[en] Many quantum systems of interest are initially correlated with their environments and the reduced dynamics of open systems are an interesting while challenging topic. Affine maps, as an extension of completely positive maps, are a useful tool to describe the reduced dynamics of open systems with initial correlations. However, it is unclear what kind of initial state shares an affine map. In this study, we give a sufficient condition of initial states, in which the reduced dynamics can always be described by an affine map. Our result shows that if the initial states of the combined system constitute a convex set, and if the correspondence between the initial states of the open system and those of the combined system, defined by taking the partial trace, is a bijection, then the reduced dynamics of the open system can be described by an affine map. (paper)

[en] Small drops bouncing across a vibrating liquid bath display many features reminiscent of quantum systems

[en] We study the excitation transfer across a fully connected quantum network whose sites energies can be artificially designed. Starting from a simplified model of a broadly-studied physical system, we systematically optimize its local energies to achieve high excitation transfer for various environmental conditions, using an adaptive Gradient Descent technique and Automatic Differentiation. We show that almost perfect transfer can be achieved with and without local dephasing, provided that the dephasing rates are not too large. We investigate our solutions in terms of resilience against variations in either the network connection strengths, or size, as well as coherence losses. We highlight the different features of a dephasing-free and dephasing-driven transfer. Our work gives further insight into the interplay between coherence and dephasing effects in excitation-transfer phenomena across fully connected quantum networks. In turn, this will help designing optimal transfer in artificial open networks through the simple manipulation of local energies.

[en] The monogamy relations satisfied by quantum correlation measures play important roles in quantum information processing. Generally they are given in summation form. In this note, we study monogamy relations in product form. We present product-form monogamy relations for Bell nonlocality for three-qubit and multi-qubit quantum systems. We then extend our studies to other quantum correlations such as concurrence. (paper)

[en] We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems, even if measurements are made in an ideal way that emulates classical ideal measurements as closely as possible. This is a genuine quantum effect that survives on a macroscopic scale. We also show that the state realized during measurements of temporal equilibrium fluctuations is a ‘squeezed equilibrium state’, which is macroscopically identical to the pre-measurement equilibrium state but is squeezed by the measurement. It is a time-evolving state, in which macrovariables fluctuate and relax. We also explain some of subtle but important points, careless treatments of which often lead to unphysical results, of the linear response theory. (special issue on statphys 26)

[en] In quantum information the fundamental information-containing system is the qubit. A measurement of a single qubit can at most yield one classical bit. However, a dichotomous measurement of an unknown qubit will yield much less information about the qubit state. We use Bayesian inference to compute how much information one progressively gets by making sucessive, individual measurements on an ensemble of identically prepared qubits. Perhaps surprisingly, even if the measurements are arranged so that each measurement yields one classical bit, that is, the two possible measurement outcomes are a priori equiprobable, it takes almost a handful of measurements before one has gained one bit of information about the gradually concentrated qubit probability density. We also show that by following a strategy that reaps the maximum information per measurement, we are led to a mutually unbiased basis as our measurement bases. This is a pleasing, although not entirely surprising, result. (paper)

[en] This article points out that observables and instruments can be combined in many ways that have natural and physical interpretations. We shall mainly concentrate on the mathematical properties of these combinations. After an introduction in section 1, section 2 reviews the basic definitions and observables are considered in section 3. We study parts of observables, post-processing, generalized convex combinations, sequential products and tensor products. These combinations are extended to instruments in section 4. We consider properties of observables measured by combinations of instruments. We introduce four special types of instruments, namely Kraus, Lüders, trivial and semitrivial instruments. We study when these types are closed under various combinations. In this work, we only consider finite-dimensional quantum systems. A few of the results presented here have appeared in the author’s previous articles Gudder (2020 arXiv:2005.08117 [quant-ph], arXiv:2005.13642 [quant-ph], arXiv:2009.07371 [quant-ph]). (paper)

[en] We propose an information-theoretic quantifier for the advantage gained from cooperation that captures the degree of dependency between subsystems of a global system. The quantifier is distinct from measures of multipartite correlations despite sharing many properties with them. It is directly computable for classical as well as quantum systems and reduces to comparing the respective conditional mutual information between any two subsystems. Exemplarily we show the benefits of using the new quantifier for symmetric quantum secret sharing. We also prove an inequality characterizing the lack of monotonicity of conditional mutual information under local operations and provide intuitive understanding for it. This underlines the distinction between the multipartite dependence measure introduced here and multipartite correlations. (paper)

[en] We introduce a modified weak value that is related to the mean value of input meter variable. With the help of the modified weak value, the validity conditions for various modified versions of weak value formalism are investigated, in terms of the dependence of the pointer shift on the mean value of the input meter. The weak value formalism, often used to represent the pointer shift, with the modified weak value is of great use in simplifying calculations and giving guidance of practical experiments whenever the mean value of the input meter variable is nonzero. The simulation in a qubit system is presented and coincident well with our theoretical result. (paper)

[en] In this paper an extension of formalism of partner groups is proposed. The partner groups as an algebraic tool for description of laboratory and intrinsic variables are shortly introduced. A natural generalisation of partner groups is recognized as the Quantum Motion Algebra. This algebra is based on a group of motions G of a given quantum system. An example of the limiting case of of the state space L ²(G,dμ(g)) is also considered. (paper)