for an unprecedented immunity from disorder-induced masking of the MBS detection in our proposed setup., Comment: Further numerical analysis is included for the revised model

Theoretical models of a spin-polarized voltage probe (SPVP) tunnel-coupled to the helical edge states (HES) of a quantum spin Hall system (QSHS) are studied. Our first model of the SPVP comprises $N_{P}$ spin-polarized modes (subprobes), each of which is locally tunnel-coupled to the HES, while the SPVP, as a whole, is subjected to a self-consistency condition ensuring zero average current on the probe. We carry out a numerical analysis which shows that the optimal situation for reading off spin-resolved voltage from the HES depends on the interplay of the probe-edge tunnel-coupling and the number of modes in the probe ($N_P$). We further investigate the stability of our findings by introducing Gaussian fluctuations in {\it{(i)}} the tunnel-coupling between the subprobes and the HES about a chosen average value and {\it{(ii)}} spin-polarization of the subprobes about a chosen direction of the net polarization of SPVP. We also perform a numerical analysis corresponding to the situation where four such SPVPs are implemented in a self-consistent fashion across a ferromagnetic barrier on the HES and demonstrate that this model facilitates the measurements of spin-resolved four-probe voltage drops across the ferromagnetic barrier. As a second model, we employ the edge state of a quantum anomalous Hall state (QAHS) as the SPVP which is tunnel-coupled over an extended region with the HES. A two-dimensional lattice simulation for the quantum transport of the proposed device setup comprising a junction of QSHS and QAHS is considered and a feasibility study of using the edge of the QAHS as an efficient spin-polarized voltage probe is carried out in presence of an optimal strength of the disorder., Comment: 13 pages, 14 figures, Revised lattice simulation with new set of parameters

Power law suppression of local electronic tunneling density of states (TDOS) in the zero-energy limit is a hallmark of Luttinger liquid (LL) phase of the interacting 1-D electron system. We present a theoretical model which hosts LL state with the surprising feature of enhancement rather than suppression in local TDOS originating from non-local and repulsive density-density interactions. Importantly, we find enhancement of TDOS in the manifold of parameter space where the system is stable in the renormalization group (RG) sense. We argue that enhancement of TDOS along with RG stability is possible only when the system has broken parity symmetry about the position of local TDOS enhancement. Such a model could be realized on the edge states of a bi-layer quantum Hall system where both intra-layer and inter-layer density-density interactions are present mimicking the role of local and non-local interactions respectively., Comment: 13 pages, 4 figures

It is possible to simulate the dynamics of a single spin-$1/2$ ($\mathsf{PT~}$ symmetric) system by conveniently embedding it into a subspace of a larger Hilbert space with unitary dynamics. Our goal is to formulate a many body generalization of this idea i.e., embedding many body non-Hermitian dynamics. As a first step in this direction, we investigate embedding of "$N$" non-interacting spin-$1/2$ ($\mathsf{PT~}$ symmetric) degrees of freedom, thereby unfolding the complex nature of such an embedding procedure. It turns out that the resulting Hermitian Hamiltonian represents a cluster of $N+1$ spin halves with "all to all", $q$-body interaction terms ($q=1,...,N+1$) in which the additional spin-$1/2$ is a part of the larger embedding space. We can visualize it as a strongly correlated central spin model with the additional spin-$1/2$ playing the role of central spin. We find that due to the orthogonality catastrophe, even a vanishing small exchange field applied along the anisotropy axis of the central spin leads to a strong suppression of its decoherence arising from spin-flipping perturbations., Comment: 10 pages, 5 figures

Fractional conductance is measured by partitioning $\nu = 1$ edge state using gate-tunable fractional quantum Hall (FQH) liquids of filling 1/3 or 2/3 for current injection and detection. We observe two sets of FQH plateaus 1/9, 2/9, 4/9 and 1/6, 1/3, 2/3 at low and high magnetic field ends of the $\nu = 1$ plateau respectively. The findings are explained by magnetic field dependent equilibration of three FQH edge modes with conductance $e^2/3h$ arising from edge reconstruction. The results reveal remarkable enhancement of the equilibration lengths of the FQH edge modes with increasing field., Comment: Supplemental information included

Geometrical and dynamical phase have competing effects as far a scattering of light form inhomogeneous anisotropic optical medium is concerned. If fine-tuned appropriately, these effects can completely cancel each other for a chosen spin component while having an additive effect on the orthogonal components. Here, we show a manifestation of extraordinary spin selective modes in Fourier spectrum of Gaussian beam transmitted through anisotropic disordered medium. We realize the concept using a twisted nematic liquid crystal-based spatial light modulator (SLM) with random gray level distribution for incident Gaussian beam.

Existence of distinctive correlation between the thermal conductance and the Josephson current across a 1-D topological Josephson junction (T-JJ) is established and an expression connecting the two is derived in the short junction limit. It is shown that the three terminal T-JJ provides us with an ideal set-up for exploiting the distinctive correlations which aid in identifying hallmarks of Majorana bound state localized at the junction. Our approach combines information form sub-gap Cooper pair transport and transport of above-gap thermally excited quasiparticle which is complementary to the existing studies., Comment: 19 pages, 8 figures

It is well known that the pristine bulk of an interacting one-dimensional system in Tomonaga-Luttinger liquid (TLL) phase shows power law suppression of quasi-particle tunneling amplitude for all values of TLL parameter $g$, in the zero energy limit. We perform a density matrix renormalization group (DMRG) study of a fully symmetric Y junction of TLL wires and observe an anomalous enhancement of the tunneling density of states (TDOS) in the vicinity of the junction for both (a) interacting bosons case and (b) interacting fermions case, when $g>1$. We also observe suppression of TDOS for $g<1$ for both bosonic and fermionic cases. We find that the TDOS enhancements follow different power laws for bosonic and fermionic cases which suggests that these represent distinct fixed points, owing to statistical correlations which play an important role at the Y junction. Analysis of static conductance for the junction indicates that the fixed point for $1

We study the dynamics of two level systems described by non-hermitian Hamiltonians with real eigenvalues. Within the framework of hermitian quantum mechanics, it is known that maximal violation of Leggett-Garg inequality is bounded by $3/2$ (Luder's bound). We show that this absolute bound can be evaded when dynamics is governed by non-hermitian Hamiltonians. Moreover, the extent of violation can be optimized to reach its algebraic maximum of $3$ which is otherwise only feasible when the Hilbert space is infinite dimensional in the hermitian case. The extreme violation of Leggett-Garg inequality is shown to be directly related to the two basic ingredients: (i) The Bloch equation for the two level system has non-linear terms which allow for accelerated dynamics of states on the Bloch sphere exceeding all known quantum speed limits of state evolution; and (ii) We need to ensure that the quantum trajectory of states always lies on a single great circle (geodesic path) on the Bloch sphere at all times., Comment: v2: Includes (a) A numerical comparison of our predictions with existing experimental results (Ref. 44 in the article) ; and (b) An extensive discussion of Leggett-Garg Inequality in the context of possible embedding of the non-hermitian dynamics within a higher dimensional Hilbert space following unitary time evolution and postselection

Topological protection of edge state in quantum spin Hall systems relies only on time-reversal symmetry. Hence, S z conservation on the edge can be relaxed which can have an interferometric manifestation in terms of spin Berry phase. Primarily it could lead to the generation of spin Berry phase arising from a closed loop dynamics of electrons. Our work provides a minimal framework to generate and detect these effects by employing both spin-unpolarized and spin-polarized leads. We show that spin-polarized leads could lead to resonances or anti-resonances in the two-terminal conductance of the interferometer. We further show that the positions of these anti-resonances (as a function of energy of the incident electron) get shifted owing to the presence of spin Berry phase. Finally, we present simulations of a device setup using KWANTpackage which put our theoretical predictions on firm footing., Comment: 13 pages, 9 figures This version includes numerical calculations in support of the theoretical results based on a lattice set-up of the interferometer using the package KWANT

We study the local group velocity defined as the weak value of the velocity operator in the (1+1) dimensional Klein-Gordon as well as Dirac theory. It was shown by Berry [ J. Phys. A 45, 185308 (2012)] that when the pre- and post-selected states for evaluating the weak value are chosen at random from an ensemble of available states, the local group velocity has a universal probability distribution which can have both subluminal and superluminal components. In this work, we numerically explore the role of Lorentz boost and its impact on the superluminal fraction of the total probability distribution. We show that the dependence (enhancement) of the superluminal fraction on Lorentz boost of the total probability distribution differs both qualitatively and quantitatively for the Klein-Gordon waves and Dirac waves. For the Klein-Gordan waves, the asymmetry in the distribution of group velocities around the zero velocity point in the laboratory frame is entirely responsible for the observation of relative enhancement in the boosted frame. On the other hand, for the Dirac waves, we observe an enhancement irrespective of whether the laboratory frame velocity distribution is symmetric or not., Comment: To appear in Modern Physics Letters A. This version includes a semi-analytic understanding of the enhancement due to boost

We theoretically investigate the emergence of Jackiw-Rebbi zero modes and their conductance signature in non-uniform topological insulator nano-wires. We modelled the non-uniform nano-wires as junction between two cylindrical nano-wires with different radius. In the limit of wire length being much larger than its radius, the surface state of the nanowire splits into one dimensional Dirac modes propagating along the axis of the cylinder owing to radial confinement. The sign of the mass gap in each of these Dirac mode is decided by angular momentum quantum number corresponding to the rotational motion of the electron about the axis of the cylindrical. Application of an external magnetic flux through the cylindrical nanowires enables us to tune the mass gap from positive to negative value across the junction. Due to this flux tunable band inversion, controlled by the external magnetic filed, Jackiw-Rebbi zero modes can be made to appear or disappear at the junction. We compute differential conductance of our topological insulator nanowire junction and show that a quantized conductance peak appears at zero-energy (zero-bias) in the presence of the Jackiw-Rebbi mode., Comment: This is the published version

We obtain an empirical relation between the zero temperature, zero frequency quantum noise ${\small{(}}S{\small{(}}\omega=0{\small{)}}{\small{)}}$ and the related power dissipation ${\small{(}}D{\small{)}}$ for chiral circuitry. We consider the case of single quantum point contact (QPC) which induces inter-edge scattering of electrons among $"n"$ number of chiral edges of $\nu=1$ quantum Hall state. The ratio of total maximum power dissipation generated at the QPC ($D_{total}$) to the sum of auto-correlated noise generated in the chiral edge channels emanating out of the QPC region ($S_{total}$) is shown to be, $D_{total}/S_{total}{\small{(}}\omega=0{\small{)}} = V/{\small{}}4 e{\small{}}$ where $e$ is the electronic charge and $V$ is the voltage imposed on any one of the "$n$" incoming edge channels while keeping remaining "$n-1$" edge channels grounded. This implies that this ratio is universal except for a linear voltage bias dependence, i.e., it is independent of details of the scattering matrix ($S$-matrix) of the QPC region. Here the maximum power dissipation in each chiral edge is defined as the rate at which energy would be lost if the non-equilibrium distribution of electrons generated by the QPC region in each chiral edge is equilibrated to the corresponding zero temperature Fermi distribution. Further, for ${\cal Z}_n$ symmetric $S$-matrix, we show that the universal behaviour persists even when all the bias voltages imposed on the incoming edge channels are kept finite and distinct., Comment: 7 pages, 4 figures

We study adiabatic charge pumping through a Majorana bound state tunnel coupled to multiple normal leads. We show that for most of the parameters such a pump does not lead to any net pumped charge between the various leads unless a multiply connected geometry is implemented. We introduce an Aharonov-Bohm ring geometry at the junction to implement such a multiply connected geometry. We further show that the Fourier transform of the pumped charge with respect to flux inserted through the ring shows a clear distinction between the case of an Andreev bound state and the Majorana bound state. Hence such a Fourier analysis can serve as a diagnostic for the detection of Majorana bound states in the proposed geometry., Comment: 7 pages, 5 figures

Superconductivity and quantum Hall effect are distinct states of matter occurring in apparently incompatible physical conditions. Recent theoretical developments suggest that the coupling of quantum Hall effect with a superconductor can provide a fertile ground for realizing exotic topological excitations such as non-abelian Majorana fermions or Fibonacci particles. As a step toward that goal, we report observation of Andreev reflection at the junction of a quantum Hall edge state in a single layer graphene and a quasi-two dimensional niobium diselenide (NbSe2) superconductor. Our principal finding is the observation of an anomalous finite-temperature conductance peak located precisely at the Dirac point, providing a definitive evidence for inter-Landau level Andreev reflection in a quantum Hall system. Our observations are well supported by detailed numerical simulations, which offer additional insight into the role of the edge states in Andreev physics. This study paves the way for investigating analogous Andreev reflection in a fractional quantum Hall system coupled to a superconductor to realize exotic quasiparticles., Comment: published verion

We theoretically investigate the transport properties of a quasi one dimensional ferromagnet-superconductor junction where the superconductor consists of mixed singlet and triplet pairings. We show that the relative orientation of the stoner field ($\bf{\tilde{h}}$) in the ferromagnetic lead and the $\bf{d}$ vector of the superconductor acts like a on-off switch for the zero bias conductance of the device. In the regime, where triplet pairing amplitude dominates over the singlet counterpart (topological phase), a pair of Majorana zero modes appear at each end of the superconducting part of the nanowire. When $\bf{\tilde{h}}$ is parallel or anti-parallel to the $\bf{d}$ vector, transport gets completely blocked due to blockage in pairing while, when $\bf{\tilde{h}}$ and $\bf{d}$ are perpendicular to each other, the zero energy two terminal differential conductance spectra exhibits sharp transition from $4e^2/h$ to $2e^2/h$ as the magnetization strength in the lead becomes larger than the chemical potential indicating the spin selective coupling of pair of Majorana zero modes to the lead., Comment: This is the published version

We show that the electrical transport across a minimal model for a time-reversal symmetry(TRS) breaking Weyl semi-metal (WSM) involving two Weyl nodes can be interpreted as an interferometer in momentum space. The interference phase depends on the distance between the Weyl nodes ($\vec{\delta k}$) and is {\it anisotropic}. It is further shown that a minimal inversion symmetry broken model for a WSM with four Weyl nodes effectively mimics a situation corresponding to having two copies of the interferometer due to the presence of an orbital pseudo-spin domain wall in momentum space. We point out that the value of the $\delta k$ and consequently the interference phase can be tuned by driving the WSMs resulting in oscillations in the two terminal conductance measured in the direction of splitting of the Weyl nodes., Comment: Accepted in J. Phys.: Condens. Matter

Pancharatnam phase was discovered in the context of polarization optics in nineteen fifties. However, its full realization in quantum many-body systems still eludes us. This is primarily due to the fact that electron spin is not easily tunable. In the present proposal, we suggest that edge states of quantum spin Hall effect (QSHE) in conjunction with spin polarized electrodes (SPE) provide us with a unique opportunity to explore the Pancharatnam phase. We demonstrate the possibility of generating and detecting the multi-electron version of this phase that can as well be interpreted as multi-particle Aharonov-Bohm (A-B) effect in spin space arising solely due to spin dynamics. We further show that our proposed set-up leads to a robust interference pattern which survives orbital dephasing., Comment: 6 pages, 4 figures. Comments welcome !

We combine the ideas of intensity interferometry, polarization optics and Bell's measurement into an experimental proposal which is hosted in a $\nu\,$=$\,2$ quantum Hall (QH) edge state. Our interferometer comprises of a single gate, that separates the spin resolved edge states of $\nu$\,=\,$2$ state. An analog of waveplate (from polarization optics) is realized by exposing the individual edges to nano-magnets over a finite length which facilitates coherent manipulation of the electron spin on the edge. We show that the in-plane rotation of magnetization direction of the nano-magnets results in oscillations observed solely in the cross-correlated noise which arises from two particle interference. Through numerical simulations we demonstrate that our proposal is well within the reach of recent experimental developments of spin manipulations on the QH edge., Comment: v2: to appear in Phys. Rev. B (Rapid Communication)

We study a ring geometry, coupled to two normal metallic leads, which has a Majorana bound state (MBS) embedded in one of its arm and is threaded by Aharonov Bohm ($\mathcal{A}\mathcal{B}$) flux $\phi$. We show that by varying the $\mathcal{AB}$ flux, the two leads go through resonance in an anti-correlated fashion while the resonance conductance is quantized to $2 e^2/h$. We further show that such anti-correlation is completely absent when the MBS is replaced by an Andreev bound state (ABS). Hence this anti-correlation in conductance when studied as a function of $\phi$ provides a unique signature of the MBS which cannot be faked by an ABS. We contrast the phase sensitivity of the MBS and ABS in terms of tunneling conductances. We argue that the relative phase between the tunneling amplitude of the electrons and holes from either lead to the level (MBS or ABS), which is constrained to $0,\pi$ for the MBS and unconstrained for the ABS, is responsible for this interesting contrast in the $\mathcal{AB}$ effect between the MBS and ABS., Comment: 6 pages, 2 figures, version to be published in Phys. Rev. Lett

The spin-momentum locked nature of the robust surface states of three dimensional topological insulators (3D TI) make them promising candidates for spintronics applications. Surface potentials which respect time reversal symmetry can exist at the surface between a 3D TI and the trivial vacuum. These potentials can distort the spin texture of the surface states while retaining their gapless nature. In this work, the effect of all such surface potentials on the spin textures is studied. Since, a tunnel magnetoresistance signal carries the information of the spin texture, it is proposed that spin-polarized tunneling of electrons to a 3D TI surface can be used to uniquely identify the surface potentials and quantitatively characterize them., Comment: 9 pages, 4 figures, version published in Physical Review B

We show that the surface states of pristine 3D topological insulators (TIs) are analogs of ferromagnetic half metals due to complete polarization of an emergent momentum independent pseudospin (SU(2)) degree of freedom on the surface. To put this claim on firm footing, we present results for TI surfaces perpendicular to the crystal growth axis, which clearly show that the tunneling conductance between two such TI surfaces of the same TI material is dominated by this half metallic behavior leading to physics reminiscent of a spin-valve. Further using the generalized tunnel magnetoresistance derived in this work we also study the tunneling current between arbitrary TI surfaces. We also perform a comprehensive study of the effect of all possible surface potentials allowed by time reversal symmetry on this spin-valve effect and show that it is robust against most of such potentials., Comment: 11 pages, 5 figures, 1 table, version published in New Journal of Physics

Quantum spin Hall effect is endowed with topologically protected edge modes with gapless Dirac spectrum. Applying a magnetic field locally along the edge leads to a gapped edge spectrum with opposite parity for winding of spin texture for conduction and valence band. Using Pancharatnam's prescription for geometric phase it is shown that mismatch of this parity across a $p$-$n$ junction, which could be engineered into the edge by electrical gate induced doping, leads to a phase dependence in the two-terminal conductance which is purely topological (0 or $\pi$). This fact results in a ${\mathbb{Z}}_2$ classification of such junctions with an associated duality. Current asymmetry measurements which are shown to be robust against electron-electron interactions are proposed to infer this topology., Comment: revised version: v2 with supplementary material added

The topological properties of the bulk band structure of a three-dimensional topological insulator (TI) manifest themselves in the form of metallic surface states. In this paper, we propose a probe which directly couples to an exotic property of these surface states, namely the spin-momentum locking. We show that the information regarding the spin textures, so extracted, for different surfaces can be put together to reconstruct the parameters characterizing the bulk band structure of the material, hence acting as a hologram. For specific TI materials like, $\text{Bi}_2\text{Se}_3, \text{Bi}_2\text{Te}_3 \text{and Sb}_2\text{Te}_3$, the planar surface states are distinct from one another with regard to their spectrum and the associated spin texture for each angle ($\theta$), which the normal to the surface makes with the crystal growth axis. We develop a tunnel Hamiltonian between such arbitrary surfaces and a spin polarized STM which provides a unique fingerprint of the dispersion and the associated spin texture corresponding to each $\theta$. Additionally, the theory presented in this article can be used to extract value of $\theta$ for a given arbitrary planar surface from the STM spectra itself hence effectively mimicking X-ray spectroscopy., Comment: 11 pages, 8 figures, version accepted in Phys. Rev. B

Majorana bound states appearing in 1-D $p$-wave superconductor ($\cal{PWS}$) are found to result in exotic quantum holonomy of both eigenvalues and the eigenstates. Induced by a degeneracy hidden in complex Bloch vector space, Majorana states are identified with a pair of exceptional point ($\cal{EP}$) singularities. Characterized by a collapse of the vector space, these singularities are defects in Hilbert space that lead to M$\ddot{\rm o}$bius strip-like structure of the eigenspace and singular quantum metric. The topological phase transition in the language of $\cal{EP}$ is marked by one of the two exception point singularity degenerating to a degeneracy point with non singular quantum metric. This may provide an elegant and useful framework to characterize the topological aspect of Majorana fermions and the topological phase transition., Comment: revised version: v2