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We consider the classical correlations that two observers can extract by measurements on a bipartite quantum state, and we discuss how they are related to the quantum mutual information of the state. We show with several examples how…
We investigate the interplay of crystal bases and completions in the sense of Enright on certain nonintegrable representations of quantum groups. We define completions of crystal bases, show that this notion of completion is compatible with…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
We provide a quantum statistical basis for (a)a characterisation of a complete set of thermodynamic variables and (b) the differentiability of the entropy function of these variables
The mathematical notion of incompleteness (eg of rational numbers, Turing-computable functions, and arithmetic proof) does not play a key role in conventional physics. Here, a reformulation of the kinematics of quantum theory is attempted,…
We compare some recent computations of the entanglement of formation in quantum information theory and of the entropy of a subalgebra in quantum ergodic theory. Both notions require optimization over decompositions of quantum states. We…
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This…
Integrability in quantum theory has been defined in more than one ways. Recently, Braak suggested a new definition that a quantum system is integrable if the number of parameters required to specify the eigenstates and the number degrees of…
Quantum mechanics for a four-state-system is derived from classical statistics. Entanglement, interference, the difference between identical fermions or bosons and the unitary time evolution find an interpretation within a classical…
The purpose of this short tutorial paper is to review various criteria that have been used to characterize the quantum character of correlations in optical systems, such as "gemellity", QND correlation, intrication, EPR correlation and Bell…
A 3-setting Bell-type inequality enforced by the indeterminacy relation of complementary local observables is proposed as an experimental test of the 2-qubit entanglement. The proposed inequality has an advantage of being a sufficient and…
Two observables are called complementary if preparing a physical object in an eigenstate of one of them yields a completely random result in a measurement of the other. We investigate small sets of complementary observables that cannot be…
Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the…
We introduce methods of characterizing entanglement, in which entanglement measures are enriched by the matrix representations of operators for observables. These observable operator matrix representations can enrich the partial trace over…
The von Neumann entropy of various quantum dissipative models is calculated in order to discuss the entanglement properties of these systems. First, integrable quantum dissipative models are discussed, i.e., the quantum Brownian motion and…
Entropic uncertainty relations, based on sums of entropies of probability distributions arising from different measurements on a given pure state, can be seen as a generalization of the Heisenberg uncertainty relation that is in many cases…
Incompatibility between conjugate variables and complementary pictures comes in two kinds, exclusive of one another. The first kind is unconditional, and the second conditional on quantum's indivisibility. We employ this distinction to…
We analyze some special properties of a system of two qubits, and in particular of the so-called Bell basis for this system, which have played an important role in recent papers on entanglement of qubits. In particular, we show which of…
In this paper, the concept of L-algebra is revisited and after that, the article is prepared to deal with the notion of the entropy of an L-algebra. If a set has an L-algebraic structure, it is possible to calculate the degree of…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…