Quantum properties and dynamics of X states

X states are a broad class of two-qubit density matrices that generalize many states of interest in the literature. In this work, we give a comprehensive account of various quantum properties of these states, such as entanglement, negativity, quantum discord and other related quantities. Moreover, we discuss the transformations that preserve their structure both in terms of continuous time evolution and discrete quantum processes.Comment: 13 page

Calculation of quantum discord in higher dimensions for X- and other specialized states

Quantum discord, a kind of quantum correlation based on entropic measures, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. Procedures are available for analytical calculation of discord when one of the parties is a qubit with dimension two and measurements made on it to get that one-way discord. We extend now to systems when both parties are of larger dimension and of interest to qudit–quDit with d, D≥ 3 or spin chains of spins ≥ 1. While recognizing that no universal scheme is feasible, applicable to all density matrices, nevertheless, a procedure similar to that for d= 2 that works for many mixed-state density matrices remains of interest as shown by recent such applications. We focus on this method that uses unitary operations to describe measurements, reducing them to a compact form so as to minimize the number of variables needed for extremizing the classical correlation, often the most difficult part of the discord calculation. Results are boiled down to a simple recipe for that extremization; for some classes of density matrices, the procedure even gives trivially the final value of the classical correlation without that extremization. A qutrit–qutrit (d= D= 3) system is discussed in detail with specific applications to density matrices for whom other calculations involved difficult numerics. Special attention is given to the so-called X-states and Werner and isotropic states when the calculations become particularly simple. An appendix discusses an independent but related question of the systematics of X-states of arbitrary dimension. It forms a second, separate, part of this paper, extending our previous group-theoretic considerations of systematics for qubits now to higher d

Correlation Dynamics of Qubit-Qutrit Systems in a Classical Dephasing Environment

We study the time evolution of classical and quantum correlations for hybrid qubit-qutrit systems in independent and common classical dephasing environments. Our discussion involves a comparative analysis of the Markovian dynamics of negativity, quantum discord, geometric measure of quantum discord and classical correlation. For the case of independent environments, we have demonstrated the phenomenon of sudden transition between classical and quantum decoherence for qubit-qutrit states. In the common environment case, we have shown that dynamics of quantum and geometric discords might be completely independent of each other for a certain time interval, although they tend to be eventually in accord.Comment: 16 pages, 2 figures. Taking the recent update of arxiv:1010.1920v3 into account, we have very slightly modified our discussion of geometric discord to avoid any misunderstanding. The results of the present version (v3), including the analysis of geometric discord, remain completely unchanged as compared to the published versio

Maximal nonlocality from maximal entanglement and mutually unbiased bases, and self-testing of two-qutrit quantum systems

Bell inequalities are an important tool in device-independent quantum information processing because their violation can serve as a certificate of relevant quantum properties. Probably the best known example of a Bell inequality is due to Clauser, Horne, Shimony and Holt (CHSH), which is defined in the simplest scenario involving two dichotomic measurements and whose all key properties are well understood. There have been many attempts to generalise the CHSH Bell inequality to higher-dimensional quantum systems, however, for most of them the maximal quantum violation---the key quantity for most device-independent applications---remains unknown. On the other hand, the constructions for which the maximal quantum violation can be computed, do not preserve the natural property of the CHSH inequality, namely, that the maximal quantum violation is achieved by the maximally entangled state and measurements corresponding to mutually unbiased bases. In this work we propose a novel family of Bell inequalities which exhibit precisely these properties, and whose maximal quantum violation can be computed analytically. In the simplest scenario it recovers the CHSH Bell inequality. These inequalities involve $d$ measurements settings, each having $d$ outcomes for an arbitrary prime number $d\geq 3$. We then show that in the three-outcome case our Bell inequality can be used to self-test the maximally entangled state of two-qutrits and three mutually unbiased bases at each site. Yet, we demonstrate that in the case of more outcomes, their maximal violation does not allow for self-testing in the standard sense, which motivates the definition of a new weak form of self-testing. The ability to certify high-dimensional MUBs makes these inequalities attractive from the device-independent cryptography point of view.Comment: 19 pages, no figures, accepted in Quantu

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