Measure Of Non-classical Correlations Research Articles

Gaussian multipartite quantum discord from classical mutual information

Quantum discord is a measure of non-classical correlations, which are excess correlations inherent in quantum states that cannot be accessed by classical measurements. For multipartite states, the classically accessible correlations can be defined by the mutual information of the multipartite measurement outcomes. In general the quantum discord of an arbitrary quantum state involves an optimisation of over the classical measurements which is hard to compute. In this paper, we examine the quantum discord in the experimentally relevant case when the quantum states are Gaussian and the measurements are restricted to Gaussian measurements. We perform the optimisation over the measurements to find the Gaussian discord of the bipartite EPR state and tripartite GHZ state in the presence of different types of noise: uncorrelated noise, multiplicative noise and correlated noise. We find that by adding uncorrelated noise and multiplicative noise, the quantum discord always decreases. However, correlated noise can either increase or decrease the quantum discord. We also find that for low noise, the measurements that maximise the classically accessible correlations are single quadrature measurements. As the noise increases, a dual quadrature measurement becomes optimal.

Local quantum uncertainty and interferometric power for a two-qubit system under decoherence channels with memory

Via local quantum uncertainty (LQU) and interferometric power (IP) as a measure of nonclassical correlations, we study the dynamics of quantum correlations for two non-interacting qubits passing through decoherence channels where the channels with successive uses are correlated. The effect of three different types of decoherence channels, such as amplitude damping, phase damping, and depolarizing channels, on quantum correlations has been discussed in detail. The explicit analytical expressions of LQU and IP for a class of Bell-diagonal states under these decoherence channels have been derived. Our results show that the behaviors of both LQU and IP exhibit similar variation under the amplitude damping and phase damping channels, with monotonic decay from an increasing decoherence rate, but decay more slowly when the memory coefficient of the channel increases. Compared to the phenomenon of LQU under a depolarizing channel, we find that there exists a sudden change of LQU under both amplitude damping and phase damping channels by choosing proper initial parameters. Finally, we compare the dynamics of LQU with that of IP under decoherence channels. Our results also confirm the amount of quantum correlations measured by LQU is smaller than IP.

Interplay between nonclassicality and PT symmetry in an effective two-level system with open system effects

A three level atom in $\Lambda$ configuration is reduced to an effective two level system, under appropriate conditions, and its $\mathcal{PT}$ symmetric properties are investigated. This effective qubit system when subjected to a beam-splitter type of interaction, it provides the scope of directly (indirectly) probing the nonclassical properties of the output (input) state. Here, we study nonclassical properties of the output state by using some well known measures of nonclassical correlations like the measurement induced disturbance, concurrence and negativity. The nonclassical features are found to enhance in the $\mathcal{PT}$ symmetric (PTS) phase compared to the $\mathcal{PT}$ symmetry broken (PTSB) phase. Further, the output ports of the beam-splitter are subjected to different quantum noise channels, both non-Markovian, e.g., random telegraph noise as well as Markovian, e.g., phase damping, and amplitude damping noise. The application of noise channels is found to decrease the degree of nonclassicality, though continuing to exhibit distinct behavior in PTS and PTSB phases, with the dominant behavior appearing in the former case.

Nonclassical correlations for quantum metrology in thermal equilibrium

Nonclassical correlations beyond entanglement might provide a resource in quantum information tasks, such as quantum computation or quantum metrology. Quantum discord is a measure of nonclassical correlations, to which entanglement belongs as a subset. Exploring the operational meaning of quantum discord as a resource in quantum information processing tasks, such as quantum metrology, is of essential importance to our understanding of nonclassical correlations. In our recent work [Phys. Rev. A, 98, 012115 (2018)], we considered a protocol---which we call the greedy local thermometry protocol--- for estimating the temperature of thermal equilibrium states from local measurements, elucidating the role of diagonal discord in enhancing the protocol sensitivity in the high-temperature limit. In this paper, we extend our results to a general greedy local parameter estimation scenario. In particular, we introduce a quantum discord---which we call discord for local metrology---to quantify the nonclassical correlations induced by the local optimal measurement on the subsystem. We demonstrate explicitly that discord for local metrology plays a role in sensitivity enhancement in the high-temperature limit by showing its relation to loss in quantum Fisher information. In particular, it coincides with diagonal discord for estimating a linear coupling parameter.

Understanding non-classical correlation using optical hybrid states in noisy quantum channels

In this article we investigate the non-classical correlation in a macroscopic physical system. As a tool, we consider an optical hybrid state that is a micro–macro entangled state. Our strategy is to study the behavior of non-classical correlation in an optical hybrid state that may go through noisy channels. We study the violation of two inequalities, which are the CHSH-inequality and the (generalized) CHSH-like-inequality, as measures of non-classical correlation. First, we find that when on/off or parity measurements are used for the side of the coherent state in an optical hybrid state, the violation of the CHSH-inequality is the same as that of the (generalized) CHSH-like-inequality. Second, we see that each measurement provides a different value of violation of (generalized) CHSH-inequality when it is an optical hybrid state that goes through noisy channels. A suprising result is that the on/off measurement can provide a violation of CHSH-inequality (or (generalized) CHSH-like-inequality) for an optical hybrid state with any amount of colored noise. This implies that colored noise cannot break the non-classical correlation in an optical hybrid state.

Discordlike correlation of bipartite coherence

Quantum discord has been studied extensively as a measure of non-classical correlations which includes entanglement as a subset. Although it is well known that non-zero discord can exist without entanglement, the origin of quantum discord is not well understood as compared to entanglement, which manifests itself more simply as inseparable higher dimensional quantum superposition. In this paper we establish the discordlike correlation of bipartite coherence and then compare it to quantum discord. Consequently, we show that the minimum of the discordlike correlation of coherence coincides with the original quantum discord. This demonstrates quantum discord as the irreducible correlated bipartite coherence. In addition, the discordlike correlated coherence is shown to admit the postulates of the quantum resource theory (QRT), although the original quantum discord is not a "good" candidate under the QRT. We also find that the relative entropy measure induced from the discordlike coherence is a well-defined coherence measure for bipartite states.

One-body information loss in fermion systems

We propose an entropic measure of non-classical correlations in general mixed states of fermion systems, based on the loss of information due to the unread measurement of the occupancy of single particle states of a given basis. When minimized over all possible single particle bases, the measure reduces to an entanglement entropy for pure states and vanishes only for states which are diagonal in a Slater determinant basis. The approach is also suitable for states having definite number parity yet not necessarily a fixed particle number, in which case the minimization can be extended to all bases related through a Bogoliubov transformation if quasiparticle mode measurements are also considered. General stationary conditions for determining the optimizing basis are derived. For a mixture of a general pure state with the maximally mixed state, a general analytic evaluation of the present measure and optimizing basis is provided, which shows that non-entangled mixed states may nonetheless exhibit a non-zero information loss.

Geometric discord of the Jaynes-Cummings model: pure dephasing regime

In this paper, the dynamical behaviour of the geometric discord of a system consisting of a two-level atom interacting with a quantised radiation field described by the Jaynes-Cummings model has been studied. The evolution of the system has been considered in the pure dephasing regime when the field is initially in a general pure state and the atom is initially in a mixed state. Dynamics of the geometric discord, as a measure of non-classical correlation, has been compared with the dynamics of negativity, as a measure of quantum entanglement. In particular, the influence of different parameters of system such as detuning and mixedness of the initial atomic state on the dynamics of geometric discord has been evaluated for when the field is initially in coherent and number states. It is shown that for asymptotically large times, the steady state geometric discord of the system presents a non-zero optimum value at some intermediate value of detuning.

Quantum discord as resource for remote state preparation

The existence of better-than-classical quantum information processing (QIP) models which consume very little or no entanglement suggests that separable or weakly entangled states could be extremely useful tools for information processing as they are much easier to prepare and control even in dissipative environments. It has been proposed that a resource of advantage is the generation of quantum discord, a measure of non-classical correlations that includes entanglement as a subset. Here we show that quantum discord is the necessary resource for quantum remote state preparation. We explicitly show that the geometric measure of quantum discord is related to the fidelity of this task, which provides its operational meaning. Our results are experimentally demonstrated using photonic quantum systems. Moreover, we demonstrate that separable states with non-zero quantum discord can outperform entangled states. Therefore, the role of quantum discord might provide fundamental insights for resource-efficient QIP. Quantum discord is the total non-classical correlation between two systems. This includes, but is not limited to, entanglement. Photonic experiments now demonstrate that separable states with non-zero quantum discord are a useful resource for quantum information processing and can even outperform entangled states.

Erratum: Measure of nonclassical correlation in coherence-vector representation [Phys. Rev. A84, 062105 (2011)

Received 31 January 2012DOI:https://doi.org/10.1103/PhysRevA.85.029904©2012 American Physical Society

EVALUATING MEASURES OF NONCLASSICAL CORRELATION IN A MULTIPARTITE QUANTUM SYSTEM

We introduce and evaluate measures of nonclassical correlation defined on the basis of a paradigm claiming that a multipartite system represented by a density matrix having no product eigenbasis possesses nonclassical correlation.

Nonclassical correlation in a multipartite quantum system: Two measures and evaluation

There is a commonly recognized paradigm in which a multipartite quantum system described by a density matrix having no product eigenbasis is considered to possess nonclassical correlation. Supporting this paradigm, we define two entropic measures of nonclassical correlation of a multipartite quantum system. One is defined as the minimum uncertainty about a joint system after we collect outcomes of particular local measurements. The other is defined by taking the maximum over all local systems about the minimum distance between a genuine set and a mimic set of eigenvalues of a reduced density matrix of a local system. The latter measure is based on an artificial game to create mimic eigenvalues of a reduced density matrix of a local system from eigenvalues of a density matrix of a global system. Numerical computation of these measures for several examples is performed.

Entangled state generation and modulation of vacuum squeezing by classical optical fields in birefringent fiber

Evolution of the vacuum fluctuations in the two-wave mixing of the optical fields propagating in a birefringent fiber is studied. The two-wave mixing in the birefringent fiber was suggested as a possible scheme for the entangled-state generation. Our treatment in studying the entangled-state generation uses depleted pump approximation and enables one to trace the influence of the input conditions of classical optical fields on the evolution of vacuum squeezing. We report the periodical modulation of the vacuum squeezing when the input relative phase of coherent waves varies. The measure of nonclassical correlations imposed on the generated light is calculated.