Experimental investigation of classical and quantum correlations under decoherence

It is well known that many operations in quantum information processing depend largely on a special kind of quantum correlation, that is, entanglement. However, there are also quantum tasks that display the quantum advantage without entanglement. Distinguishing classical and quantum correlations in quantum systems is therefore of both fundamental and practical importance. In consideration of the unavoidable interaction between correlated systems and the environment, understanding the dynamics of correlations would stimulate great interest. In this study, we investigate the dynamics of different kinds of bipartite correlations in an all-optical experimental setup. The sudden change in behaviour in the decay rates of correlations and their immunity against certain decoherences are shown. Moreover, quantum correlation is observed to be larger than classical correlation, which disproves the early conjecture that classical correlation is always greater than quantum correlation. Our observations may be important for quantum information processing.Comment: 7 pages, 4 figures, to appear in Nature Communication

Quantum Discord in a spin-1/2 transverse XY Chain Following a Quench

We report a study on the zero-temperature quantum discord as a measure of two-spin correlation of a transverse XY spin chain following a quench across a quantum critical point and investigate the behavior of mutual information, classical correlations and hence of discord in the final state as a function of the rate of quenching. We show that though discord vanishes in the limit of very slow as well as very fast quenching, it exhibits a peak for an intermediate value of the quenching rate. We show that though discord and also the mutual information exhibit a similar behavior with respect to the quenching rate to that of concurrence or negativity following an identical quenching, there are quantitative differences. Our studies indicate that like concurrence, discord also exhibits a power law scaling with the rate of quenching in the limit of slow quenching though it may not be expressible in a closed power law form. We also explore the behavior of discord on quenching linearly across a quantum multicritical point (MCP) and observe a scaling similar to that of the defect density.Comment: 6 pages, 5 figure

The sudden change phenomenon of quantum discord

Even if the parameters determining a system's state are varied smoothly, the behavior of quantum correlations alike to quantum discord, and of its classical counterparts, can be very peculiar, with the appearance of non-analyticities in its rate of change. Here we review this sudden change phenomenon (SCP) discussing some important points related to it: Its uncovering, interpretations, and experimental verifications, its use in the context of the emergence of the pointer basis in a quantum measurement process, its appearance and universality under Markovian and non-Markovian dynamics, its theoretical and experimental investigation in some other physical scenarios, and the related phenomenon of double sudden change of trace distance discord. Several open questions are identified, and we envisage that in answering them we will gain significant further insight about the relation between the SCP and the symmetry-geometric aspects of the quantum state space.Comment: Lectures on General Quantum Correlations and their Applications, F. F. Fanchini, D. O. Soares Pinto, and G. Adesso (Eds.), Springer (2017), pp 309-33

Algebraic characterization of X-states in quantum information

A class of two-qubit states called X-states are increasingly being used to discuss entanglement and other quantum correlations in the field of quantum information. Maximally entangled Bell states and "Werner" states are subsets of them. Apart from being so named because their density matrix looks like the letter X, there is not as yet any characterization of them. The su(2) X su(2) X u(1) subalgebra of the full su(4) algebra of two qubits is pointed out as the underlying invariance of this class of states. X-states are a seven-parameter family associated with this subalgebra of seven operators. This recognition provides a route to preparing such states and also a convenient algebraic procedure for analytically calculating their properties. At the same time, it points to other groups of seven-parameter states that, while not at first sight appearing similar, are also invariant under the same subalgebra. And it opens the way to analyzing invariant states of other subalgebras in bipartite systems.Comment: 4 pages, 1 figur

Quantum Correlations in NMR systems

In conventional NMR experiments, the Zeeman energy gaps of the nuclear spin ensembles are much lower than their thermal energies, and accordingly exhibit tiny polarizations. Generally such low-purity quantum states are devoid of quantum entanglement. However, there exist certain nonclassical correlations which can be observed even in such systems. In this chapter, we discuss three such quantum correlations, namely, quantum contextuality, Leggett-Garg temporal correlations, and quantum discord. In each case, we provide a brief theoretical background and then describe some results from NMR experiments.Comment: 21 pages, 7 figure

Quantum Discord and entropic measures of quantum correlations: Optimization and behavior in finite XYXY spin chains

We discuss a generalization of the conditional entropy and one-way information deficit in quantum systems, based on general entropic forms. The formalism allows to consider simple entropic forms for which a closed evaluation of the associated optimization problem in qudit-qubit systems is shown to become feasible, allowing to approximate that of the quantum discord. As application, we examine quantum correlations of spin pairs in the exact ground state of finite $XY$ spin chains in a magnetic field through the quantum discord and information deficit. While these quantities show a similar behavior, their optimizing measurements exhibit significant differences, which can be understood and predicted through the previous approximations. The remarkable behavior of these quantities in the vicinity of transverse and non-transverse factorizing fields is also discussed.Comment: 10 pages, 3 figure

Geometric measure of quantum discord and the geometry of a class of two-qubit states

We investigate the geometric picture of the level surfaces of quantum entanglement and geometric measure of quantum discord (GMQD) of a class of X-states, respectively. This pictorial approach provides us a direct understanding of the structure of entanglement and GMQD. The dynamic evolution of GMQD under two typical kinds of quantum decoherence channels is also investigated. It is shown that there exists a class of initial states for which the GMQD is not destroyed by decoherence in a finite time interval. Furthermore, we establish a factorization law between the initial and final GMQD, which allows us to infer the evolution of entanglement under the influences of the environment.Comment: 10 pages, 4 figures, comments are welcom

Overview on the phenomenon of two-qubit entanglement revivals in classical environments

The occurrence of revivals of quantum entanglement between separated open quantum systems has been shown not only for dissipative non-Markovian quantum environments but also for classical environments in absence of back-action. While the phenomenon is well understood in the first case, the possibility to retrieve entanglement when the composite quantum system is subject to local classical noise has generated a debate regarding its interpretation. This dynamical property of open quantum systems assumes an important role in quantum information theory from both fundamental and practical perspectives. Hybrid quantum-classical systems are in fact promising candidates to investigate the interplay among quantum and classical features and to look for possible control strategies of a quantum system by means of a classical device. Here we present an overview on this topic, reporting the most recent theoretical and experimental results about the revivals of entanglement between two qubits locally interacting with classical environments. We also review and discuss the interpretations provided so far to explain this phenomenon, suggesting that they can be cast under a unified viewpoint.Comment: 16 pages, 9 figures. Chapter written for the upcoming book "Lectures on general quantum correlations and their applications

Frozen and Invariant Quantum Discord under Local Dephasing Noise

In this chapter, we intend to explore and review some remarkable dynamical properties of quantum discord under various different open quantum system models. Specifically, our discussion will include several concepts connected to the phenomena of time invariant and frozen quantum discord. Furthermore, we will elaborate on the relation of these two phenomena to the non-Markovian features of the open system dynamics and to the usage of dynamical decoupling protocols.Comment: 29 pages, 8 figure