107 research outputs found
Entanglement criterion via general symmetric informationally complete measurements
We study the quantum separability problem by using general symmetric
informationally complete measurements and present a separability criterion for
arbitrary dimensional bipartite systems. We show by detailed examples that our
criterion is more powerful than the existing ones in entanglement detection.Comment: 8 pages, 5 figure
On the structure of the body of states with positive partial transpose
We show that the convex set of separable mixed states of the 2 x 2 system is
a body of constant height. This fact is used to prove that the probability to
find a random state to be separable equals 2 times the probability to find a
random boundary state to be separable, provided the random states are generated
uniformly with respect to the Hilbert-Schmidt (Euclidean) distance. An
analogous property holds for the set of positive-partial-transpose states for
an arbitrary bipartite system.Comment: 10 pages, 1 figure; ver. 2 - minor changes, new proof of lemma
Convex set of quantum states with positive partial transpose analysed by hit and run algorithm
The convex set of quantum states of a composite system with
positive partial transpose is analysed. A version of the hit and run algorithm
is used to generate a sequence of random points covering this set uniformly and
an estimation for the convergence speed of the algorithm is derived. For this algorithm works faster than sampling over the entire set of states and
verifying whether the partial transpose is positive. The level density of the
PPT states is shown to differ from the Marchenko-Pastur distribution, supported
in [0,4] and corresponding asymptotically to the entire set of quantum states.
Based on the shifted semi--circle law, describing asymptotic level density of
partially transposed states, and on the level density for the Gaussian unitary
ensemble with constraints for the spectrum we find an explicit form of the
probability distribution supported in [0,3], which describes well the level
density obtained numerically for PPT states.Comment: 11 pages, 4 figure
Computing quantum discord is NP-complete
We study the computational complexity of quantum discord (a measure of
quantum correlation beyond entanglement), and prove that computing quantum
discord is NP-complete. Therefore, quantum discord is computationally
intractable: the running time of any algorithm for computing quantum discord is
believed to grow exponentially with the dimension of the Hilbert space so that
computing quantum discord in a quantum system of moderate size is not possible
in practice. As by-products, some entanglement measures (namely entanglement
cost, entanglement of formation, relative entropy of entanglement, squashed
entanglement, classical squashed entanglement, conditional entanglement of
mutual information, and broadcast regularization of mutual information) and
constrained Holevo capacity are NP-hard/NP-complete to compute. These
complexity-theoretic results are directly applicable in common randomness
distillation, quantum state merging, entanglement distillation, superdense
coding, and quantum teleportation; they may offer significant insights into
quantum information processing. Moreover, we prove the NP-completeness of two
typical problems: linear optimization over classical states and detecting
classical states in a convex set, providing evidence that working with
classical states is generically computationally intractable.Comment: The (published) journal version
http://iopscience.iop.org/1367-2630/16/3/033027/article is more updated than
the arXiv versions, and is accompanied with a general scientific summary for
non-specialists in computational complexit
On the infeasibility of entanglement generation in Gaussian quantum systems via classical control
This paper uses a system theoretic approach to show that classical linear
time invariant controllers cannot generate steady state entanglement in a
bipartite Gaussian quantum system which is initialized in a Gaussian state. The
paper also shows that the use of classical linear controllers cannot generate
entanglement in a finite time from a bipartite system initialized in a
separable Gaussian state. The approach reveals connections between system
theoretic concepts and the well known physical principle that local operations
and classical communications cannot generate entangled states starting from
separable states.Comment: 6 pages, 3 figures. To appear in IEEE Transactions on Automatic
Control, 201
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