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The standard randomized benchmarking protocol requires access to often complex operations that are not always directly accessible. Compiler optimization does not always ensure equal sequence length of the directly accessible universal gates for each random operation. We introduce a version of the RB protocol that creates Haar-randomness using a directly accessible universal gate set of equal sequence length rather than relying upon a t-design or even an approximate one. This makes our protocol highly resource efficient and practical for small qubit numbers. We exemplify our protocol for creating Haar-randomness in the case of single and two qubits. Benchmarking our result with the standard RB protocol, allows us to calculate the overestimation of the average gate fidelity as compared to the standard technique. We augment our findings with a noise analysis which demonstrates that our method could be an effective tool for building accurate models of experimental noise., Comment: 13 pages, 11 figures

A quantum many-body system undergoes phase transitions of distinct species with variations of local and global parameters. We propose a framework in which a dynamical quantity can change its behavior for quenches across global (coarse-grained criterion) or local system parameters (fine-grained criterion), revealing the global transition points. We illustrate our technique by employing the long-range extended Ising model in the presence of a transverse magnetic field. We report that by distinguishing between algebraic and exponential scaling of the total correlation in the steady state, one can identify the first transition point that conventional indicators such as the rate function fail to detect. To determine the second one, we exploit the traditional local quenches. During quenches with and without crossing the critical points along the local parameter, total correlation follows either the same or different scaling laws depending on its global phase., Comment: v1: 13 pages, 5 figures; v2: new results added and title changed

We present a set of methods to generate less complex error channels by quantum circuit parallelisation. The resulting errors are simplified as a consequence of their symmetrisation and randomisation. Initially, the case of a single error channel is analysed; these results are then generalised to multiple error channels. Error simplification for each method is shown to be either constant, linear, or exponential in terms of system size. Finally, example applications are provided, along with experiments run on superconducting quantum hardware and numerical simulation. These applications are: (1) reducing the sample complexity of matrix-inversion measurement error mitigation by error symmetrisation, (2) improving the effectiveness of noise-estimation circuit error mitigation by error randomisation, and (3) improving the predictability of noisy circuit performance by error randomisation., Comment: 19 pages, 11 figures, additional numerics for time-dependent error stabilisation, corrected typos, some restructuring

Considering an example of the long-range Kitaev model, we are looking for a correlation length in a model with long range interactions whose correlation functions away from a critical point have power-law tails instead of the usual exponential decay. It turns out that quasiparticle spectrum depends on a distance from the critical point in a way that allows to identify the standard correlation length exponent, $\nu$. The exponent implicitly defines a correlation length $\xi$ that diverges when the critical point is approached. We show that the correlation length manifests itself also in the correlation function but not in its exponential tail because there is none. Instead $\xi$ is a distance that marks a crossover between two different algebraic decays with different exponents. At distances shorter than $\xi$ the correlator decays with the same power law as at the critical point while at distances longer than $\xi$ it decays faster, with a steeper power law. For this correlator it is possible to formulate the usual scaling hypothesis with $\xi$ playing the role of the scaling distance. The correlation length also leaves its mark on the subleading anomalous fermionic correlator but, interestingly, there is a regime of long range interactions where its short distance critical power-law decay is steeper than its long distance power law tail., Comment: 7 pages, 4 figures

Driving a homogeneous system across a quantum phase transition in a quench-time $\tau_Q$ generates excitations on wavelengths longer than the Kibble-Zurek (KZ) length $\hat\xi\propto\tau_Q^{\nu/(1+z\nu)}$ within the KZ time window $\hat t\propto\tau_Q^{z\nu/(1+z\nu)}$, where $z$ and $\nu$ are the critical exponents. Quenches designed with local time-dependent inhomogeneity can introduce a gap in the spectrum. For a variety of setups with short-range interactions, they have been shown to suppress excitations if the spatial velocity of the inhomogenous front is below the characteristic KZ velocity $\hat v \propto \hat\xi/\hat t$. Ising-like models with long-range interactions can have no sonic horizon, spreading information instantaneously across the system. Usually, this should imply that inhomogenous transitions will render the dynamics adiabatic regardless of the front velocity. However, we show that we get an adiabatic transition with no defects only when the inhomogeneous front moves slower than a characteristic crossover velocity $\tilde v \propto \theta^{(z-1)\nu/(1+\nu)}$, where $\theta$ is the slope of the inhomogeneous front at the critical point. The existence of this crossover velocity and adiabaticity of the model is a consequence of the energy gap in the quasiparticle spectrum that is opened by the inhomogeneity. This effect can be employed for efficient adiabatic quantum state preparation in systems with long-range interactions., Comment: 12 pages, 10 figures (closed to published version)

A system gradually driven through a symmetry-breaking phase transition is subject to the Kibble-Zurek mechanism (KZM). As a consequence of the critical slowing down, its state cannot follow local equilibrium, and its evolution becomes non-adiabatic near the critical point. In the simplest approximation, that stage can be regarded as "impulse" where the state of the system remains unchanged. It leads to the correct KZM scaling laws. However, such "freeze-out" might suggest that the coherence length of the nascent order parameter remains unchanged as the critical region is traversed. By contrast, the original causality-based discussion emphasized the role of the {\it sonic horizon}: domains of the broken symmetry phase can expand with a velocity limited by the speed of the relevant sound. This effect was demonstrated in the quantum Ising chain where the dynamical exponent $z=1$ and quasiparticles excited by the transition have a fixed speed of sound. To elucidate the role of the sonic horizon, in this paper we study two systems with $z>1$ where the speed of sound is no longer fixed, and the fastest excited quasiparticles set the size of the sonic horizon. Their effective speed decays with the increasing transition time. In the extreme case, the dynamical exponent $z$ can diverge such as in the Griffiths region of the random Ising chain where localization of excited quasiparticles freezes the growth of the correlation range when the critical region is traversed. Of particular interest is an example with $z<1$ -- the long-range extended Ising chain, where there is no upper limit to the velocity of excited quasiparticles with small momenta. Initially, the power-law tail of the correlation function grows adiabatically, but in the non-adiabatic stage it lags behind the adiabatic evolution -- in accord with a generalized Lieb-Robinson bound., Comment: minor corrections, accepted in PRB

We investigate bipartite entanglement in random quantum $XY$ models at equilibrium. Depending on the intrinsic time scales associated with equilibration of the random parameters and measurements associated with observation of the system, we consider two distinct kinds of disorder, namely annealed and quenched disorders. We conduct a comparative study of the effects of disorder on nearest-neighbor entanglement, when the nature of randomness changes from being annealed to quenched. We find that entanglement properties of the annealed and quenched disordered systems are drastically different from each other. This is realized by identifying the regions of parameter space in which the nearest-neighbor state is entangled, and the regions where a disorder-induced enhancement of entanglement $-$ order-from-disorder $-$ is obtained. We also analyze the response of the quantum phase transition point of the ordered system with the infusion of disorder., Comment: 12 pages, 7 figures

We report all phases and corresponding critical lines of the quantum anisotropic transverse XY model with Dzyaloshinskii-Moriya (DM) interaction along with uniform and alternating transverse magnetic fields (ATXY) by using appropriately chosen order parameters. We prove that when DM interaction is weaker than the anisotropy parameter, it has no effect at all on the zero-temperature states of the XY model with uniform transverse magnetic field which is not the case for the ATXY model. However, when DM interaction is stronger than the anisotropy parameter, we show appearance of a new gapless phase - a chiral phase - in the XY model with uniform as well as alternating field. We further report that first derivatives of nearest neighbor two-site entanglement with respect to magnetic fields can detect all the critical lines present in the system. We also observe that the factorization surface at zero-temperature present in this model without DM interaction becomes a volume on the introduction of the later. We find that DM interaction can generate bipartite entanglement sustainable at large times, leading to a proof of ergodic nature of bipartite entanglement in this system, and can induce a transition from non-monotonicity of entanglement with temperature to a monotonic one., Comment: 19 pages, 14 figures

There exist zero-temperature states in quantum many-body systems that are fully factorized, thereby possessing vanishing entanglement, and hence being of no use as resource in quantum information processing tasks. Such states can become useful for quantum protocols when the temperature of the system is increased, and when the system is allowed to evolve under either the influence of an external environment, or a closed unitary evolution driven by its own Hamiltonian due to a sudden change in the system parameters. Using the one-dimensional anisotropic XY model in a uniform and an alternating transverse magnetic field, we show that entanglement of the thermal states, corresponding to the factorization points in the space of the system parameters, revives once or twice with increasing temperature. We also study the closed unitary evolution of the quantum spin chain driven out of equilibrium when the external magnetic fields are turned off, and show that considerable entanglement is generated during the dynamics, when the initial state has vanishing entanglement. Interestingly, we find that creation of entanglement for a pair of spins is possible when the system is made open to an external heat bath, interacting through that spin-pair having a repetitive quantum interaction., Comment: 10 pages, 6 figures, close to published version

We review concepts and methods associated with quantum discord and related topics. We also describe their possible connections with other aspects of quantum information and beyond, including quantum communication, quantum computation, many-body physics, and open quantum dynamics. Quantum discord in the multiparty regime and its applications are also discussed., Comment: 65 pages, 20 figures, Review

We show that bipartite entanglement in a one-dimensional quantum spin model undergoing time-evolution under local Markovian environments can be frozen over time. We demonstrate this by using a number of paradigmatic quantum spin models in one dimension, including the anisotropic XY model in the presence of a uniform and an alternating transverse magnetic field (ATXY), the XXZ model, the XYZ model, and the $J_1-J_2$ model involving the next-nearest-neighbor interactions. We show that the length of the freezing interval, for a chosen pair of nearest-neighbor spins, may remain independent of the length of the spin-chain, for example, in paramagnetic phases of the ATXY model, indicating a scale-invariance. Such freezing of entanglement is found to be robust against a change in the environment temperature, presence of disorder in the system, and whether the noise is dissipative, or not dissipative. Moreover, we connect the freezing of entanglement with the propagation of information through a quantum many-body system, as considered in the Lieb-Robinson theorem. We demonstrate that the variation of the freezing duration exhibits a quadratic behavior against the distance of the nearest-neighbor spin-pair from the noise-source, obtained from exact numerical simulations, in contrast to the linear one as predicted by the Lieb-Robinson theorem., Comment: 13 pages, 6 figures, close to published version

We investigate the static and dynamical patterns of entanglement in an anisotropic XY model with an alternating transverse magnetic field, which is equivalent to a two-component one-dimensional Fermi gas on a lattice, a system realizable with current technology. Apart from the antiferromagnetic and paramagnetic phases, the model possesses a dimer phase which is not present in the transverse XY model. At zero temperature, we find that the first derivative of bipartite entanglement can detect all the three phases. We analytically show that the model has a "factorization line" on the plane of system parameters, in which the zero temperature state is separable. Along with investigating the effect of temperature on entanglement in a phase plane, we also report a non-monotonic behavior of entanglement with respect to temperature in the anti-ferromagnetic and paramagnetic phases, which is surprisingly absent in the dimer phase. Since the time dynamics of entanglement in a realizable physical system plays an important role in quantum information processing tasks, the evolutions of entanglement at small as well as large time are examined. Consideration of large time behavior of entanglement helps us to prove that in this model, entanglement is always ergodic. We observe that other quantum correlation measures can qualitatively show similar features in zero and finite temperatures. However, unlike nearest-neighbor entanglement, the nearest-neighbor information theoretic measures can be both ergodic as well as non-ergodic, depending on the system parameters., Comment: 20 Pages, 13 Figures, 2 Tables, Published version

Multiparty quantum states are useful for a variety of quantum information and computation protocols. We define a multiparty entanglement measure based on local measurements on a multiparty quantum state, and an entanglement measure averaged on the post-measurement ensemble. Using the generalized geometric measure as the measure of multipartite entanglement for the ensemble, we demonstrate, in the case of several well-known classes of multipartite pure states, that the localized multipartite entanglement can exceed the entanglement present in the original state. We also show that measurement over multiple parties may be beneficial in enhancing localizable multipartite entanglement. We point out that localizable generalized geometric measure faithfully signals quantum critical phenomena in well-known quantum spin models even when considerable finite-size effect is present in the system., Comment: 14 pages, 4 figures, 2 tables, published version

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the information-theoretic paradigm, exhibit a universal behaviour. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distribution corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as the Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information theoretic measures violate the Benford's law. We quantitatively discuss the violation of the Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions., Comment: v1: 11 pages, 5 figures, 2 tables; v2: 11 pages, 6 figures, 2 tables, new results added, extended version of the published paper

We address the issue of reducing the resource required to compute information-theoretic quantum correlation measures like quantum discord and quantum work deficit in two qubits and higher dimensional systems. We show that determination of the quantum correlation measure is possible even if we utilize a restricted set of local measurements. We find that the determination allows us to obtain a closed form of quantum discord and quantum work deficit for several classes of states, with a low error. We show that the computational error caused by the constraint over the complete set of local measurements reduces fast with an increase in the size of the restricted set, implying usefulness of constrained optimization, especially with the increase of dimensions. We perform quantitative analysis to investigate how the error scales with the system size, taking into account a set of plausible constructions of the constrained set. Carrying out a comparative study, we show that the resource required to optimize quantum work deficit is usually higher than that required for quantum discord. We also demonstrate that minimization of quantum discord and quantum work deficit is easier in the case of two-qubit mixed states of fixed ranks and with positive partial transpose in comparison to the corresponding states having non-positive partial transpose. Applying the methodology to quantum spin models, we show that the constrained optimization can be used with advantage in analyzing such systems in quantum information-theoretic language. For bound entangled states, we show that the error is significantly low when the measurements correspond to the spin observables along the three Cartesian coordinates, and thereby we obtain expressions of quantum discord and quantum work deficit for these bound entangled states., Comment: 19 pages, 14 figures, 3 tables

Classical correlations of ground states typically decay exponentially and polynomially, respectively for gapped and gapless short-ranged quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder., Comment: 10 pages, 7 figures

We consider paradigmatic quenched disordered quantum spin models, viz., the XY spin glass and random-field XY models, and show that quenched averaged quantum correlations can exhibit the order-from-disorder phenomenon for finite-size systems as well as in the thermodynamic limit. Moreover, we find that the order-from-disorder can get more pronounced in the presence of temperature by suitable tuning of the system parameters. The effects are found for entanglement measures as well as for information-theoretic quantum correlation ones, although the former show them more prominently. We also observe that the equivalence between the quenched averages and their self-averaged cousins -- for classical and quantum correlations -- is related to the quantum critical point in the corresponding ordered system., Comment: 12 pages, 11 figures, RevTeX4-1

There exist diverse no-go theorems, ranging from no-cloning to monogamies of quantum correlations and Bell inequality violations, which restrict the processing of information in the quantum world. In a multipartite scenario, monogamy of Bell inequality violation and exclusion principle of dense coding are such theorems, which impede the ability of the system to have quantum advantage between all its parts. In ordered spin systems, the twin restrictions of translation invariance and monogamy of quantum correlations, in general, enforce the bipartite states to be neither Bell inequality violating nor dense-codeable. We show that these quantum characteristics, viz. Bell inequality violation and dense-codeability, can be resurrected, and thereby the no-go theorems overcome, by having quenched disorder in the system parameters leading to quantum spin glass or quantum random field models. We show that the quantum characteristics are regained even though the quenched averaging keeps the disordered spin chains translationally invariant at the physically relevant level of observables. The results show that it is possible to conquer constraints imposed by quantum mechanics in ordered systems by introducing impurities., Comment: 9 pages, 6 figures, RevTeX 4.1