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- W2898014783 abstract "Milz and Strunz ({it J. Phys. A}: {bf{48}} [2015] 035306) recently studied the probabilities that two-qubit and qubit-qutrit states, randomly generated with respect to Hilbert-Schmidt (Euclidean/flat) measure, are separable. They concluded that in both cases, the separability probabilities (apparently exactly $frac{8}{33}$ in the two-qubit scenario) hold {it constant} over the Bloch radii ($r$) of the single-qubit subsystems, jumping to 1 at the pure state boundaries ($r=1$). Here, firstly, we present evidence that in the qubit-qutrit case, the separability probability is uniformly distributed, as well, over the {it generalized} Bloch radius ($R$) of the qutrit subsystem. While the qubit (standard) Bloch vector is positioned in three-dimensional space, the qutrit generalized Bloch vector lives in eight-dimensional space. The radii variables $r$ and $R$ themselves are the lengths/norms (being square roots of {it quadratic} Casimir invariants) of these (coherence) vectors. Additionally, we find that not only are the qubit-qutrit separability probabilities invariant over the quadratic Casimir invariant of the qutrit subsystem, but apparently also over the {it cubic} one--and similarly the case, more generally, with the use of random induced measure. We also investigate two-qutrit ($3 times 3$) and qubit-{it qudit} ($2 times 4$) systems--with seemingly analogous {it positive-partial-transpose}-probability invariances holding over what have been termed by Altafini, the {it partial} Casimir invariants of these systems." @default.
- W2898014783 created "2018-10-26" @default.
- W2898014783 creator A5051990622 @default.
- W2898014783 date "2015-12-22" @default.
- W2898014783 modified "2023-09-27" @default.
- W2898014783 title "Invariance of Bipartite Separability and PPT-Probabilities over Subsystem Casimir Invariants" @default.
- W2898014783 hasPublicationYear "2015" @default.
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