English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The probability that a generic real, complex or quaternionic two-qubit stateis separable can be considered to be the sum of three contributions. One isfrom those states that are absolutely separable, that is those (which can notbe entangled by unitary transformations) for which the maximal concurrence overspectral orbits (C_{max}) is zero. The other two contributions are from thestates for which C_{max} in [0,1/2], and for which C_{max} in [1/2,1]. We havepreviously (arXiv:0805.0267) found exact formulas for the absolutely separablecontributions in terms of the Hilbert-Schmidt metric over the quantum states,and here advance hypotheses as to the exact contributions for C_{max} in[1/2,1]. A crucial element in understanding the other two contributions is thenature of the ratio (R) of the C_{max}-parameterized separability function forthe complex states to the square of the comparable function for the realstates--both such functions having clearly displayed jump discontinuities atC_{max}=1/2. For C_{max} in [0,1/2], R appears to be of the form 1+ k C_{max},except near C_{max}=1/2, while for C_{max} in [1/2,1], it seems to be aconstant (thus according to the Dyson-index pattern of random matrix theory).Related phenomena also occur for the minimally-degenerate two-qubit states andthe qubit-qutrit states. Our results have immediate application to thecomputation of separability probabilities in terms of other metrics, such asthe Bures (minimal monotone) metric. The paper begins with continuousembeddings of the separability probability question in terms of four metrics ofinterest, using "generalized Peres-Horodecki conditions".

Ratios of maximal concurrence-parameterized separability functions, and generalized Peres-Horodecki conditions