Let $S(\rho)$ be the von Neumann entropy of a density matrix $\rho$. Weak monotonicity asserts that $S(\rho_{AB}) - S(\rho_A) + S(\rho_{BC}) S(\rho_C)\geq 0$ for any tripartite $\rho_{ABC}$, fact is equivalent to strong subadditivity entropy. We prove an operator inequality, which, upon taking expectation value with respect state reduces weak inequality. Generalizations this inequality one invo...

We study L-systems whose main operators are extensions of one-dimensional half-line Schr\"odinger with deficiency indices $(1, 1)$, the L-systems. Introducing new concepts an c-entropy and dissipation coefficient for L-system we discuss following dual problems: describe (1) a given minimal coefficient, (2) maximal c-entropy. Also, analyze in detail problems sectorial extremal operators.

Abstract— The direct part of Stein’s lemma in quantum hypothesis testing is revisited based on a key operator inequality between a density operator and its pinching. The operator inequality is used to show a simple proof of the direct part of Stein’s lemma without using Hiai-Petz’s theorem, along with an operator monotone function, and in addition it is also used to show a new proof of Hiai-Pet...

1 Information characteristics of a quantum channel During the last couple of years an impressive progress has been achieved in the theory of transmission of classical information through quantum communication channels (see [8] for a comprehensive survey). The problem of sending quantum information is much less understood; we refer in particular to the papers [10], [2], [1], initiating the study...

In this paper, we have investigated the dependence of the spectral entanglement and indistinguishability of photon pairs produced by the spontaneous parametric down-conversion (SPDC) procedure on the bandwidth of spectral filters used in the detection setup. The SPDC is a three-wave mixing process which occurs in a nonlinear crystal and generates entangled photon pairs and utilizes as one of th...

For two gaussian states with given correlation matrices, in order that relative entropy between them is practically calculable, I in this paper describe the ways of transforming the correlation matrix to matrix in the exponential density operator. Gaussian relative entropy of entanglement is proposed as the minimal relative entropy of the gaussian state with respect to separable gaussian state ...

We evoke situations where large fluctuations in the entropy are induced, our main example being a spacetime containing a potential black hole whose formation depends on the outcome of a quantum mechanical event. We argue that the teleological character of the event horizon implies that the consequent entropy fluctuations must be taken seriously in any interpretation of the quantal formalism. We...

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving co...