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We conjecture a chaos energy bound, an upper bound on the energy dependence of the Lyapunov exponent for any classical/quantum Hamiltonian mechanics and field theories. The conjecture states that the Lyapunov exponent $\lambda(E)$ grows no faster than linearly in the total energy $E$ in the high energy limit. In other words, the exponent $c$ in $\lambda(E) \propto E^c \,(E\to\infty)$ satisfies $c\leq 1$. This chaos energy bound stems from thermodynamic consistency of out-of-time-order correlators (OTOC's) and applies to any classical/quantum system with finite $N$ / large $N$ ($N$ is the number of degrees of freedom) under plausible physical conditions on the Hamiltonians. To the best of our knowledge the chaos energy bound is satisfied by any classically chaotic Hamiltonian system known, and is consistent with the cerebrated chaos bound by Maldacena, Shenker and Stanford which is for quantum cases at large $N$. We provide arguments supporting the conjecture for generic classically chaotic billiards and multi-particle systems. The existence of the chaos energy bound may put a fundamental constraint on physical systems and the universe., Comment: 3 pages, plus 7 pages of supplemental material; v2: minor revision with a reference and a footnote added

datasets and codes used in analysis of "Information-theoretic measures of superconductivity in a two-dimensional doped Mott insulator"

Quantum simulations with ultra-cold atoms in optical lattices open up an exciting path towards understanding strongly interacting quantum systems. Atom gas microscopes are crucial for this as they offer single-site density resolution, unparalleled in other quantum many-body systems. However, currently a direct measurement of local coherent currents is out of reach. In this work, we show how to achieve that by measuring densities that are altered in response to quenches to non-interacting dynamics, e.g., after tilting the optical lattice. For this, we establish a data analysis method solving the closed set of equations relating tunnelling currents and atom number dynamics, allowing to reliably recover the full covariance matrix, including off-diagonal terms representing coherent currents. The signal processing builds upon semi-definite optimization, providing bona fide covariance matrices optimally matching the observed data. We demonstrate how the obtained information about non-commuting observables allows to lower bound entanglement at finite temperature which opens up the possibility to study quantum correlations in quantum simulations going beyond classical capabilities., 19 pages, 17 figures. Scheme simplified, substantial material added

A multiple access channel (MAC) consists of multiple senders simultaneously transmitting their messages to a single receiver. For the classical-quantum case (CQ MAC), achievable rates are known assuming that all the messages are decoded, a common assumption in quantum network design. However, such a conventional design approach ignores the global network structure, i.e., the network topology. When a CQ MAC is given as a part of quantum network communication, this work shows that computation properties can be used to boost communication speeds with code design dependent on the network topology. We quantify achievable quantum communication rates of codes with the computation property for a two-sender CQ MAC. When the two-sender CQ MAC is a boson coherent channel with binary discrete modulation, we show that it achieves the maximum possible communication rate (the single-user capacity), which cannot be achieved with conventional design. Further, such a rate can be achieved by different detection methods: quantum (with and without quantum memory), on-off photon counting, and homodyne (each at different photon power). Finally, we describe two practical applications, one of which cryptographic., M.H. is supported in part by Guangdong Provincial Key Laboratory (Grant No. 2019B121203002).

Quantifying entanglement properties of mixed states in quantum field theory via entanglement of purification and reflected entropy is a new and challenging subject. In this work, we study both quantities for two spherical subregions far away from each other in the vacuum of a conformal field theory in any number of dimensions. Using lattice techniques, we find an elementary proof that the decay of both, the entanglement of purification and reflected entropy, is enhanced with respect to the mutual information behaviour by a logarithm of the distance between the subregions. In the case of the Ising spin chain at criticality and the related free fermion conformal field theory, we compute also the overall coefficients numerically for the both quantities of interest., 5 pages, 2 figures + appendices; v2: previous results unchanged, added proof of the long-distance behaviour of EoP, reorganized presentation

We investigate the role of nonclassical temporal correlations in enhancing the performance of ticking clocks in a discrete-time scenario. We show that the problem of optimal models for ticking clocks is related to the violation of Leggett-Garg-type temporal inequalities formulated in terms of, possibly invasive, sequential measurements, but on a system with a bounded memory capacity. Ticking clocks inspire the derivation of a family of temporal inequalities showing a gap between classical and quantum correlations, despite involving no input. We show that quantum ticking-clock models achieving accuracy beyond the classical bound are also those violating Leggett-Garg-type temporal inequalities for finite sequences and we investigate their continuous-time limit. Interestingly, we show that optimal classical clock models in the discrete-time scenario do not have a well-defined continuous-time limit, a feature that is absent in quantum models., Physical Review Research, 3 (3), ISSN:2643-1564

Bell inequalities are mathematical constructs that demarcate the boundary between quantum and classical physics. A new class of multiplicative Bell inequalities originating from a volume maximization game (based on products of correlators within bipartite systems) has been recently proposed. For these new Bell parameters, it is relatively easy to find the classical and quantum, i.e., Tsirelson, limits. Here, we experimentally test the Tsirelson bounds of these inequalities using polarization-entangled photons for a different number of measurements (n), each party can perform. For n = 2, 3, 4, we report the experimental violation of local hidden variable theories. In addition, we experimentally compare the results with the parameters obtained from a fully deterministic strategy, and observe the conjectured nature of the ratio. Finally, utilizing the principle of “relativistic independence” encapsulating the locality of uncertainty relations, we theoretically derive and experimentally test new and richer quantum bounds for both the multiplicative and the additive Bell parameters for n = 2. Our findings strengthen the deep correspondence between local and nonlocal correlations, and pave the way for both theoretical (e.g., better understanding of nonlocal correlations) and practical (e.g., Bell tests and quantum technologies with inefficient detectors) applications.

Quantum magnonics is an emerging research field, with great potential for applications in magnon based hybrid systems and quantum information processing. Quantum correlation, such as entanglement, is a central resource in many quantum information protocols that naturally comes about in any study toward quantum technologies. This applies also to quantum magnonics. Here, we investigate antiferromagnetic coupling of two ferromagnetic sublattices that can have two different magnon modes. We show how this may lead to experimentally measurable bipartite continuous-variable magnon-magnon entanglement. The entanglement can be fully characterized via a single squeezing parameter or, equivalently, entanglement parameter. The clear relation between the entanglement parameter and the Einstein, Podolsky, and Rosen (EPR) function of the ground state opens up for experimental quantification magnon-magnon continuous-variable entanglement and EPR nonlocality. We propose a practical experimental realization to measure the EPR function of the ground state, in a setting that relies on magnon-photon interaction in a microwave cavity.

Beam splitters are routinely used for generating entanglement between modes in the optical and microwave domains, requiring input states that are not convex combinations of coherent states. This leads to the ability to generate entanglement at a beam splitter as a notion of quantumness. A similar, yet distinct, notion of quantumness is the amount of entanglement generated by two-mode squeezers (i.e., four-wave mixers). We show that squeezed-vacuum states, paradoxically, both minimize and maximize these notions of quantumness, with the crucial resolution of the paradox hinging upon the relative phases between the input states and the devices. Our notion of quantumness is intrinsically related to eigenvalue equations involving creation and annihilation operators, governed by a set of inequalities that leads to generalized cat and squeezed-vacuum states., Comment: 12 pages including 2 figures and 1 appendix. Comments welcome!

Incompatible measurements, i.e., measurements that cannot be simultaneously performed, are necessary to observe nonlocal correlations. It is natural to ask, e.g., how incompatible the measurements have to be to achieve a certain violation of a Bell inequality. In this work, we provide the direct link between Bell nonlocality and the quantification of measurement incompatibility. This includes quantifiers for both incompatible and genuine-multipartite incompatible measurements. Our method straightforwardly generalizes to include constraints on the system's dimension (semi-device-independent approach) and on projective measurements, providing improved bounds on incompatibility quantifiers, and to include the prepare-and-measure scenario., Comment: 15 pages, 4 figures. Comments welcome! v2: Accepted version

Random quantum circuits are a central concept in quantum information theory with applications ranging from demonstrations of quantum computational advantage to descriptions of scrambling in strongly-interacting systems and black holes. The utility of random quantum circuits in these settings stems from their ability to rapidly generate quantum pseudo-randomness. In a seminal paper by Brand\~ao, Harrow, and Horodecki, it was proven that the $t$-th moment operator of local random quantum circuits on $n$ qudits with local dimension $q$ has a spectral gap of at least $\Omega(n^{-1}t^{-5-3.1/\log(q)})$, which implies that they are efficient constructions of approximate unitary designs. As a first result, we use Knabe bounds for the spectral gaps of frustration-free Hamiltonians to show that $1D$ random quantum circuits have a spectral gap scaling as $\Omega(n^{-1})$, provided that $t$ is small compared to the local dimension: $t^2\leq O(q)$. This implies a (nearly) linear scaling of the circuit depth in the design order $t$. Our second result is an unconditional spectral gap bounded below by $\Omega(n^{-1}\log^{-1}(n) t^{-\alpha(q)})$ for random quantum circuits with all-to-all interactions. This improves both the $n$ and $t$ scaling in design depth for the non-local model. We show this by proving a recursion relation for the spectral gaps involving an auxiliary random walk. Lastly, we solve the smallest non-trivial case exactly and combine with numerics and Knabe bounds to improve the constants involved in the spectral gap for small values of $t$., Comment: 27 pages, 2 figures

We study the entanglement dynamics between two cavities when one of them is harmonically shaken in the context of quantum information theory. We find four different regimes depending on the frequency of the motion and the spectrum of the moving cavity. If the moving cavity is three dimensional only two modes inside get coupled and the entanglement can either degrade asymptotically with time or oscillate depending on the driving. On the other hand, if the cavity has an equidistant spectrum the entanglement can either vanish asymptotically if it is driven with its fundamental frequency or have a sudden death if it is driven with an uneven harmonic frequency., 15 pages, 8 figures

Tesis (Doctor en Física)--Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación, 2020 La tesis abarca tres importantes áreas de la información cuántica: correlaciones cuánticas, comunicación (i.e. transmisión de información por medio de ensambles) y distinguibilidad de estados cuánticos. Se estudia la aplicabilidad y validez de distintas medidas de correlaciones en estados bipartitos en dimensión finita; profundizando el aspecto conceptual de las correlaciones haciendo uso de medidas de distinguibilidad. Asimismo, haciendo uso del concepto de "no conmutatividad" propuesto por Y. Guo en 2016, propusimos una nueva medida de correlaciones cuántica y demostramos que la misma satisface uno de los principales requisitos para constituirse una medida válida dentro de la teoría de recursos actual. En cuanto a comunicación, obtuvimos un "teorema de Holevo" generalizado en función de distancias cuánticas, siendo el teorema original un caso particular de la entropía relativa. This thesis comprises three important areas of quantum information: quantum correlations, communication (i.e. transmission of information through ensembles) and distinguishability quantum states. We studied the applicability and validity of different quantum correlation measures in bipartite states (finite-dimensional spaces), exploring the connection to distinguishability measures. Besides, making use of the concept of "non-commutativity" proposed by Y. Guo in 2016, we proposed a new quantum correlation measure and demonstrated that it satisfies one important requirement to constitute a valid monotone within the current resource theory. Regarding communication, we obtained a generalized "Holevo's theorem" as a function of quantum distances with the original theorem being a particular case of relative entropy. Fil: Bussandri, Diego Gastón. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina.

We characterize metrologically useful multipartite entanglement by representing partitions with Young diagrams. We derive entanglement witnesses that are sensitive to the shape of Young diagrams and show that Dyson's rank acts as a resource for quantum metrology. Common quantifiers, such as the entanglement depth and $k$-separability are contained in this approach as the diagram's width and height. Our methods are experimentally accessible in a wide range of atomic systems, as we illustrate by analyzing published data on the quantum Fisher information and spin-squeezing coefficients., Comment: 6 + 7 pages, 5 + 8 figures

We examine, in correlated mixed states of qudit-qubit systems, the set of all conditional qubit states that can be reached after local measurements at the qudit based on rank-1 projectors. While for a similar measurement at the qubit, the conditional post-measurement qudit states lie on the surface of an ellipsoid, for a measurement at the qudit we show that the set of post-measurement qubit states can form more complex solid regions. In particular, we show the emergence, for some classes of mixed states, of sets which are the convex hull of solid ellipsoids and which may lead to cone-like and triangle-like shapes in limit cases. We also analyze the associated measurement dependent conditional entropy, providing a full analytic determination of its minimum and of the minimizing local measurement at the qudit for the previous states. Separable rank-2 mixtures are also discussed., 12 pages, 7 figures, final version

Bell's theorem shows that local measurements on entangled states give rise to correlations incompatible with local hidden variable models. The degree of quantum nonlocality is not maximal though, as there are even more nonlocal theories beyond quantum theory still compatible with the nonsignalling principle. In spite of decades of research, we still have a very fragmented picture of the whole geometry of these different sets of correlations. Here we employ both analytical and numerical tools to ameliorate that. First, we identify two different classes of Bell scenarios where the nonsignalling correlations can behave very differently: in one case, the correlations are generically quantum and nonlocal while on the other quite the opposite happens as the correlations are generically classical and local. Second, by randomly sampling over nonsignalling correlations, we compute the distribution of a nonlocality quantifier based on the trace distance to the local set. With that, we conclude that the nonlocal correlations can show concentration phenomena: their distribution is peaked at a distance from the local set that increases both with the number of parts or measurements being performed., Comment: Minor modifications. Still with 13 pages, 8 figures, 5 tables. Comments are welcome!

In this work (multipartite) entanglement, discord, and coherence are unified as different aspects of a single underlying resource theory defined through simple and operationally meaningful elemental operations. This is achieved by revisiting the resource theory defining entanglement, local operations, and classical communication (LOCC), placing the focus on the underlying quantum nature of the communication channels. Taking the natural elemental operations in the resulting generalization of LOCC yields a resource theory that singles out coherence in the wire connecting the spatially separated systems as an operationally useful resource. The approach naturally allows us to consider a reduced setting as well, namely, the one with only the wire connected to a single quantum system, which leads to discordlike resources. The general form of free operations in this latter setting is derived and presented as a closed form. We discuss in what sense the present approach defines a resource theory of quantum discord and in which situations such an interpretation is sound—and why in general discord is not a resource. This unified and operationally meaningful approach makes transparent many features of entanglement that in LOCC might seem surprising, such as the possibility to use a particle to entangle two parties, without it ever being entangled with either of them, or that there exist different forms of multipartite entanglement., Facultad de Ciencias Exactas, Instituto de Física La Plata

Wave-particle duality has become one of the flagships of quantum mechanics. This counter-intuitive concept is highlighted in a delayed choice experiment, where the experimental setup that reveals either the particle or wave nature of a quantum system is decided after the system has entered the apparatus. Here we consider delayed choice experiments from the perspective of device-independent causal models and show their equivalence to a prepare-and-measure scenario. Within this framework, we consider Wheeler's original proposal and its variant using a quantum control and show that a simple classical causal model is capable of reproducing the quantum mechanical predictions. Nonetheless, among other results, we show that in a slight variant of Wheeler's Gedankenexperiment, a photon in an interferometer can indeed generate statistics incompatible with any non-retrocausal hidden variable model whose dimensionality is the same as that of the quantum system it is supposed to mimic. Our proposal tolerates arbitrary losses and inefficiencies making it specially suited to loophole-free experimental implementations., 5 pages (main text) + 2 pages (appendix), 4 figures. This version includes some simple corrections, and one new figure

Measurements performed on distant parts of an entangled quantum state can generate correlations incompatible with classical theories respecting the assumption of local causality. This is the phenomenon known as quantum nonlocality that, apart from its fundamental role, can also be put to practical use in applications such as cryptography and distributed computing. Clearly, developing ways of quantifying nonlocality is an important primitive in this scenario. Here, we propose to quantify the nonlocality of a given probability distribution via its trace distance to the set of classical correlations. We show that this measure is a monotone under the free operations of a resource theory and, furthermore, that it can be computed efficiently with a linear program. We put our framework to use in a variety of relevant Bell scenarios also comparing the trace distance to other standard measures in the literature

Quantum resource theories seek to quantify sources of non-classicality that bestow quantum technologies their operational advantage. Chief among these are studies of quantum correlations and quantum coherence. The former to isolate non-classicality in the correlations between systems, the latter to capture non-classicality of quantum superpositions within a single physical system. Here we present a scheme that cyclically inter-converts between these resources without loss. The first stage converts coherence present in an input system into correlations with an ancilla. The second stage harnesses these correlations to restore coherence on the input system by measurement of the ancilla. We experimentally demonstrate this inter-conversion process using linear optics. Our experiment highlights the connection between non-classicality of correlations and non-classicality within local quantum systems, and provides potential flexibilities in exploiting one resource to perform tasks normally associated with the other., 8 pages, 4 figures, comments welcome

The modeling of natural phenomena via a Markov process --- a process for which the future is independent of the past, given the present--- is ubiquitous in many fields of science. Within this context, it is of foremost importance to develop ways to check from the available empirical data if the underlying mechanism is indeed Markovian. A paradigmatic example is given by data processing inequalities, the violation of which is an unambiguous proof of the non-Markovianity of the process. Here, our aim is twofold. First we show the existence of a monogamy-like type of constraints, beyond data processing, respected by Markov chains. Second, to show a novel connection between the quantification of causality and the violation of both data processing and monogamy inequalities. Apart from its foundational relevance in the study of stochastic processes we also consider the applicability of our results in a typical quantum information setup, showing it can be useful to witness the non-Markovianity arising in a sequence of quantum non-projective measurements., 9 pages + appendix, 2 figures

We report on the quantum storage of a heralded frequency-multiplexed single photon in an integrated laser-written rare-earth doped waveguide. The single photon contains 15 discrete frequency modes separated by 261 MHz and spaning across 4 GHz. It is obtained from a non-degenerate photon pair created via cavity-enhanced spontaneous down conversion, where the heralding photon is at telecom wavelength and the heralded photon is at 606 nm. The frequency-multimode photon is stored in a praseodymium-doped waveguide using the atomic frequency comb (AFC) scheme, by creating multiple combs within the inhomogeneous broadening of the crystal. Thanks to the intrinsic temporal multimodality of the AFC scheme, each spectral bin includes 9 temporal modes, such that the total number of stored modes is about 130. We demonstrate that the storage preserves the non-classical properties of the single photon, and its normalized frequency spectrum., Comment: 10 pages, 14 figures (4 in the main text, 10 in Appendix), 1 table in the main text