[en] The ensemble N-representability problem for the k-th order reduced density matrix (k-RDM) as well as the problem of reconstruction of the N-particle system density matrices (N-DM) from a given k-RDM are studied. The spatial parts of the k-RDM expansion in terms of spin tensorial operators Θ_λ are represented using particular values (at specially chosen Ξ = Ξ_o) of the Radon transform D_Nλ D_Nλ(Ξ) of the N-DM spatial parts (or their sums) D_Nλ(χ'|χ double-prime) (here, Ξ is a d-plane in the n-space Re double-prime of χ = (χ', χ double-prime), with n = 6N, d = 3(N - k), χ' double-bond ' (r'₁,...,r_N'), χ double-prime double-prime triple-bond (r₁ double-prime,...,r_N double-prime)). In this way, the problem is reduced to investigation of the properties of the functions D_Nλ(Ξ). For a normalizable N - DM, it is proved that D_Nλ(Ξ) are bounded functions. The properties of D_Nλ(Ξ) implied by the N-DM permutational symmetry, Hermiticity, and positive definiteness are found. A formal procedure of reconstruction of all N-DM corresponding to a given k-RDM is proposed. 38 refs

[en] Grand-canonical like descriptions of many electron atomic and molecular open systems which are characterized by a non-integer number of electrons are presented. Their associated reduced density matrices (RDMs) are obtained by introducing the contracting mapping for this type of distributions. It is shown that there is loss of information when connecting RDMs of different order by partial contractions. The energy convexity property of these systems simplifies the description. Consequently, this formulation opens the possibility to a new look for chemical descriptors such as chemical potential and reactivity among others. Examples are presented to discuss the theoretical aspects of this work

[en] In the present paper we give approximative expressions of the generalized density matrix of Bloch, which can be calculated exactly for the case of free electrons in a uniform magnetic field, while for the case of lattice electrons it can be expressed by the help of the Wannier functions. For the case of high temperatures the generalized density matrix coincides to the Green-function

[en] This paper divides into two main parts. The first one discusses authentication of quantum messages. The protocol proposed in [1] for one qubit message-length case is especially considered. The protocol uses a shared EPR pair as a secret key. In the second part, it is shown how such a protocol can be simulated using the Quantum-Octave package. Quantum-Octave is a set of functions for a Matlab-like numerical environment allowing calculations with general density matrices.

[en] Without attempting to identify ontological interpretation with a mathematical structure, we reduce philosophical speculation to five theses. In the discussion of these, a central role is devoted to the mathematical problem of the evolution of the density matrix. This article relates to the first 3 of these 5 theses

[en] We develop an efficient scheme for controllably generating electromagnetically induced transparency (EIT) with a superconducting qutrit driven by tunable drivings. At an optimal bias point, the first three level states of a charge-phase quantum circuit constitute our qutrit. Allowed by the level transition rule, V- and -type interactions between the qutrit and driving fields can be obtained individually. By the technique of density matrix, we analytically derive and numerically address two cases of EIT for an identical probe field only by tuning the frequency of control driving. Thanks to the tunable interactions within the qutrit having sufficient level anharmonicity, our strategy offers a promising approach to generate EIT in a controllable manner, which could be highly preferable to experimentally investigate EIT with superconducting artificial atoms. (letter)

[en] We consider the state determination problem using mutually unbiased bases (MUBs). For spin-1, spin-3/2 and spin-2 systems, analogous to Pauli operators of spin-1/2 system, which are experimentally implementable and correspond to the optimum measurement in characterizing the density matrix, we describe a procedure to construct an orthonormal set of operators from MUBs. The constructed operators are maximally commuting, can be physically realized, and correspond to physical observables. The method of construction is general enough to allow for extensions to higher-dimensional spin systems and arbitrary density matrices in finite dimensions for which MUBs are known to exist. (paper)

[en] In this paper we consider some statistical properties of the entropy due to the time development of a two-level system. Analytic expression for the density matrix is obtained to investigate the influence of the mean photon number on the atomic inversion, field and atomic Wehrl entropies. The results show that the general features of both entropies are similar

[en] The solution of the equation for the density matrix of the electron moving in a spatially periodic field is found. The observed solution is in line with the mixed state of the system

[en] A stochastic transport description for the single-particle density matrix is briefly discussed. It is shown that the stochastic description contains, in addition to incoherent binary collisions, a coherent damping mechanism due to coupling between mean-field fluctuations and single-particle motion, and an expression for the coherent collision term is derived. In the limit of small fluctuations around equilibrium, the collective and single-particle self-energies due to the coherent mechanism are deduced