5 research outputs found
A note on one-way quantum deficit and quantum discord
One-way quantum deficit and quantum discord are two important measures of
quantum correlations. We revisit the relationship between them in two-qubit
systems. We investigate the conditions that both one-way quantum deficit and
quantum discord have the same optimal measurement ensembles, and demonstrate
that one-way quantum deficit can be derived from the quantum discord for a
class of X states. Moreover, we give an explicit relation between one-way
quantum deficit and entanglement of formation. We show that under phase damping
channel both one-way quantum deficit and quantum discord evolve exactly in the
same way for four parameters X states. Some examples are presented in details.Comment: 12 page
Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states
A method for calculating the one-way quantum deficit is developed. It
involves a careful study of post-measured entropy shapes.
We discovered that in some regions of X-state space the post-measured entropy
as a function of measurement angle exhibits a
bimodal behavior inside the open interval , i.e., it has two
interior extrema: one minimum and one maximum. Furthermore, cases are found
when the interior minimum of such a bimodal function
is less than that one at the endpoint or
.
This leads to the formation of a boundary between the phases of one-way
quantum deficit via
{\em finite} jumps of optimal measured angle from the endpoint to the
interior minimum. Phase diagram is built up for a two-parameter family of X
states. The subregions with variable optimal measured angle are around 1 of
the total region, with their relative linear sizes achieving , and the
fidelity between the states of those subregions can be reduced to .
In addition, a correction to the one-way deficit due to the interior minimum
can achieve
. Such conditions are favorable to detect the subregions with variable
optimal measured angle of one-way quantum deficit in an experiment.Comment: 14 pages, 8 figure
Quantum discord of X-states as optimization of one variable function
We solve the quantum discord completely as an optimization of certain one
variable function for arbitrary two qubit X state. Exact solutions of the
quantum discord are obtained for several nontrivial regions of the five
parametric space for the quantum state. Exceptional solutions are determined
via an iterative algorithm.Comment: 17 pages. Revised version with New title, and more references are
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On the quantum correlations in two-qubit XYZ spin chains with Dzyaloshinsky-Moriya and Kaplan-Shekhtman-Entin-Wohlman-Aharony interactions
The anisotropic Heisenberg two-spin-1/2 model in an inhomogeneous magnetic
field with both antisymmetric Dzyaloshinsky-Moriya and symmetric
Kaplan-Shekhtman-Entin-Wohlman-Aharony cross interactions is considered at
thermal equilibrium. Using a group-theoretical approach, we find fifteen spin
Hamiltonians and as many corresponding Gibbs density matrices (quantum states)
whose eigenvalues are expressed only through square radicals. We also found
local unitary transformations that connect nine of this fifteen state
collection, and one of them is the X quantum state. Since such quantum
correlations as quantum entanglement, quantum discord, one-way quantum work
deficit, and others are known for the X state, this allows to get the quantum
correlations for any member from the nine state family. Further, we show that
the remaining six quantum states are separable, that they are also connected by
local unitary transformations, but, however, now the case with known
correlations beyond entanglement is generally not available.Comment: 18 pages, no figure
Temperature-field phase diagrams of one-way quantum work deficit in two-qubit XXZ spin systems
The spin-1/2 XXZ chain in a uniform magnetic field at thermal equilibrium is
considered. For this model, we give a complete classification of all
qualitatively different phase diagrams for the one-way quantum work
(information) deficit. The diagrams can contain regions (phases, fractions)
with both stationary and variable (state-dependent) angles of optimal
measurement. We found cases of phase diagrams in which the sizes of regions
with the variable optimal measurement angle are large and perhaps such regions
can be detected experimentally. We also established a relationship between the
behavior of optimal measurement angles near the boundaries separated different
regions and Landau's theory of phase transitions of the second and first kind.Comment: 23 pages, 12 figures (34 eps files