On numerical solving the spherical separability problem

2015 ◽  
Vol 66 (1) ◽  
pp. 21-34 ◽  
Author(s):  
M. Gaudioso ◽  
T. V. Gruzdeva ◽  
A. S. Strekalovsky
Keyword(s):  
Separability Problem

scholarly journals On the separability problem for circulant S-rings

2016 ◽  
Vol 28 (1) ◽  
pp. 21-35
Author(s):  
S. Evdokimov ◽  
I. Ponomarenko
Keyword(s):  
Separability Problem

SEPARABILITY: A NEW APPROACH FROM THE CONIC STRUCTURE OF POSITIVE OPERATORS

2011 ◽  
Vol 09 (supp01) ◽  
pp. 415-422
Author(s):  
D. SALGADO ◽  
J. L. SÁNCHEZ-GÓMEZ ◽  
M. FERRERO
Keyword(s):  
Pure State ◽  
Convex Combination ◽  
Quantum States ◽  
Necessary Condition ◽  
New Approach ◽  
Product Matrix ◽  
Separability Problem ◽  
Multipartite System ◽  
Arbitrary Dimensions ◽  
Bipartite Case

We exploit the cone structure of unnormalized quantum states to reformulate the separability problem. Firstly a convex combination of every quantum state ρ in terms of a state Cρ with the same rank and another one Eρ with lower rank is perfomed, with weights 1 − λρ and λρ, respectively. Secondly a scalar [Formula: see text] is computed. Then ρ is separable if, and only if, [Formula: see text]. The computation of [Formula: see text] has been undergone under the simplest choice for Cρ as a product matrix and Eρ being a pure state, valid for any bipartite and multipartite system in arbitrary dimensions. A necessary condition is also formulated when Eρ is not pure in the bipartite case.

Separability criteria based on the Bloch representation of density matrices

2007 ◽  
Vol 7 (7) ◽  
pp. 624-638
Author(s):  
J. de Vicente
Keyword(s):  
Sufficient Conditions ◽  
Quantum Systems ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Pure Product ◽  
Separability Problem ◽  
Arbitrary Dimensions ◽  
Necessary And Sufficient ◽  
Bloch Representation

We study the separability of bipartite quantum systems in arbitrary dimensions using the Bloch representation of their density matrix. This approach enables us to find an alternative characterization of the separability problem, from which we derive a necessary condition and sufficient conditions for separability. For a certain class of states the necessary condition and a sufficient condition turn out to be equivalent, therefore yielding a necessary and sufficient condition. The proofs of the sufficient conditions are constructive, thus providing decompositions in pure product states for the states that satisfy them. We provide examples that show the ability of these conditions to detect entanglement. In particular, the necessary condition is proved to be strong enough to detect bound entangled states.

Voting on referenda: the separability problem and possible solutions

1997 ◽  
Vol 16 (3) ◽  
pp. 359-377 ◽  
Author(s):  
Steven J Brams ◽  
D Marc Kilgour ◽  
William S Zwicker
Keyword(s):  
Separability Problem

scholarly journals On the Tensor Convolution and the Quantum Separability Problem

2010 ◽  
Vol 17 (04) ◽  
pp. 331-346
Author(s):  
Gabriel Pietrzkowski
Keyword(s):  
Abelian Group ◽  
Tensor Product ◽  
Hermitian Operator ◽  
Product Formula ◽  
Locally Compact Abelian Group ◽  
Locally Compact ◽  
Equivalent Problem ◽  
Finite Dimensional ◽  
Separability Problem ◽  
Convolution Formula

We consider the problem of separability: decide whether a Hermitian operator on a finite dimensional Hilbert tensor product [Formula: see text] is separable or entangled. We show that the tensor convolution [Formula: see text] defined for mappings [Formula: see text] on an almost arbitrary locally compact abelian group G , gives rise to formulation of an equivalent problem to the separability one.

scholarly journals Simulating arbitrary pair-interactions by a given Hamiltonian: graph-theoretical bounds on the time-complexity

2002 ◽  
Vol 2 (2) ◽  
pp. 117-132
Author(s):  
P. Wocjan ◽  
D. Janzing ◽  
T. Beth
Keyword(s):  
Quantum Computer ◽  
Pair Interaction ◽  
Hamiltonian Graph ◽  
Lower And Upper Bounds ◽  
Convex Optimization Problem ◽  
Minimal Time ◽  
Natural Time ◽  
Separability Problem ◽  
Time Overhead ◽  
Pair Interactions

We consider a quantum computer consisting of n spins with an arbitrary but fixed pair-interaction Hamiltonian and describe how to simulate other pair-interactions by interspersing the natural time evolution with fast local transformations. Calculating the minimal time overhead of such a simulation leads to a convex optimization problem. Lower and upper bounds on the minimal time overhead are derived in terms of chromatic indices of interaction graphs and spectral majorization criteria. These results classify Hamiltonians with respect to their computational power. For a specific Hamiltonian, namely \sigma_z\otimes\sigma_z-interactions between all spins, the optimization is mathematically equivalent to a separability problem of n-qubit density matrices. We compare the complexity defined by such a quantum computer with the usual gate complexity.

scholarly journals Truncated moment sequences and a solution to the channel separability problem

2020 ◽  
Vol 102 (5) ◽  
Author(s):  
N. Milazzo ◽  
D. Braun ◽  
O. Giraud
Keyword(s):  
Separability Problem
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