Characterizing Quantum Correlations Research Articles

Characterizing quantum correlations dynamics in Heisenberg system with Dzyaloshinskii–Moriya interaction

Characterizing quantum correlations dynamics in Heisenberg system with Dzyaloshinskii–Moriya interaction

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.

Quantum correlations and entanglement in coupled optomechanical resonators with photon hopping via Gaussian interferometric power analysis

Quantum correlations that surpass entanglement are of great importance in the realms of quantum information processing and quantum computation. Essentially, for quantum systems prepared in pure states, it is difficult to differentiate between quantum entanglement and quantum correlation. Nonetheless, this indistinguishability is no longer holds for mixed states. To contribute to a better understanding of this differentiation, we have explored a simple model for both generating and measuring these quantum correlations. Our study concerns two macroscopic mechanical resonators placed in separate Fabry–Pérot cavities, coupled through the photon hopping process. this system offers a comprehensively way to investigate and quantify quantum correlations beyond entanglement between these mechanical modes. The key ingredient in analyzing quantum correlation in this system is the global covariance matrix. It forms the basis for computing two essential metrics: the logarithmic negativity ( ENm ) and the Gaussian interferometric power ( PGm ). These metrics provide the tools to measure the degree of quantum entanglement and quantum correlations, respectively. Our study reveals that the Gaussian interferometric power ( PGm ) proves to be a more suitable metric for characterizing quantum correlations among the mechanical modes in an optomechanical quantum system, particularly in scenarios featuring resilient photon hopping.

Work fluctuations and entanglement in quantum batteries

We consider quantum batteries given by composite interacting quantum systems in terms of the thermodynamic work cost of local random unitary processes. We characterize quantum correlations by monitoring the average energy change and its fluctuations in the high-dimensional bipartite systems. We derive a hierarchy of bounds on high-dimensional entanglement (the so-called Schmidt number) from the work fluctuations and thereby show that larger work fluctuations can verify the presence of stronger entanglement in the system. Finally, we develop two-point measurement protocols with noisy detectors that can estimate work fluctuations, showing that the dimensionality of entanglement can be probed in this manner.

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.

Quantum fluctuations and correlations in open quantum Dicke models

In the vicinity of ground-state phase transitions quantum correlations can display non-analytic behavior and critical scaling. This signature of emergent collective effects has been widely investigated within a broad range of equilibrium settings. However, under nonequilibrium conditions, as found in open quantum many-body systems, characterizing quantum correlations near phase transitions is challenging. Moreover, the impact of local and collective dissipative processes on quantum correlations is not broadly understood. This is, however, indispensable for the exploitation of quantum effects in technological applications, such as sensing and metrology. Here we consider as a paradigmatic setting the superradiant phase transition of the open quantum Dicke model and characterize quantum and classical correlations across the phase diagram. We develop an approach to quantum fluctuations which allows us to show that local dissipation, which cannot be treated within the commonly employed Holstein-Primakoff approximation, rather unexpectedly leads to an enhancement of collective quantum correlations, and to the emergence of a nonequilibrium superradiant phase in which the bosonic and spin degrees of freedom of the Dicke model are entangled.

Dynamics of quantum correlations in a quantum dot system with intrinsic decoherence effects

In this paper, we explore the dynamics of quantum correlations in an isolated physical quantum dot under the influence of intrinsic decoherence (ID). We characterize quantum correlations in the quantum dot system using Concurrence to capture the amount of entanglement, and we use Trace Distance Discord (TDD) and Local Quantum Uncertainty (LQU) to measure nonclassical correlations. Likewise, we investigate the effect of ID on the temporal evolution of these quantifiers. In particular, the behavior of the two discord-like quantifiers in terms of the system parameters and the ID rate is investigated and analyzed in detail. We found that TDD and LQU behave similarly for different parameters characterizing the considered system and that TDD is more resistant than Concurrence and LQU against the ID effects. Our results also show that the robustness of quantum correlations can be modulated by adjusting the ID rate, quantum dot physical properties and initial conditions.

Multipartite quantum nonlocality and Bell-type inequalities in a spin-1/2 model with topological quantum phase transitions

Multipartite quantum nonlocality and Bell-type inequalities are used to characterize quantum correlations in an infinite-size bond-alternating spin-$\frac{1}{2}$ Heisenberg chain with next-nearest-neighbor interactions. With the help of powerful tensor-network algorithms, both zero and finite temperatures are considered. First, at zero temperature, both in the even-Haldane phase and in the odd-Haldane phase, a high hierarchy of multipartite nonlocality is observed. Nevertheless, in the two phases, the spread of the multipartite nonlocality among the lattice is different. Thereby, the nonlocality measures are relatively large in one phase and vanish in the other phase, and provide quite sharp signals for the topological quantum phase transitions (QPTs) between these two phases. The influence of the next-nearest-neighbor coupling $\ensuremath{\alpha}$ upon the multipartite nonlocality in the model is also discussed. Second, we find that the footprints of the QPTs survive at low temperatures. Third, based upon the scaling behavior of the finite-temperature nonlocality measure, we propose a quantity $\mathcal{K}$ to characterize the finite-temperature nonlocality in the large-$n$ limit. We find that in high-temperature regions, $\mathcal{K}$ is reduced linearly as the temperature rises.

Characterizing quantum correlations one step at a time

Characterizing quantum correlations one step at a time

Local quantum uncertainty as a robust metric to characterize discord-like quantum correlations in subsets of the chromophores in photosynthetic light-harvesting complexes

Green sulfur bacteria is a photosynthetic organism whose light-harvesting complex accommodates a pigment-protein complex called Fenna-Matthews-Olson (FMO). The FMO complex sustains quantum coherence and quantum correlations between the electronic states of spatially separated pigment molecules as energy moves with nearly a 100% quantum efficiency to the reaction center. We present a method based on the quantum uncertainty associated to local measurements to quantify discord-like quantum correlations between two subsystems where one is a qubit and the other is a qudit. We implement the method by calculating local quantum uncertainty (LQU), concurrence, and coherence between subsystems of pure and mixed states represented by the eigenstates and by the thermal equilibrium state determined by the FMO Hamiltonian. Three partitions of the seven chromophores network define the subsystems: one chromophore with six chromophores, pairs of chromophores, and one chromophore with two chromophores. Implementation of the LQU approach allows us to characterize quantum correlations that had not been studied before, identify the most quantum correlated subsets of chromophores, and determine that, in the strongest associations of chromophores, the LQU is a monotonically increasing function of the coherence.

Discriminating quantum correlations with networking quantum teleportation

The Bell inequality, and its substantial experimental violation, offers a seminal paradigm for showing that the world is not in fact locally realistic. Here, going beyond the scope of Bell's inequality on physical states, we show that quantum teleportation can be used to quantitatively characterize quantum correlations of physical processes. The validity of the proposed formalism is demonstrated by considering the problem of teleportation through a linear three-node quantum network. A hierarchy is derived between the Bell nonlocality, nonbilocality, steering and nonlocality-steering hybrid correlations based on a process fidelity constraint. The proposed framework can be directly extended to reveal the nonlocality structure of teleportation through any linear many-node quantum network. The formalism provides a faithful identification of quantum teleportation and demonstrates the use of quantum-information processing as a means of quantitatively discriminating quantum correlations.

Almost-Quantum Correlations Violate the No-Restriction Hypothesis.

To identify which principles characterize quantum correlations, it is essential to understand in which sense this set of correlations differs from that of almost-quantum correlations. We solve this problem by invoking the so-called no-restriction hypothesis, an explicit and natural axiom in many reconstructions of quantum theory stating that the set of possible measurements is the dual of the set of states. We prove that, contrary to quantum correlations, no generalized probabilistic theory satisfying the no-restriction hypothesis is able to reproduce the set of almost-quantum correlations. Therefore, any theory whose correlations are exactly, or very close to, the almost-quantum correlations necessarily requires a rule limiting the possible measurements. Our results suggest that the no-restriction hypothesis may play a fundamental role in singling out the set of quantum correlations among other nonsignaling ones.

Investigating Einstein-Podolsky-Rosen steering of continuous-variable bipartite states by non-Gaussian pseudospin measurements

EPR steering is an asymmetric form of correlations which is intermediate between quantum entanglement and Bell nonlocality, and can be exploited for quantum communication with one untrusted party. In particular, steering of continuous variable Gaussian states has been extensively studied as a manifestation of the EPR paradox. While most of these studies focused on quadrature measurements for steering detection, two recent works revealed that there exist Gaussian states which are only steerable by non-Gaussian measurements. In this paper we perform a systematic investigation of EPR steering of bipartite Gaussian states by pseudospin measurements, complementing and extending previous findings. We first derive the density matrix elements of two-mode squeezed thermal states in the Fock basis, which may be of independent interest. We then use such a representation to investigate steering of these states as detected by a nonlinear criterion, based on second moments of the pseudospin correlation matrix. This analysis reveals previously unexplored regimes where non-Gaussian measurements are more effective than Gaussian ones to witness steering of Gaussian states in the presence of local noise. We further consider an alternative set of pseudospin observables, whose expectation value can be expressed compactly in terms of Wigner functions for all two-mode Gaussian states. However, according to the adopted criterion, these observables are found to be always less sensitive than Gaussian observables for steering detection. Finally, we investigate continuous variable Werner states, which are non-Gaussian mixtures of Gaussian states, and find that pseudospin measurements are always more effective than Gaussian ones to reveal their steerability. Our results provide useful insights on the role of non-Gaussian measurements in characterizing quantum correlations of Gaussian and non-Gaussian states.

Geometric quantum discords of interacting qubits in thermal reservoir

We examined decay dynamics of various geometric quantum discords (GQDs) for two interacting qubits described by the Heisenberg XY model and further coupled independently to their respective thermal reservoirs. Compared to the case of noninteracting qubits, our results showed that decay rates of the GQDs can be retarded apparently by properly choosing system parameters of the interaction term. In the long-time limit, the asymptotic values of the GQDs are enhanced evidently by tuning anisotropy of the model and strength of the transverse magnetic field. We further illuminated the relations between different GQDs on characterizing quantum correlations, and observed multiple sudden change behaviors of their dynamics.

Bridging the gap between general probabilistic theories and the device-independent framework for nonlocality and contextuality

Characterizing quantum correlations in terms of information-theoretic principles is a popular chapter of quantum foundations. Traditionally, the principles adopted for this scope have been expressed in terms of conditional probability distributions, specifying the probability that a black box produces a certain output upon receiving a certain input. This framework is known as device-independent. Another major chapter of quantum foundations is the information-theoretic characterization of quantum theory, with its sets of states and measurements, and with its allowed dynamics. The different frameworks adopted for this scope are known under the umbrella term general probabilistic theories. With only a few exceptions, the two programmes on characterizing quantum correlations and characterizing quantum theory have so far proceeded on separate tracks, each one developing its own methods and its own agenda. This paper aims at bridging the gap, by comparing the two frameworks and illustrating how the two programmes can benefit each other.

Sudden change of geometric quantum discord in finite temperature reservoirs

We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively.

Characterizing Quantum Correlations in Arbitrary-Dimensional Bipartite Systems Using Hurwitz's Theory

Quantum correlations play vital roles in the quantum features in quantum information processing tasks. Among the measures of quantum correlations, quantum discord (QD) and entanglement of formation (EOF) are two significant ones. Recent research has shown that there exists a relation between QD and EOF, which makes QD more significant in quantum information theory. However, until now, there exists no general method of characterizing quantum discord in high-dimensional quantum systems. In this paper, we have proposed a general method for calculating quantum discord in arbitrary-dimensional bipartite quantum systems in terms of Hurwitz's theory. Applications including the Werner state, the spin-1 XXZ model thermal equilibrium state, the Horodecki state, and the separable-bound-free entanglement state are investigated. We present the method of obtaining the EOF of arbitrary-dimensional bipartite quantum states via purification, and the relationship between QD and EOF.

Correlation measurements with on-off detectors

We present a general method to detect nonclassical radiation fields with systems of on-off detectors. We especially study higher order correlations for the identification of nonclassical radiation. This allows us to directly characterize quantum correlations by the statistics measured with systems of on-off detectors. Additionally, we generalize our method to multiple detector systems for measurements of correlations between light fields. We also consider multi-mode radiation fields and isolate nonclassicality in terms of the space time correlations. Finally, we present results for the quantum statistics using on-off detectors operating in nonlinear detection modes.

Quasiprobabilities for multipartite quantum correlations of light

Regular quasiprobabilities are introduced for the aim of characterizing quantum correlations of multimode radiation fields. Negativities of these quantum-correlation quasiprobabilities are necessary and sufficient for any quantum correlation encoded in the multimode Glauber-Sudarshan P function. The strength of the method is demonstrated for a two-mode phase randomized squeezed-vacuum state. It has no entanglement, no quantum discord, a positive Wigner function, and a classical reduced single-mode representation. Our method clearly visualizes the quantum correlations of this state.