Classical correlations and entanglement in quantum measurements

We analyze a quantum measurement where the apparatus is initially in a mixed state. We show that the amount of information gained in a measurement is not equal to the amount of entanglement between the system and the apparatus, but is instead equal to the degree of classical correlations between the two. As a consequence, we derive an uncertainty-like expression relating the information gain in the measurement and the initial mixedness of the apparatus. Final entanglement between the environment and the apparatus is also shown to be relevant for the efficiency of the measurement.     

Thermodynamical approach to quantifying quantum correlations

We consider the amount of work which can be extracted from a heat bath using a bipartite state rho shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. In particuar, for pure states the work deficit is exactly equal to the distillable entanglement of the state. A form of complementarity exists between physical work which can be extracted and distillable entanglement. The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum nonlocality.     

Subsystem purity as an enforcer of entanglement

We show that entanglement can always arise in the interaction of an arbitrarily large system in any mixed state with a single qubit in a pure state. This small initial purity is enough to enforce entanglement even when the total entropy is close to maximum. We demonstrate this feature using the Jaynes-Cummings interaction of a two-level atom in a pure state with a field in a thermal state at an arbitrarily high temperature. We find the time and temperature variation of a lower bound on the amount of entanglement produced and study the classical correlations quantified by the mutual information.     

Are there phase transitions in information space?

The interplay between two basic quantities--quantum communication and information--is investigated. Quantum communication is an important resource for quantum states shared by two parties and is directly related to entanglement. Recently, the amount of local information that can be drawn from a state has been shown to be closely related to the nonlocal properties of the state. Here we consider both formation and extraction processes, and analyze informational resources as a function of quantum communication. The resulting diagrams in information space allow us to observe phaselike transitions when correlations become classical.     

Universal measure of entanglement

A general framework is developed for separating classical and quantum correlations in a multipartite system. Entanglement is defined as the difference in the correlation information encoded by the state of a system and a suitably defined separable state with the same marginals. A generalization of the Schmidt decomposition is developed to implement the separation of correlations for any pure, multipartite state. The measure based on this decomposition is a generalization of the entanglement of formation to multipartite systems, provides an upper bound for the relative entropy of entanglement, and is directly computable on pure states. The example of pure three-qubit states is analyzed in detail, and a classification based on minimal, four-term decompositions is developed.     

Two-qubit correlations via a periodic plasmonic nanostructure

We theoretically investigate the generation of quantum correlations by using two distant qubits in free space or mediated by a plasmonic nanostructure. We report both entanglement of formation as well as quantum discord and classical correlations. We have found that for proper initial state of the two-qubit system and distance between the two qubits we can produce quantum correlations taking significant value for a relatively large time interval so that it can be useful in quantum information and computation processes.     

Influences of Initial States on Entanglement Dynamics of Two Central Spins in a Spin Environment

We investigate the entanglement dynamics of two electronic spins coupled to a bath of nuclear spins for two special cases, one is that two central spins both interact with a common bath, and the other is that one of two spins interacts with a bath. We consider three types of initial states with different correlations between the system and the bath, i.e., quantum correlation, classical correlation, and no-correlation. We show that the initial correlations (no matter quantum correlations or classical correlations) can effectively avoid the occurrence of entanglement sudden death. Irrespective of whether both two spins or only one of the two spins interacts with the bath, the system can gain more entanglement in the process of the time evolution for initial quantum correlations. In addition, we find that the effects of the distribution of coupling constants on entanglement dynamics crucially depend on the initial state of the spin bath.     

多粒子纠缠的保护方案

量子纠缠是量子信息的重要物理资源. 然而当量子系统与环境相互作用时, 会不可避免地产生消相干导致纠缠下降, 因此保护纠缠不受环境的影响具有重要意义. 振幅衰减是一种典型的衰减机制. 如果探测环境保证没有激发从系统中流出, 即视为对系统的一种弱测量. 本文基于局域脉冲序列和弱测量, 提出了一种可以保护多粒子纠缠不受振幅衰减影响的有效物理方案, 保护的对象是在量子通信和量子计算中发挥重要作用的Cluster态和Maximal slice态.     

Decoherence from a spin chain with Dzyaloshinskii—Moriya interaction

We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya interaction.In the case of a two-qubit with an initial pure state,quantum correlations decay to zero at the critical point of the environment in a very short time.In the case of a two-qubit with initial mixed state,it is found that quantum discord may get maximized due to the quantum critical behavior of the environment,while entanglement vanishes under the same condition.Besides,we observed a sudden transition between classical and quantum decoherence when only a single qubit interacts with the environment.The effects of Dzyaloshinsky-Moriya interaction on quantum correlations are considered in the two cases.The decay of quantum correlations is always strengthened by Dzyaloshinsky-Moriya interaction.     

Entanglement and Classical Correlations in the Quantum Frame

The frame of classical probability theory can be generalized by enlarging the usual family of random variables in order to encompass nondeterministic ones. This leads to a frame in which two kinds of correlations emerge: the classical correlation that is coded in the mixed state of the physical system and a new correlation, to be called probabilistic entanglement, which may occur also at pure states. We examine to what extent this characterization of correlations can be applied to quantum mechanics. Explicit calculations on simple examples outline that a same quantum state can show only classical correlations or only entanglement depending on its statistical content; situations may also arise in which the two kinds of correlations compensate each other.     

Operational quantification of continuous-variable correlations

We quantify correlations (quantum and/or classical) between two continuous-variable modes as the maximal number of correlated bits extracted via local quadrature measurements. On Gaussian states, such "bit quadrature correlations" majorize entanglement, reducing to an entanglement monotone for pure states. For non-Gaussian states, such as photonic Bell states, photon-subtracted states, and mixtures of Gaussian states, the bit correlations are shown to be a monotonic function of the negativity. This quantification yields a feasible, operational way to measure non-Gaussian entanglement in current experiments by means of direct homodyne detection, without a complete state tomography.     

Dynamics of entanglement protection of two qubits using a driven laser field and detunings:Independent and common,Markovian and/or non-Markovian regimes

Preventing quantum entanglement from decoherence effect is of theoretical and practical importance in the quantum information processing technologies.In this regard,we consider the entanglement dynamics of two identical qubits where the qubits which are coupled to two independent(Markovian and/or non-Markovian) as well as a common reservoir at zero temperature are further interacted with a classical driving laser field.Then,we study the preservation of generated two-qubit entanglement in various situations using the concurrence measure.It is shown that by applying the classical driving field and so the possibility of controlling the Rabi frequency,the amount of entanglement of the two-qubit system is improved in the off-resonance condition between the qubit and the central cavity frequencies(central detuning) in both non-Markovian and Markovian reservoirs.While the central detuning has a constructive role,the detuning between the qubit and the classical field(laser detuning) affects negatively on the entanglement protection.The obtained results show that long-living entanglement in the non-Markovian reservoir is more accessible than in the Markovian reservoir.We demonstrate that,in a common reservoir non-zero stationary entanglement is achievable whenever the two-qubit system is coupled to the reservoir with appropriate values of relative coupling strengths.     

Entanglement of electronic subbands and coherent superposition of spin states in a Rashba nanoloop

The present work is concerned with an analysis of the entanglement between the electronic coherent superpositions of spin states and subbands in a quasi-one-dimensional Rashba nanoloop acted upon by a strong perpendicular magnetic field. We explicitly include the confining potential and the Rashba spin-orbit coupling into the Hamiltonian and then proceed to calculate the von Neumann entropy, a measure of entanglement, as a function of time. An analysis of the von Neumann entropy demonstrates that, as expected, the dynamics of entanglement strongly depends upon the initial state and electronic subband excitations. When the initial state is a pure one formed by a subband excitation and the z-component of spin states, the entanglement exhibits periodic oscillations with local minima (dips). On the other hand, when the initial state is formed by the subband states and a coherent superposition of spin states, the entanglement still periodically oscillates, exhibiting stronger correlations, along with elimination of the dips. Moreover, in the long run, the entanglement for the latter case undergoes the phenomenon of collapse-revivals. This behaviour is absent for the first case of the initial states. We also show that the degree of entanglement strongly depends upon the electronic subband excitations in both cases.     

Mode analysis of surface plasmon metal-dielectric-metal nanowire array waveguide at sub-wavelength scale

The investigation of quantum and classical correlations has mostly concentrated on two-qubit states because the minimization in the classical correlation is quite complicated for high-dimensional states. Thermal quantum and classical correlations are studied for a two-qutrit system with various coupling constants, external magnetic fields, and temperatures as well, where the quantum correlation is described in terms of the quantum discord that has been extensively used in recent literature. The entanglement negativity is calculated for comparison. It is shown that the discord is nonzero whereas the negativity is zero in some ranges of system parameters and temperature. Moreover, the discord is more robust than the entanglement against temperature and magnetic field. However, at lower temperatures all three correlations behave similarly. Those are useful for understanding quantum correlations in high-dimensional mixed states and quantum information processing.     

Conditional Information and Hidden Correlations in Single-qudit States

We discuss the notions of mutual information and conditional information for noncomposite systems, classical and quantum; both the mutual information and the conditional information are associated with the presence of hidden correlations in the state of a single qudit. We consider analogs of the entanglement phenomena in the systems without subsystems related to strong hidden quantum correlations.     

Measurement-induced nonlocality and geometric quantum discord in two SC-charge qubits

By using geometric quantum discord and measurement-induced nonlocality, quantum correlations are investigated for two superconducting (SC) charge qubits that share a large Josephson junction where the field is assumed to be prepared initially in a coherent state. It is found that the difference between measure measurement-induced nonlocality and geometric quantum discord, of the final state of the two SC-charge qubits system which is especial case of X-states, is equal to a constant value. It is found that the quantum correlations and entanglement of the qubits are very sensitive to the mean number of the coherent photons. The entanglement exists in small intervals of death quantum discord and measurement-induced nonlocality. This is further evidence in support of the fact that quantum correlation and entanglement are not synonymous.     

Transverse Ising model: Markovian evolution of classical and quantum correlations under decoherence

The transverse Ising Model (TIM) in one dimension is the simplest model which exhibits a quantum phase transition (QPT). Quantities related to quantum information theoretic measures like entanglement, quantum discord (QD) and fidelity are known to provide signatures of QPTs. The issue is less well explored when the quantum system is subjected to decoherence due to its interaction, represented by a quantum channel, with an environment. In this paper we study the dynamics of the mutual information I(ρ _AB ), the classical correlations C(ρ _AB ) and the quantum correlations Q(ρ _AB ), as measured by the QD, in a two-qubit state the density matrix of which is the reduced density matrix obtained from the ground state of the TIM in 1d. The time evolution brought about by system-environment interactions is assumed to be Markovian in nature and the quantum channels considered are amplitude damping, bit-flip, phase-flip and bit-phase-flip. Each quantum channel is shown to be distinguished by a specific type of dynamics. In the case of the phase-flip channel, there is a finite time interval in which the quantum correlations are larger in magnitude than the classical correlations. For this channel as well as the bit-phase-flip channel, appropriate quantities associated with the dynamics of the correlations can be derived which signal the occurrence of a QPT.     

Controlling transfer of quantum correlations among bi-partitions of a composite quantum system by combining different noisy environments

The correlation dynamics are investigated for various bi-partitions of a composite quantum system consisting of two qubits and two independent and non-identical noisy environments. The two qubits have no direct interaction with each other and locally interact with their environments. Classical and quantum correlations including the entanglement are initially prepared only between the two qubits. We find that contrary to the identical noisy environment case, the quantum correlation transfer direction can be controlled by combining different noisy environments. The amplitude-damping environment determines whether there exists the entanglement transfer among bi-partitions of the system. When one qubit is coupled to an amplitude-damping environment and the other one to a bit-flip one, we find a very interesting result that all the quantum and the classical correlations, and even the entanglement, originally existing between the qubits, can be completely transferred without any loss to the qubit coupled to the bit-flit environment and the amplitude-damping environment. We also notice that it is possible to distinguish the quantum correlation from the classical correlation and the entanglement by combining different noisy environments.