Zobrazeno 1 - 10
of 46
pro vyhledávání: '"SKOWRONEK, ŁUKASZ"'
There is no direct generalization of positive partial transpose criterion to the three-by-three case
Autor:
Skowronek, Łukasz
We show that there cannot exist a straightforward generalization of the famous positive partial transpose criterion to three-by-three systems. We call straightforward generalizations that use a finite set of positive maps and arbitrary local rotation
Externí odkaz:
http://arxiv.org/abs/1605.05254
Autor:
Skowronek, Łukasz
We present solutions to a set of problems that arise in quantum entanglement theory, whose common trait is the use of algebraic methods. The backbone of the thesis consists of two general theorems, pertaining to specific convex sets of quantum maps.
Externí odkaz:
http://arxiv.org/abs/1305.2435
Publikováno v:
Linear Algebra and Its Applications, 438:3062-3075, 2013
We answer in the affirmative a recently-posed question that asked if there exists an "untypical" convex mapping cone -- i.e., one that does not arise from the transpose map and the cones of k-positive and k-superpositive maps. We explicitly construct
Externí odkaz:
http://arxiv.org/abs/1209.0437
Autor:
Skowronek, Łukasz
Publikováno v:
J. Math. Phys. 52, 122202 (2011)
We discuss the subject of Unextendible Product Bases with the orthogonality condition dropped and we prove that the lowest rank non-separable positive-partial-transpose states, i.e. states of rank 4 in 3 x 3 systems are always locally equivalent to a
Externí odkaz:
http://arxiv.org/abs/1105.2709
Autor:
Puchała, Zbigniew, Gawron, Piotr, Miszczak, Jarosław Adam, Skowronek, Łukasz, Choi, Man-Duen, Życzkowski, Karol
Publikováno v:
Linear Algebra Appl., 434 (2011) 327-342
We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Pr
Externí odkaz:
http://arxiv.org/abs/1008.3482
Autor:
Skowronek, Łukasz
Publikováno v:
Lin. Alg. Appl. 435 (2011), 361--370
In the finite-dimensional case, we present a new approach to the theory of cones with a mapping cone symmetry, first introduced by St{\o}rmer. Our method is based on a definition of an inner product in the space of linear maps between two algebras of
Externí odkaz:
http://arxiv.org/abs/1008.3237
Autor:
Skowronek, Łukasz, Størmer, Erling
Publikováno v:
J. Func. Anal. 262 (2012), 639--647
We study positive maps of B(K) into B(H) for finite-dimensional Hilbert spaces K and H. Our main emphasis is on how Choi matrices and estimates of their norms with respect to mapping cones reflect various properties of the maps. Special attention wil
Externí odkaz:
http://arxiv.org/abs/1008.3126
Autor:
Skowronek, Lukasz
Publikováno v:
Int. J. Quantum Inf. Vol. 8, No. 5 (2010) 721-754
We present a survey on mathematical topics relating to separable states and entanglement witnesses. The convex cone duality between separable states and entanglement witnesses is discussed and later generalized to other families of operators, leading
Externí odkaz:
http://arxiv.org/abs/1001.3655
Autor:
Gawron, Piotr, Puchała, Zbigniew, Miszczak, Jarosław Adam, Skowronek, Łukasz, Życzkowski, Karol
Publikováno v:
J. Math. Phys. 51, 102204 (2010)
Numerical range of a Hermitian operator X is defined as the set of all possible expectation values of this observable among a normalized quantum state. We analyze a modification of this definition in which the expectation value is taken among a certa
Externí odkaz:
http://arxiv.org/abs/0905.3646
Autor:
Skowronek, Lukasz, Zyczkowski, Karol
Publikováno v:
J. Phys. A: Math. Theor. 42 (2009) 325302
We link the study of positive quantum maps, block positive operators, and entanglement witnesses with problems related to multivariate polynomials. For instance, we show how indecomposable block positive operators relate to biquadratic forms that are
Externí odkaz:
http://arxiv.org/abs/0903.3042