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Quantum Information Processing
Erschienen in: Quantum Information Processing 10/2017

01.10.2017

Extremal properties of conditional entropy and quantum discord for XXZ, symmetric quantum states

verfasst von: M. A. Yurischev

Erschienen in: Quantum Information Processing | Ausgabe 10/2017

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Abstract

For the XXZ subclass of symmetric two-qubit X states, we study the behavior of quantum conditional entropy \(S_{cond}\) as a function of measurement angle \(\theta \in [0,\pi /2]\). Numerical calculations show that the function \(S_{cond}(\theta )\) for X states can have at most one local extremum in the open interval from zero to \(\pi /2\) (unimodality property). If the extremum is a minimum, the quantum discord displays region with variable (state-dependent) optimal measurement angle \(\theta ^*\). Such \(\theta \)-regions (phases, fractions) are very tiny in the space of X-state parameters. We also discover the cases when the conditional entropy has a local maximum inside the interval \((0,\pi /2)\). 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.
Vorheriger Artikel Quantum discord protection of a two-qutrit V-type atomic system from decoherence by partially collapsing measurements
Nächster Artikel Relationship between the field local quadrature and the quantum discord of a photon-added correlated channel under the influence of scattering and phase fluctuation noise

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Fußnoten
1
Unfortunately, the authors of Ref. [16] have made a few mistakes. In particular, their Eq. (23) is incorrect and their conclusion about the existence of the region with mysterious measurement \(\sigma _?\) is wrong.
 
2
At present, the maximum clock frequency of Intel and AMD microprocessors is around 8.7–8.8 GHz.
 
3
In Eq. (19) of Ref. [20] the common multiplier \(\frac{1}{4}\) in the expression for \({\varLambda }_{1,2}\) should be replaced by \(\frac{1}{2}\) (as in Refs. [18, 19]).
 
4
Results of papers [21, 34] are restricted to \(p_3+p_4\ge 0\) and \(p_3-p_4\ge 0\) (one needs every time to reduce the initial X density matrix to a form with real nonnegative off-diagonal entries) whereas our expressions (A1) and (B1) are automatically valid in the whole seven-parameter domain of X states thanks to the quantity w [18‐20].
 
5
Most recently [37] a counterexample has been found which shows that in some regions of parameter space the function \(f_2(\cos \theta )\) can exhibit bimodal behavior. At the same time the function \(f_1(\cos \theta )\) in those regions stays unimodal.
 
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Metadaten
Titel
Extremal properties of conditional entropy and quantum discord for XXZ, symmetric quantum states
verfasst von
M. A. Yurischev
Publikationsdatum
01.10.2017
Verlag
Springer US
Erschienen in
Quantum Information Processing / Ausgabe 10/2017
Print ISSN: 1570-0755
Elektronische ISSN: 1573-1332
DOI
https://doi.org/10.1007/s11128-017-1701-0

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