[en] We propose the reference section method to obtain a geometric phase for the mixed states in nonunitary evolution. The reference connection on density operator space is defined. That the parallel transport method and reference section method are essentially two aspects of in phase concept is pointed out. (paper)

[en] Mixing between the 2³S₁ and 1³D₁ D_s is studied within the ³P₀ model. If mixing between these two 1^- states exists, D_s1^* (2700)± and D_sJ^* (2860)± could be interpreted as the two orthogonal mixed states with mixing angle θ≈-80° in the case of a special β for each meson. However, in the case of a universal β for all mesons, D_s1^* (2700)± could be interpreted as the mixed state of 2³S₁ and 1³D₁ with mixing angle 12° < θ < 21° but D_s^*J (2860)^± seems difficult to interpret as the orthogonal partner of D_s1^* (2700)^±. (authors)

[en] We consider the problem of discriminating general quantum operations. Using the definition of mapping operator to vector, and by some calculating skills, we derive an explicit formulation as a new bound on the minimum-error probability for ambiguous discrimination between arbitrary m quantum operations. This formulation consists only of Kraus-operators, the dimension, and the priori probabilities of the discriminated quantum operations, and is independent of input states. To some extent, we further generalize the bounds on the minimum-error probability for discriminating mixed states to quantum operations. (general)

[en] In this paper we investigate the efficiency of quantum cloning of N identical mixed qubits. We employ a recently introduced measure of distinguishability of quantum states called the quantum Chernoff bound. We evaluate the quantum Chernoff bound between the output clones generated by the cloning machine and the initial mixed qubit state. Our analysis is illustrated by performing numerical calculation of the quantum Chernoff bound for different scenarios that involves the number of initial qubits N and the number of output imperfect copies M. (paper)

[en] Measurement-induced nonlocality (MIN), a quantum correlation measure for bipartite systems, is an indicator of maximal global effects due to locally invariant von Neumann projective measurements. It is originally defined as the maximal square of the Hilbert–Schmidt norm of the difference between pre- and post-measurement states. In this article, we propose a new form of MIN based on affinity. This quantity satisfies all the criteria of a bona fide measure of quantum correlation measures. This quantity is evaluated for both arbitrary pure and 2 × n dimensional (qubit–qudit) mixed states. The operational meaning of the proposed quantity is interpreted in terms of the interferometric power of the quantum state. We apply these results on two-qubit mixed states, such as the Werner, isotropic and Bell diagonal states. (paper)

[en] Highlights: • Long distance mixed state transfer. • Unitary transformation of extended receiver as a tool for quantum state restoring. • Perfect transfer of 0-order coherence matrix. • Information encoded into higher-order coherence matrices. • Scale factors of state restoring. In this work, we study optimal transfer of quantum states via spin chains. We develop the protocol for structural restoring of multi-quantum coherence matrices of multi-qubit quantum states transferred from sender to receiver along a spin-1/2 chain. We also develop a protocol for constructing such 0-order coherence matrix that can be perfectly transferred in this process. The restoring protocol is based on the specially constructed unitary transformation applied to the state of the extended receiver. This transformation for a given length of the chain and Hamiltonian is universally optimal in the sense that ones constructed it can be applied to optimally restore any higher-order coherence matrices.

[en] We give a criterion of classicality for mixed states in terms of expectation values of a quantum observable. Using group representation theory, we identify all cases when the criterion can be computed exactly in terms of the spectrum of a single operator. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Coherent states: mathematical and physical aspects’. (paper)

[en] In this work, we consider a different model of density operator and a heuristic procedure that interpolates a photonic system from pure to mixed states. It is interpreted as if, during the time evolution of the system, the variables of a (hidden) system reservoir being traced. The aim is to study the time evolution of statistical properties while the system loses its initial purity. For this purpose, the system impurity, the evolution of Mandel parameter and entropy were calculated. A comparison between Shannon and von Neumann entropies in the present scenario is done, which could be of interest in quantum information. Another comparison, between the present approach with the traditional treatment concerning decoherence of a system state, was also considered. Graphical abstract:

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[en] An interaction free evolving state of a closed bipartite system composed of two interacting subsystems is a generally mixed state evolving as if the interaction were a c-number. In this paper we find the characteristic equation of states possessing similar properties for a bipartite systems governed by a linear dynamical equation whose generator is sum of a free term and an interaction term. In particular in the case of a small system coupled to its environment, we deduce the characteristic equation of decoherence free states namely mixed states evolving as if the interaction term were effectively inactive. Several examples illustrate the applicability of our theory in different physical contexts. (paper)

[en] We consider the characterization of quantum superposition states beyond the pattern ‘dead and alive’. We propose a measure that is applicable to superpositions of multiple macroscopically distinct states, superpositions with different weights as well as mixed states. The measure is based on the mutual information to characterize the distinguishability between the multiple branches of the superposition. This allows us to overcome limitations of previous proposals, and to bridge the gap between general measures for macroscopic quantumness and measures for Schrödinger-cat type superpositions. We discuss a number of relevant examples, provide an alternative definition using basis-dependent quantum discord and reveal connections to other proposals in the literature. Finally, we also show the connection between the size of quantum states as quantified by our measure and their vulnerability to noise. (paper)