Narrow Results

Quantum mutual information and concurrence are two important measures of quantum correlations, and their similar behavior for a bipartite pure state calls for inspecting whether such a behavior remains for a multipartite pure state. The dynamical correlation of quantum mutual information and tripartite entanglement is analytically and numerically studied for initial states, total boson numbers and coupling parameters in a symmetric trimer molecule, where the entanglement is measured in terms of concurrence. A correlation parameter is introduced to describe the correlation between mutual information and concurrence. It is shown that both quantities are positively or anti-correlated in irregular manner. However, they exhibit completely positive correlation for suitable states, with their explicit expressions being presented for arbitrary model parameters. The dynamical correlation between bipartite and tripartite entanglement is discussed as well. Those shed new light on the understanding of quantum correlations of vibrational states in polyatomic molecules.

We study the dynamics of classical-quantum correlations in the nonadiabatic regime, using the rotating wave approximation (RWA), between two movable mirrors of two spatially separated Fabry–Pérot cavities, each of the two cavities having a movable end-mirror and coupled to a two-mode squeezed light from spontaneous parametric down-conversion. This work completes our previous work [M. Amazioug, M. Nassik and N. Habiballah, Eur. Phys. J. D72, 171 (2018)] where we have studied the transfer of quantum correlations in steady state. The Bures distance is used to quantify the amount of entanglement of the symmetrical squeezed thermal state, and the Gaussian quantum discord is considered to quantify the quantumness of the quantum correlations even though the two movable mirrors are separable. Furthermore, total correlations are quantified using quantum mutual information. Indeed, these three indicators depend mainly on the temperature of the movable mirror and the squeezing parameter in strong coupling regime.

An elementary introduction into algebraic approach to unified quantum information theory and operational approach to quantum entanglement as generalized encoding is given. After introducing compound quantum state and two types of informational divergences, namely, Araki–Umegaki (a-type) and of Belavkin–Staszewski (b-type) quantum relative entropic information, this paper treats two types of quantum mutual information via entanglement and defines two types of corresponding quantum channel capacities as the supremum via the generalized encodings. It proves the additivity property of quantum channel capacities via entanglement, which extends the earlier results of Belavkin to products of arbitrary quantum channels for quantum relative entropy of any type.

It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kähler manifold. In this paper, we consider the notion of mutual information among continuous random variables in relation to the geometric description of a composite quantum system introducing a new measure of total correlations that can be computed in terms of Gaussian integrals.

In a two-mode Gaussian state ${\widehat{\varrho }}_{AB}$, we report on stationary evolution of three measures of correlations defined via the Rényi-2 entropy, i.e. quantum mutual information (QMI) ${{ℐ}}_{R,2}$, the Gaussian–Rényi-2 entanglement (GR2E) ${{ℰ}}_{R,2}$ and Gaussian quantum steering (GQS) ${𝒢}$. We evaluate analytical expression of the covariance matrix fully describing the state ${\widehat{\varrho }}_{AB}$. Further, we study, under influences of parameters characterizing the state at hand and its environment, the behavior of the three considered measures. We find that quantum steering ${𝒢}$ is always upper bounded by (GR2E) ${{ℰ}}_{R,2}$, which in turn is found always upper bounded by half of the QMI ${{ℐ}}_{R,2}$. This therefore satisfies the hierarchical relation $\frac{1}{2}{{ℐ}}_{R,2}\ge {{ℰ}}_{R,2}\ge {𝒢}$ established in [L. Lami, C. Hirche, G. Adesso and A. Winter, Phys. Rev. Lett.117 (2016) 220502]. Importantly, we find that both GR2E ${{ℰ}}_{R,2}$ and GQS ${𝒢}$ are strongly affected by the thermal effects. Remarkably, when the GR2E ${{ℰ}}_{R,2}$ thoroughly vanishes, the GMI ${{ℐ}}_{R,2}$ exhibits a freezing behavior, and seems to be captured within a wide range of temperature.

We review the basic properties of the quantum relative entropy for finite-dimensional Hilbert spaces. In particular, we focus on several inequalities that are related to the second law of thermodynamics, where the positivity and the monotonicity of the quantum relative entropy play key roles; these properties are directly applicable to derivations of the second law (e.g., the Clausius inequality). Moreover, the positivity is closely related to the quantum fluctuation theorem, while the monotonicity leads to a quantum version of the Hatano-Sasa inequality for nonequilibrium steady states. Based on the monotonicity, we also discuss the data processing inequality for the quantum mutual information, which has a similar mathematical structure to that of the second law. Moreover, we derive a generalized second law with quantum feedback control. In addition, we review a proof of the monotonicity in line with Petz.¹⁰⁰