We examine the entanglement of cyclic spin 1/2 chains with anisotropic XY Z Heisenberg couplings of arbitrary range at transverse factorizing magnetic fields. At these fields the system exhibits a degenerate symmetry-breaking separable ground state (GS). It is shown, however, that the side limits of the GS pairwise entanglement at these fields are actually non-zero in finite chains, corresponding such fields to a GS spin-parity transition. These limits exhibit universal properties like being independent of the pair separation and interaction range, and are directly related to the magnetization jump. Illustrative exact results are shown for chains with I) full range and II) nearest neighbor couplings. Global entanglement properties at such points are also discussed.Comment: 5 pages, 4 figure

We examine the quantum discord between two spins in the exact ground state of finite spin-1/2 arrays with anisotropic XY couplings in a transverse field B. It is shown that in the vicinity of the factorizing field B s , the discord approaches a common finite non-negligible limit which is independent of the pair separation and the coupling range. An analytic expression of this limit is provided. The discord of a mixture of aligned pairs in two different directions, crucial for the previous results, is analyzed in detail, including the evaluation of coherence effects, relevant in small samples and responsible for a parity splitting at B s . Exact results for finite chains with first-neighbor and full-range couplings and their interpretation in terms of such mixtures are provided.

No abstract

We determine the conditions for the existence of a pair of degenerate parity breaking separable eigenstates in general arrays of arbitrary spins connected through XY Z couplings of arbitrary range and placed in a transverse field, not necessarily uniform. Sufficient conditions under which they are ground states are also provided. It is then shown that in finite chains, the associated definite parity states, which represent the actual ground state in the immediate vicinity of separability, can exhibit entanglement between any two spins regardless of the coupling range or separation, with the reduced state of any two subsystems equivalent to that of pair of qubits in an entangled mixed state. The corresponding concurrences and negativities are exactly determined. The same properties persist in the mixture of both definite parity states. These effects become specially relevant in systems close to the XXZ limit. The possibility of field induced alternating separable solutions with controllable entanglement side limits is also discussed. Illustrative numerical results for the negativity between the first and the j th spin in an open spin s chain for different values of s and j are as well provided.

We examine the inference of quantum density operators from incomplete information by means of the maximization of general non-additive entropic forms. Extended thermodynamic relations are given. When applied to a bipartite spin 1 2 system, the formalism allows to avoid fake entanglement for data based on the Bell-CHSH observable, and, in general, on any set of Bell constraints. Particular results obtained with the Tsallis entropy and with an introduced exponential entropic form are also discussed. 03.65.Ud The relation between two fundamental concepts, entropy and quantum entanglement, has recently aroused great interest in quantum information theory [1][2][3][4][5][6][7][8]. A system composed of two subsystems A and B is said to be unentangled or separable, if and only if the density operator ρ can be written as a convex combination of uncorrelated densities, i.e., ρ = j q j ρ A j ⊗ ρ B j , with q j ≥ 0. In this case the system admits a local description in terms of hidden variables. Otherwise, it is said to be entangled or inseparable. The system becomes then suitable, in principle, for applications like quantum cryptography [9] and teleportation [10].When the available information about the system is incomplete, consisting for instance of the expectation values of a reduced set of observables, one faces the problem of first determining if entanglement is actually implied by the data, and then selecting the most probable or representative density operator compatible with these data. An ideal inference scheme in this scenario should then a) avoid fake entanglement [1], i.e., should not yield an entangled density if there is a separable density that reproduces the data, b) be least biased, in the sense that some measure of lack of information is maximized, and c) be simple enough to be readily applied. As shown in [1], the standard approach based on the direct maximization of the von Neumann entropy S = −Tr ρ ln ρ, does not comply with a) already for two spin 1 2 systems. The essential reason is that this entropy is not a good entanglement indicator [5,7,8], even in those cases where entanglement is fully determined by the eigenvalues of ρ. A solution was also provided in [1]: one should first determine the set of densities that minimize entanglement, and then maximize entropy within this set. Although certainly rigorous, this procedure is not easy to implement in general, and departs conceptually from a more basic approach based on the maximization of a single information measure.As is well known, the von Neumann entropy is based on the Shannon information measure, which is the unique one satisfying the four Khinchin axioms [11]. However, if the fourth axiom, which is concerned with additivity, is lifted, other information measures become feasible. The most famous recent example is the Tsallis entropy [12], which has been applied to a wide range of phenomena characterized by non-extensivity [13], including recently the problem of quantum entanglement [3,4].The aim of this work is first to discuss more gener...