On completely positive non-Markovian evolution of a d-level system
A sufficient condition for non-Markovian master equation which ensures the complete positivity of the resulting time evolution is presented.
quant-ph↗
arXiv subjects
Andrzej Kossakowski
Publications and source records attributed to Andrzej Kossakowski.
How to construct entanglement witnesses
We present very simple method for constructing indecomposable entanglement witnesses out of a given pair -- an entanglement witness W and the corresponding state detected by W. This method may be used to produce new classes of atomic witnesses which are able to detect the `weakest' quantum entanglement. Actually, it works perfectly in the multipartite case, too. Moreover, this method provides a powerful tool for constructing new examples of bound entangled states.
quant-ph↗
A class of positive atomic maps
We construct a new class of positive indecomposable maps in the algebra of `d x d' complex matrices. These maps are characterized by the `weakest' positivity property and for this reason they are called atomic. This class provides a new reach family of atomic entanglement witnesses which define important tool for investigating quantum entanglement. It turns out that they are able to detect states with the `weakest' quantum entanglement.
quant-ph↗
Multipartite circulant states with positive partial transposes
We construct a large class of multipartite qudit states which are positive under the family of partial transpositions. The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure and hence generalizes a class of bipartite circulant states proposed recently by the authors. This class contains many well known examples of multipartite quantum states from the literature and gives rise to a huge family of completely new states.
quant-ph↗
Quantum states with strong positive partial transpose
We construct a large class of bipartite M x N quantum states which defines a proper subset of states with positive partial transposes (PPT). Any state from this class is PPT but the positivity of its partial transposition is recognized with respect to canonical factorization of the original density operator. We propose to call elements from this class states with strong positive partial transposes (SPPT). We conjecture that all SPPT states are separable.
quant-ph↗
On circulant states with positive partial transpose
We construct a large class of quantum "d x d" states which are positive under partial transposition (so called PPT states). The construction is based on certain direct sum decomposition of the total Hilbert space displaying characteristic circular structure - that is way we call them circulant states. It turns out that partial transposition maps any such decomposition into another one and hence both original density matrix and its partially transposed partner share similar cyclic properties. This class contains many well known examples of PPT states from the literature and gives rise to a huge family of completely new states.
quant-ph↗
On non-Markovian time evolution in open quantum systems
Non-Markovian reduced dynamics of an open system is investigated. In the case the initial state of the reservoir is the vacuum state, an approximation is introduced which makes possible to construct a reduced dynamics which is completely positive.
quant-ph↗
Rotationally invariant multipartite states
We construct a class of multipartite states possessing rotational SO(3) symmetry -- these are states of K spin-j_A particles and K spin-j_B particles. The construction of symmetric states follows our two recent papers devoted to unitary and orthogonal multipartite symmetry. We study basic properties of multipartite SO(3) symmetric states: separability criteria and multi-PPT conditions.
quant-ph↗
On the structure of entanglement witnesses and new class of positive indecomposable maps
We construct a new class of positive indecomposable maps in the algebra of 'd x d' complex matrices. Each map is uniquely characterized by a cyclic bistochastic matrix. This class generalizes a Choi map for d=3. It provides a new reach family of indecomposable entanglement witnesses which define important tool for investigating quantum entanglement.
quant-ph↗
A new class of states with positive partial transposition
We construct a new class of PPT states for bipartite "d x d" systems. This class is invariant under the maximal commutative subgroup of U(d) and contains as special cases almost all known examples of PPT states. Theses states may be used to test the atomic property of positive maps which are crucial in studying quantum entanglement.
quant-ph↗
On multipartite invariant states I. Unitary symmetry
We propose a natural generalization of bipartite Werner and isotropic states to multipartite systems consisting of an arbitrary even number of d-dimensional subsystems (qudits). These generalized states are invariant under the action of local unitary operations. We study basic properties of multipartite invariant states: separability criteria and multi-PPT conditions.
quant-ph↗
On multipartite invariant states II. Orthogonal symmetry
We construct a new class of multipartite states possessing orthogonal symmetry. This new class defines a convex hull of multipartite states which are invariant under the action of local unitary operations introduced in our previous paper "On multipartite invariant states I. Unitary symmetry". We study basic properties of multipartite symmetric states: separability criteria and multi-PPT conditions.
quant-ph↗
On partially entanglement breaking channels
Using well known duality between quantum maps and states of composite systems we introduce the notion of Schmidt number of a quantum channel. It enables one to define classes of quantum channels which partially break quantum entanglement. These classes generalize the well known class of entanglement breaking channels.
quant-ph↗
The Bloch-vector space for N-level systems -- the spherical-coordinate point of view
Bloch-vector spaces for $N$-level systems are investigated from the spherical-coordinate point of view in order to understand their geometrical aspects. We show that the maximum radius in each direction, which is due to the construction of the Bloch-vector space, is determined by the minimum eigenvalue of the corresponding observable (orthogonal generator of SU(N)). From this fact, we reveal the dual property of the structure of the Bloch-vector space; if in some direction the space reachs the large sphere (pure state), then in the opposite direction the space can only get to the small sphere, and vice versa. Another application is a parameterization with simple ranges of density operators. We also provide three classes of quantum-state representation based on actual measurements beyond the Bloch vector and discuss their state-spaces.
quant-ph↗
A Description of Quantum Chaos
A measure describing the chaos of a dynamics was introduced by two complexities in information dynamics, and it is called the chaos degree. In particular, the entropic chaos degree has been used to characterized several dynamical maps such that logistis, Baker's, Tinckerbel's in classical or quantum systems. In this paper, we give a new treatment of quantum chaos by defining the entropic chaos degree for quantum transition dynamics, and we prove that every non-chaotic quantum dynamics, e.g., dissipative dynamics, has zero chaos degree. A quantum spin 1/2 system is studied by our chaos degree, and it is shown that this degree well describes the chaotic behavior of the spin system.
quant-ph↗
How Can We Observe and Describe Chaos?
We propose a new approach to define chaos in dynamical systems from the point of view of Information Dynamics. Observation of chaos in reality depends upon how to observe it, for instance, how to take the scale in space and time. Therefore it is natural to abandon taking several mathematical limiting procedures. We take account of them, and chaos degree previously introduced is redefined in this paper.
quant-ph↗
A Class of Linear Positive Maps in Matrix Algebras
A class of linear positive, trace preserving maps in $M_n$ is given in terms of affine maps in $\bBR^{n^2-1}$ which map the closed unit ball into itself.
quant-ph↗