Phase diagram for the one-way quantum deficit of two-qubit X states

@article{Yurischev2019PhaseDF,
  title={Phase diagram for the one-way quantum deficit of two-qubit X states},
  author={Mikhail A. Yurischev},
  journal={Quantum Information Processing},
  year={2019},
  volume={18},
  pages={1-20}
}
  • M. Yurischev
  • Published 10 April 2018
  • Physics
  • Quantum Information Processing
The one-way quantum deficit, a measure of quantum correlation, can exhibit for X quantum states the regions (subdomains) with the phases $$\varDelta _0$$Δ0 and $$\varDelta _{\pi /2}$$Δπ/2 which are characterized by constant (i.e., universal) optimal measurement angles, correspondingly, zero and $$\pi /2$$π/2 with respect to the z-axis and a third phase $$\varDelta _\vartheta $$Δϑ with the variable (state-dependent) optimal measurement angle $$\vartheta $$ϑ. We build the complete phase diagram… 
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References

SHOWING 1-10 OF 38 REFERENCES
Bimodal behavior of post-measured entropy and one-way quantum deficit for two-qubit X states
TLDR
It is discovered that in some regions of X-state space the post-measured entropy exhibits a bimodal behavior inside the open interval, which leads to the formation of a boundary between the phases of one-way quantum deficit via finite jumps of optimal measured angle from the endpoint to the interior minimum.
Extremal properties of conditional entropy and quantum discord for XXZ, symmetric quantum states
TLDR
It is remarkable that the maxima exist in surprisingly wide regions, and the boundaries for such regions are defined by the same bifurcation conditions as for those with a minimum.
On the quantum discord of general X states
TLDR
It is found that the transitions between Q_{\theta }$$Qθ subdomains occur suddenly, but continuously and smoothly, i.e., nonanalyticity is hidden and can be observed in higher order derivatives of discord function.
Quantum discord for two-qubit X states: Analytical formula with very small worst-case error
Quantum discord is a measure of quantum correlation beyond entanglement. Computing quantum discord for simple quantum states is a basic problem. An analytical formula of quantum discord for two-qubit
Quantum discord for general X and CS states: A piecewise-analytic-numerical formula
Quantum discord is a function of density-matrix elements (and through them, e.~g., of temperature, applied fields, time, and so forth). The domain of such a function in the case of two-qubit system
Analytical solutions and criteria for the quantum discord of two-qubit X-states
TLDR
This paper presents analytical solutions for computing quantum discord of the most general class of $$X$$X-states and the criteria for each analytical solution to be valid and applies the formalism to study both arbitrary $$X $$X- states and$$X$$ X-states with certain symmetries.
Calculation of quantum discord for qubit-qudit or N qubits
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. It has been discussed so far for small
A note on one-way quantum deficit and quantum discord
TLDR
The conditions that both one-way quantum deficit and quantum discord have the same optimal measurement ensembles are investigated, and it is demonstrated that one- way quantum deficit can be derived from the quantum discord for a class of X states.
NMR dynamics of quantum discord for spin-carrying gas molecules in a closed nanopore
A local orthogonal transformation that transforms any centrosymmetric density matrix of a two-qubit system to the X form has been found. A piecewise-analytic-numerical formula Q = min{Qπ/2, Qθ, Q0},
Quantum discord for qubit–qudit systems
We present two formulae to calculate quantum discord, a kind of quantum correlation, between a qubit and a second party of arbitrary dimension d. The first formula is the original entropic definition
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