683 research outputs found
Quantum discord and information deficit in spin chains
We examine the behavior of quantum correlations of spin pairs in a finite
anisotropic spin chain immersed in a transverse magnetic field, through
the analysis of the quantum discord and the conventional and quadratic one
way-information deficits. We first provide a brief review of these measures,
showing that the last ones can be obtained as particular cases of a generalized
information deficit based on general entropic forms. All these measures
coincide with an entanglement entropy in the case of pure states, but can be
non-zero in separable mixed states, vanishing just for classically correlated
states. It is then shown that their behavior in the exact ground state of the
chain exhibits similar features, deviating significantly from that of the pair
entanglement below the critical field. In contrast with entanglement, they
reach full range in this region, becoming independent of the pair separation
and coupling range in the immediate vicinity of the factorizing field. It is
also shown, however, that significant differences between the quantum discord
and the information deficits arise in the local minimizing measurement that
defines them. Both analytical and numerical results are provided.Comment: 14 pages, 5 figure
Measurements, quantum discord and parity in spin 1 systems
We consider the evaluation of the quantum discord and other related measures
of quantum correlations in a system formed by a spin 1 and a complementary spin
system. A characterization of general projective measurements in such system in
terms of spin averages is thereby introduced, which allows to easily visualize
their deviation from standard spin measurements. It is shown that the
measurement optimizing these measures corresponds in general to a non-spin
measurement. The important case of states that commute with the total
spin parity is discussed in detail, and the general stationary measurements for
such states (parity preserving measurements) are identified. Numerical and
analytical results for the quantum discord, the geometric discord and the one
way information deficit in the relevant case of a mixture of two aligned spin 1
states are also presented.Comment: 6 pages, 2 figures, References adde
Quantum discord in finite XY chains
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.Comment: 9 pages, 6 figure
Generalized mean field description of entanglement in dimerized spin systems
We discuss a generalized self-consistent mean field (MF) treatment, based on
the selection of an arbitrary subset of operators for representing the system
density matrix, and its application to the problem of entanglement evaluation
in composite quantum systems. As a specific example, we examine in detail a
pair MF approach to the ground state (GS) of dimerized spin 1/2 systems with
anisotropic ferromagnetic-type XY and XYZ couplings in a transverse field,
including chains and arrays with first neighbor and also longer range
couplings. The approach is fully analytic and able to capture the main features
of the GS of these systems, in contrast with the conventional single spin MF.
Its phase diagram differs significantly from that of the latter, exhibiting
(Sz) parity breaking just in a finite field window if the coupling between
pairs is sufficiently weak, together with a fully dimerized phase below this
window and a partially aligned phase above it. It is then shown that through
symmetry restoration, the approach is able to correctly predict not only the
concurrence of a pair, but also its entanglement with the rest of the chain,
which shows a pronounced peak in the parity breaking window. Perturbative
corrections allow to reproduce more subtle observables like the entanglement
between weakly coupled spins and the low lying energy spectrum. All predictions
are tested against exact results for finite systems.Comment: 13 pages, 9 figures. Final versio
Factorization and entanglement in general XYZ spin arrays in non-uniform transverse fields
We determine the conditions for the existence of a pair of degenerate parity
breaking separable eigenstates in general arrays of arbitrary spins connected
through 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
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
spin in an open spin chain for different values of and are as well
provided.Comment: 6 pages, figures adde
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