Searching for extremal PPT entangled states (2009)
Augusiak, Remigiusz, Grabowski, Janusz, Kus, Marek, Lewenstein, Maciej
We formulate a simple operational criterion allowing to judge if a given entangled state with positive partial transpose (PPTES) is extremal in the convex set of all PPTES. The criterion reduces the...
Wigner's Theorem and geometry of extreme positive maps (2009)
Grabowski, Janusz, Kus, Marek, Marmo, Giuseppe
We consider transformation maps on the space of states which are symmetries in the sense of Wigner. Due to the convex nature of the space of states, the set of these maps has a convex structure. We...
On the relation between states and maps in infinite dimensions (2007)
Grabowski, Janusz, Kus, Marek, Marmo, Giuseppe
Relations between states and maps, which are known for quantum systems in finite-dimensional Hilbert spaces, are formulated rigorously in geometrical terms with no use of coordinate (matrix)...
Separability, entanglement and full families of commuting normal matrices (2007)
Samsonowicz, Jan, Kus, Marek, Lewenstein, Maciej
We reduce the question whether a given quantum mixed state is separable or entangled to the problem of existence of a certain full family of commuting normal matrices whose matrix elements are...
Level dynamics and the ten-fold way (2007)
Huckleberry, Alan T., Kus, Marek, Schuetzdeller, Patrick
We investigate the parameter dynamics of eigenvalues of Hamiltonians ('level dynamics') defined on symmetric spaces relevant for condensed matter and particle physics. In particular we: 1) identify...
On determination of statistical properties of spectra from parametric level dynamics (2006)
Hardej, Miroslaw, Kus, Marek, Gonera, Cezary, Kosinski, Piotr
We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show...
Demkowicz-Dobrzanski, Rafal, Buchleitner, Andreas, Kus, Marek, Mintert, Florian
We discuss the monotonicity under local operations and classical communication (LOCC) of systematically constructed quantities aiming at quantification of entanglement properties of multipartite...
Symmetries, group actions, and entanglement (2006)
Grabowski, Janusz, Kus, Marek, Marmo, Giuseppe
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical...
Measures and dynamics of entangled states (2005)
Mintert, Florian, Carvalho, Andre R. R., Kus, Marek, Buchleitner, Andreas
We develop an original approach for the quantitative characterisation of the entanglement properties of, possibly mixed, bi- and multipartite quantum states of arbitrary finite dimension. Particular...
Concurrence of mixed multi-partite quantum states (2004)
Mintert, Florian, Kus, Marek, Buchleitner, Andreas
We propose generalizations of concurrence for multi-partite quantum systems that can distinguish qualitatively distinct quantum correlations. All introduced quantities can be evaluated efficiently...
Global entangling properties of the coupled kicked tops (2004)
Demkowicz-Dobrzanski, Rafal, Kus, Marek
We study global entangling properties of the system of coupled kicked tops testing various hypotheses and predictions concerning entanglement in quantum chaotic systems. In order to analyze the...
Concurrence of mixed bipartite quantum states in arbitrary dimensions (2004)
Mintert, Florian, Kus, Marek, Buchleitner, Andreas
We derive a lower bound for the concurrence of mixed bipartite quantum states, valid in arbitrary dimensions. As a corollary, a weaker, purely algebraic estimate is found, which detects mixed...
Birkhoff's polytope and unistochastic matrices, N=3 and N=4 (2004)
Bengtsson, Ingemar, Ericsson, Asa, Kus, Marek, Tadej, Wojciech, Zyczkowski, Karol
The set of bistochastic or doubly stochastic N by N matrices form a convex set called Birkhoff's polytope, that we describe in some detail. Our problem is to characterize the set of unistochastic...
Cloning of spin-coherent states (2003)
Demkowicz-Dobrzanski, Rafal, Kus, Marek, Wodkiewicz, Krzysztof
We consider optimal cloning of the spin coherent states in Hilbert spaces of different dimensionality d. We give explicit form of optimal cloning transformation for spin coherent states in the...
Manifolds of interconvertible pure states (2001)
Sinolecka, Magdalena M., Zyczkowski, Karol, Kus, Marek
Local orbits of a pure state of an N x N bi-partite quantum system are analyzed. We compute their dimensions which depends on the degeneracy of the vector of coefficients arising by the Schmidt...
Separable approximation for mixed states of composite quantum systems (2001)
We describe a purely algebraic method for finding the best separable approximation to a mixed state of a composite 2x2 quantum system, consisting of a decomposition of the state into a linear...
Quantum Correlations in Two-Fermion Systems (2000)
Schliemann, John, Cirac, J. Ignacio, Kus, Marek, Lewenstein, Maciej, Loss, Daniel
We characterize and classify quantum correlations in two-fermion systems having 2K single-particle states. For pure states we introduce the Slater decomposition and rank (in analogy to Schmidt...
Classical 1D maps, quantum graphs and ensembles of unitary matrices (2000)
Pakonski, Prot, Zyczkowski, Karol, Kus, Marek
We study a certain class of classical one dimensional piecewise linear maps. For these systems we introduce an infinite family of Markov partitions into equal cells. The symbolic dynamics generated...
Level Dynamics and Universality of Spectral Fluctuations (2000)
Braun, Peter, Gnutzmann, Sven, Haake, Fritz, Kus, Marek, Zyczkowski, Karol
The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we...
Geometry of entangled states (2000)
Geometric properties of the set of quantum entangled states are investigated. We propose an explicit method to compute the dimension of local orbits for any mixed state of the general K x M problem...
Composed ensembles of random unitary matrices (1997)
Pozniak, Marcin, Zyczkowski, Karol, Kus, Marek
Composed ensembles of random unitary matrices are defined via products of matrices, each pertaining to a given canonical circular ensemble of Dyson. We investigate statistical properties of spectra...
Secular determinants of random unitary matrices (1996)
Haake, Fritz, Kus, Marek, Sommers, Hans-Jurgen, Schomerus, Henning, Zyczkowski, Karol
We consider the characteristic polynomials of random unitary matrices U drawn from various circular ensembles. In particular, the statistics of the coefficients of these polynomials are studied. The...
Secular determinants of random unitary matrices (1996)
Haake, Fritz, Kus, Marek, Sommers, Hans-Jurgen, Schomerus, Henning, Zyczkowski, Karol
We consider the characteristic polynomials of random unitary matrices U drawn from various circular ensembles. In particular, the statistics of the coefficients of these polynomials are studied. The...
Secular determinants of random unitary matrices. (1996)
Haake, Fritz, Kus, Marek, Sommers, Hans-Jurgen, Schomerus, Henning, Zyczkowski, Karol
We consider the characteristic polynomials of random unitary matrices U drawn from various circular ensembles. In particular, the statistics of the coefficients of these polynomials are studied. The...