Erratum: Unknown quantum states: The quantum de Finetti representation [J. Math. Phys. 44, 4537 (2002)]

2008 ◽  
Vol 49 (1) ◽  
pp. 019902 ◽  
Author(s):  
Carlton M. Caves ◽  
Christopher A. Fuchs ◽  
Rüdiger Schack
Keyword(s):  
Quantum States ◽  
De Finetti Representation ◽  
De Finetti ◽  
Math Phys

scholarly journals Unknown quantum states: The quantum de Finetti representation

2002 ◽  
Vol 43 (9) ◽  
pp. 4537-4559 ◽  
Author(s):  
Carlton M. Caves ◽  
Christopher A. Fuchs ◽  
Rüdiger Schack
Keyword(s):  
Quantum States ◽  
De Finetti Representation ◽  
De Finetti

A note on the degree conjecture for separability of multipartite quantum states

2021 ◽  
pp. 2050048
Author(s):  
Zhen Wang ◽  
Ming-Jing Zhao ◽  
Zhi-Xi Wang
Keyword(s):  
Quantum States ◽  
Point Graph ◽  
Mixed States ◽  
Degree Condition ◽  
Graph Laplacians ◽  
Nearest Point ◽  
Necessary And Sufficient ◽  
Ppt Criterion ◽  
Math Phys ◽  
Degree Criterion

The degree conjecture for bipartite quantum states which are normalized graph Laplacians was first put forward by Braunstein et al. [Phys. Rev. A 73 (2006) 012320]. The degree criterion, which is equivalent to PPT criterion, is simpler and more efficient to detect the separability of quantum states associated with graphs. Hassan et al. settled the degree conjecture for the separability of multipartite quantum states in [J. Math. Phys. 49 (2008) 0121105]. It is proved that the conjecture is true for pure multipartite quantum states. However, the degree condition is only necessary for separability of a class of quantum mixed states. It does not apply to all mixed states. In this paper, we show that the degree conjecture holds for the mixed quantum states of nearest point graph. As a byproduct, the degree criterion is necessary and sufficient for multipartite separability of [Formula: see text]-qubit quantum states associated with graphs.

A COMPARISON BETWEEN WEHRL–LIEB AND VON NEUMANN ENTROPIES FOR TIME-EVOLVING SPIN-1/2 MIXED STATES

1994 ◽  
Vol 08 (16) ◽  
pp. 995-1006 ◽  
Author(s):  
S. S. MIZRAHI ◽  
V. V. DODONOV ◽  
D. OTERO
Keyword(s):  
Harmonic Oscillator ◽  
Coherent States ◽  
Quantum States ◽  
Alternative Formulation ◽  
Spin States ◽  
Continuous Representation ◽  
Commun Math Phys ◽  
Mixed States ◽  
Von Neumann ◽  
Math Phys

Years ago, A. Wehrl (Rev. Mod. Phys.50, 221 (1978)) introduced the concept of classicallike entropy of quantum states when a two-label continuous representation is used; for instance, the harmonic oscillator coherent states. Subsequently, E. H. Lieb (Commun. Math. Phys.62, 35 (1978)) extended that concept of entropy to the Bloch coherent spin states. Here, we consider spin-1/2 systems and calculate both the Wehrl–Lieb and von Neumann entropies, and then we compare the results and discuss the Wehrl–Lieb entropy as an alternative formulation to von Neumann's. As illustration, three examples are worked out: (i) the decoherence of a quantum state in a measurement process, (ii) the conservation of coherence, and (iii) the recoherence phenomena that appear in the solutions of a specific master equation that originates from a nonlinear Schrödinger equation.

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