Bipartite Correlations Research Articles

Beating one bit of communication with and without quantum pseudo-telepathy

According to Bell’s theorem, certain entangled states cannot be simulated classically using local hidden variables (LHV). Suppose that we can augment LHV by some amount of classical communication. The question then arises as to how many bits are needed to simulate entangled states? There is very strong evidence that a single bit of communication is powerful enough to simulate projective measurements on any two-qubit entangled state. However, the problem of simulating measurements on higher-dimensional systems remains largely unexplored. In this study, we present Bell-like scenarios, even with three inputs per party, in which bipartite correlations resulting from measurements on higher-dimensional states cannot be simulated with a single bit of communication. We consider the case where the communication direction is fixed and the case where it is bidirectional. To this end, we introduce constructions based on parallel repetition of pseudo-telepathy games and an original algorithm based on branch-and-bound technique to compute the one-bit classical bound. Two copies of emblematic Bell expressions, such as the Magic square pseudo-telepathy game, prove to be particularly powerful, requiring a 16 × 16 state to beat the bidirectional one-bit classical bound, and look a promising candidate for implementation on an optical platform.

Quantum state over time is unique

The conventional framework of quantum theory treats space and time in vastly different ways by representing temporal correlations via quantum channels and spatial correlations via multipartite quantum states—an imbalance absent in classical probability theory. Since Leifer and Spekkens [] called for a causally neutral formulation of quantum theory in their seminal work, numerous attempts have been made to rectify this asymmetry by proposing a dynamical description of a quantum system encapsulated by a static , without a definite consensus on which one is most appropriate. In this paper, we propose sets of operationally motivated axioms for quantum states over time alternative to the ones proposed by Fullwood and Parzygnat [], which we show is unable to induce a unique quantum state over time. Our proposed axioms are better suited to describe quantum states over any spacetime regions beyond two points. Through this reformulation, we prove that the Fullwood-Parzygnat state over time uniquely satisfies all these operational axioms, unifying the bipartite spacetime correlations of quantum systems. Published by the American Physical Society 2024

Quantifying quantumness in three-flavor neutrino oscillations

We characterize quantum correlations encoded in a three-flavor oscillating neutrino system by using both plane-wave and wave-packet approach. By means of the Complete Complementarity Relations (CCR) we study the trade-off of predictability, local coherence and non-local correlations in terms of the relevant parameters, chosen from recent neutrino experiments. Although the CCR describe very well the contributions associated to bipartite correlations, an attempt of promoting these relations to include the genuine tri-partite contributions in the pure-state case leads to a not completely meaningful result. However, we provide an analysis of the genuine tripartite contributions both for the pure instance and for the mixed case, independently of CCR.

Complete complementarity relations for quantum correlations in neutrino oscillations with CP violation

We characterize quantum correlations encoded in a three-flavor oscillating neutrino system by taking into account CP violation. By means of the complete complementarity relations (CCR), we study the trade-off of predictability, local coherence and nonlocal correlations by using relevant parameters given by neutrino oscillation experiments. Although the CCR describe very well the contributions associated to bipartite correlations, we explore the possible presence of genuine tripartite correlations, by exploiting polygamy relations. We also provide some observations about the nonlocal advantage of quantum coherence, a mazy quantum correlation characterizing the most valuable, nonlocal, portion of quantum coherence in a multi-partite system.

Quantitative bounds to propagation of quantum correlations in many-body systems

We investigate how much information about a quantum system can be simultaneously communicated to independent observers, by establishing quantitative limits to bipartite quantum correlations in many-body systems. As recently reported in Girolami et al. (2022) [16], bounds on quantum discord and entanglement of formation between a single quantum system and its environment, e.g., a large number of photons, dictate that independent observers which monitor environment fragments inevitably acquire only classical information about the system. Here, we corroborate and generalize those findings. First, we calculate continuity bounds of quantum discord, which establish how much states with a small amount of quantum correlations deviate from being embeddings of classical probability distributions. Also, we demonstrate a universally valid upper bound to the bipartite entanglement of formation between an arbitrary pair of components of a many-body quantum system. The results confirm that proliferation of classical information in the Universe suppresses quantum correlations.

Manipulating bipartite and tripartite quantum correlations of mechanical oscillators via optomechanical interaction.

The entanglement of macroscopic mechanical oscillators is always an interesting domain. How to entangle multiple mechanical oscillators is still not well answered. In this paper, we investigate the bipartite and tripartite quantum correlations among three distinct mechanical oscillators interacting with one cavity pumped by a multi-tone driving laser. Floquet cavity modes, resulting from different frequency components of the multi-tone driven cavity, are used to construct channels for quantum correlations between mechanical oscillators. By modulating the effective optomechanical coupling, we can manipulate the mechanical entanglement and EPR steering. The numerical results show that the two-tone driving widely employed is not enough to generate tripartite entanglement, while three- and four-tone driving can be employed to generate and enhance genuine tripartite entanglement. All bipartite entanglement can also be modulated. In addition, we demonstrate the monogamous relation of tripartite EPR steering and manipulate the asymmetry of steering. This work provides a method for manipulating the quantum correlation among multiple macroscopic objects.

Non-Gaussian quantum correlations from a four-well Bose–Hubbard system

We propose and analyse a four-well Bose–Hubbard model in a star configuration, with pumping in the middle well and damping at the three end wells. We find that the system can operate in a stationary regime and exhibits non-Gaussian quantum correlations. Bipartite and tripartite quantum correlations can be established between the end wells of the system which can be measured either in situ or in the outcoupled beams. Symmetric EPR steering can be achieved between the end wells at steady state. While in some cases, there exists asymmetric EPR steering between the middle well and one of the end wells during the transients, although it tends to be symmetric at steady state. The results show that quantum correlations depend deeply on the choice of collisional nonlinearity and the intensity of pumping. Different from the optical cavity, where dissipation is inevitable, our scheme allows for selective addition of pumping and damping. This feature makes it a flexible and controllable resource for experimental investigations and future technological applications.

Squashed entanglement in one-dimensional quantum matter

Squashed entanglement and its universal upper bound, the quantum conditional mutual information, are faithful measures of bipartite quantum correlations defined in terms of multipartitions. As such, they are sensitive to the fine-grain structure of quantum systems. Building on this observation, we introduce the concept of quantum conditional mutual information between the edges of quantum many-body systems. We show that this quantity characterizes unambiguously one-dimensional topological insulators and superconductors, being equal to Bell-state entanglement in the former and to half Bell-state entanglement in the latter, mirroring the different statistics of the edge modes in the two systems. The edge-to-edge quantum conditional mutual information is robust in the presence of disorder or local perturbations, converges exponentially with the system size to a quantized topological invariant, even in the presence of interactions, and vanishes in the trivial phase. We thus conjecture that it coincides with the edge-to-edge squashed entanglement in the entire ground-state phase diagram of symmetry-protected topological systems, and we provide some analytical evidence supporting the claim. By comparing them with the entanglement negativity, we collect further indications that the quantum conditional mutual information and the squashed entanglement provide a very accurate characterization of nonlocal correlation patterns in one-dimensional quantum matter.

Bipartite entanglement and the arrow of time

We provide a different perspective on the close relationship between entanglement and time. Our main focus is on bipartite entanglement, where this connection is foreshadowed both in the positive partial transpose criterion due to Peres [A. Peres, Phys. Rev. Lett. 77, 1413 (1996)] and in the classification of quantum within more general nonsignaling bipartite correlations [M. Frembs and A. D\"oring, Phys. Rev. A 106, 062420 (2022)]. Extracting the relevant common features, we identify a necessary and sufficient condition for bipartite entanglement in terms of a compatibility condition with respect to time orientations in local observable algebras, which express the dynamics in the respective subsystems. As an outlook and a program for future work, we discuss the relevance of the latter in the broader context of von Neumann algebras and the thermodynamical notion of time naturally arising within the latter.

Characterization of nonsignaling bipartite correlations corresponding to quantum states

Characterizing quantum correlations from physical principles is a central problem in the field of quantum information theory. Entanglement breaks bounds on correlations put forth by Bell's theorem, thus challenging the notion of local causality as a physical principle. A natural relaxation is to study no-signalling as a constraint on joint probability distributions. It was shown that, when considered with respect to so-called locally quantum observables, bipartite nonsignalling correlations never exceed their quantum counterparts; still, such correlations generally do not derive from quantum states. This leaves open the search for additional principles which identify quantum states within the larger set of (collections of) nonsignalling joint probability distributions over locally quantum observables. Here, we suggest a natural generalization of no-signalling in the form of no-disturbance to dilated systems. We prove that nonsignalling joint probability distributions satisfying this extension correspond with bipartite quantum states up to a choice of time orientation in subsystems.

Timelike correlations and quantum tensor product structure

The state space structure for a composite quantum system is postulated among several mathematically consistent possibilities that are compatible with local quantum description. For instance, unentangled Gleason's theorem allows a state space that includes density operators as a proper subset among all possible composite states. However, bipartite correlations obtained in Bell type experiments from this broader state space are in-fact quantum simulable, and hence such spacelike correlations are no good to make distinction among different compositions. In this work we analyze communication utilities of these different composite models and show that they can lead to distinct utilities in a simple communication game involving two players. Our analysis, thus, establishes that beyond quantum composite structure can lead to beyond quantum correlations in timelike scenario and hence welcomes new principles to isolate the quantum correlations from the beyond quantum ones. We also prove a no-go that the classical information carrying capacity of different such compositions cannot be more than the corresponding quantum composite systems.

Information scrambling and redistribution of quantum correlations through dynamical evolution in spin chains

We investigate the propagation of local bipartite quantum correlations, along with the tripartite mutual information to characterize the information scrambling through dynamical evolution of spin chains. Starting from an initial state with the first pair of spins in a Bell state, we study how quantum correlations spread to other parts of the system, using different representative spin Hamiltonians, viz. the Heisenberg Model, a spin-conserving model, the transverse-field XY model, a non-conserving but integrable model, and the kicked Harper model, a spin conserving but nonintegrable model. We show that the local correlations spread consistently in the case of spin-conserving dynamics in both integrable and nonintegrable cases, with a strictly nonnegative tripartite mutual information. In contrast, in the case of non-conserving dynamics, tripartite mutual information is negative and local pair correlations do not propagate.

Entanglement harvesting of three Unruh-DeWitt detectors

We analyze a tripartite entanglement harvesting protocol with three Unruh-DeWitt detectors adiabatically interacting with a quantum scalar field. We consider linear, equilateral triangular, and scalene triangular configurations for the detectors. We find that, under the same parameters, more entanglement can be extracted in the linear configuration than the equilateral one, consistent with single instantaneous switching results. No bipartite entanglement is required to harvest tripartite entanglement. Furthermore, we find that tripartite entanglement can be harvested even if one detector is at larger spacelike separations from the other two than in the corresponding bipartite case. We also find that for small detector separations bipartite correlations become larger than tripartite ones, leading to an apparent violation of the Coffman-Kundu-Wootters (CKW) inequality. We show that this is not a consequence of our perturbative expansion but that it instead occurs because the harvesting qubits are in a mixed state.

Intrinsic decoherence effects on nonclassical correlations in a symmetric spin–orbit model

Nonclassical correlations dynamics of local quantum Fisher information, trace-norm measurement-induced nonlocality, and log-negativity are investigated in a symmetric spin–orbit model. This model is described by a Heisenberg XYZ two-spin system exposed to the magnetic field and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interaction under the intrinsic decoherence effects. To evaluate the resourcefulness of this model for the generation and preservation of quantum correlations, we consider two qubits that are initially prepared in two different states, namely uncorrelated and maximally correlated states. The magnetic field is discovered to be effective at generating and preserving nonclassical correlations. Besides, we find that the KSEA interaction can alter the generation, preservation, and revival features of nonclassical correlations in the two-qubit system. However, the bipartite nonclassical correlations become extremely fragile when intrinsic decoherence effects appear.

Dynamics of quantum resources in regular and Majorana fermion systems

In recent years, the reassessment of quantum physical phenomena under the framework of resource theories has triggered the design of novel quantum technologies that take advantage from quantum resources, such as entanglement and quantum coherence. Bearing this in mind, in this work we study the dynamics of quantum resources for two solid-state fermionic quantum devices: (i) a system composed by a pair of Majorana fermions and (ii) another comprising a pair of regular fermions. In both systems, the fermionic species are coupled to a single-level quantum dot. From the interaction of these tripartite systems with a dissipative reservoir, we were able to characterize the dynamics of the devices for some initial states. By employing a time-nonlocal master-equation approach, we obtain the evolution for fermionic occupations, quantum correlations, and quantum coherences in both the Markovian and non-Markovian dissipating regimes. We investigate the interconversion of local coherence and bipartite correlations for the marginal states in each device. While the dynamics of the entanglement and quantum coherence depend quite strongly on the temperature of the reservoir for regular fermions, we found these evolutions are qualitatively similar for the case of Majorana bound states regardless of temperature. Our results illustrate the use of quantum information-theoretic measures to characterize the role of quantum resources in fermion systems.

Effects of symmetry breaking of the structurally-disordered Hamiltonian ensembles on the anisotropic decoherence of qubits

It is commonly known that the dephasing in open quantum systems is due to the establishment of bipartite correlations with ambient environments, which are typically difficult to be fully characterized. Recently, a new approach of average over disordered Hamiltonian ensemble is developed and shown to be capable of describing the nonclassicality of incoherent dynamics based on inferring the nonclassical nature of the correlations. Here we further extend the approach of Hamiltonian ensemble in the canonical form to the realm of structural disorder. Under the variable separation of the probability distribution within the Hamiltonian ensemble, the geometrical structure is easily visualized and can be characterized according to the degree of symmetry. We demonstrate four degrees and investigate the effects of different types of symmetry breaking on the incoherent dynamics. We show that these effects are easily understood from the emergences of additional terms in the master equations, leading to rather general master equations and, consequently, going beyond the previous frameworks of pure dephasing or isotropic depolarization.

Evolution of Gaussian Rényi-2 quantum correlations in a squeezed thermal environment

In this paper, we investigate, in the framework of the theory of open quantum systems, based on completely positive dynamical semigroups, the Markovian dynamics of Gaussian Rényi-2 correlations — quantum entanglement, quantum discord, mutual information and classical correlations in a system composed of two bosonic modes, interacting with a squeezed thermal bath. We show that the time evolution of the Rényi-2 correlations strongly depends on the parameters of the initial Gaussian squeezed thermal state of the considered system and on the parameters characterizing the squeezed thermal bath. It is shown that while Gaussian Rényi-2 entanglement is suppressed in a finite time, due to the interaction with the squeezed thermal bath, the correlations beyond entanglement — Gaussian Rényi-2 discord, classical correlations and mutual information undergo a freezing-like behavior, namely they decay only asymptotically, in the limit of large times. We also illustrate a fundamental hierarchy for bipartite Gaussian correlations.

Quantum Fisher information and skew information correlations in dipolar spin system

Quantum Fisher information (QFI) and skew information (SI) plays a key role in the quantum resource theory. Understanding these measures in the physical system has practical significance in the state parameter estimation and quantum metrology. In this article, we consider a pair of spin-1/2 particles coupled with dipolar and Dzyaloshinsky-Moriya (DM) interactions, serving as the physical carrier of quantum information. We examine the bipartite nonlocal correlations of pair of spin-1/2 particle system for the thermal equilibrium states, characterized by local quantum uncertainty (LQU) and local quantum Fisher information (lQFI). The effects of dipolar coupling constants on quantum correlation quantifiers are studied. The DM interaction greatly enhances the quantum correlation in the system whereas the temperature tends to annihilate the amount of quantum correlations.

Quantifying Quantum Correlation of Quasi‐Werner State and Probing Its Suitability for Quantum Teleportation (Ann. Phys. 10/2021)

Quantum Correlations In article number 2100201, Arpita Chatterjee, Kishore Thapliyal, and Anirban Pathak establish the relevance of photon addition in the enhancement of single- and two-mode (bipartite correlations) nonclassical properties and teleportation performance using the Wigner function, entanglement, and discord of the two-mode quasi-Werner state. Efficacy of photon addition in the entanglement distillation is also established.

Two-beam light with ’checkered-pattern’ photon-number distributions

Photon-number-resolved post-selection on one beam out of a correlated system of three beams with bi-partite photon-number correlations gives rise to joint photon-number distributions with the probabilities forming checkered patterns. These patterns originate in the convolution of two constituting photon-number distributions, one endowed with correlations in photon numbers, the other exhibiting anti-correlations in photon-number fluctuations. Using three twin beams of comparable intensity whose constituting beams suitably overlap on the photocathode of a photon-number-resolving iCCD camera, we experimentally as well as theoretically analyze the properties of such states as they change with the varying ratio of the correlated and anti-correlated contributions. The experimental photocount 2D histograms of the fields post-selected by the iCCD camera that are reconstructed by the maximum-likelihood approach confirm their non-classicality though the limited detection efficiency in post-selection conceals the checkered patterns. Contrary to this, the maximum-likelihood reconstruction of the experimental 3D photocount histogram similarly as a suitable 3D Gaussian fit, that reveal the states as they would be obtained by ideal post-selection, provide the photon-number distributions with the checkered patterns. The corresponding quasi-distributions of integrated intensities are determined. Nonclassical properties of the generated states are investigated using suitable non-classicality criteria and the corresponding non-classicality depths. These states with their correlations of varying intensity are prospective for two-photon excitations of atoms and molecules as well as two-photon spectroscopy.