Related papers: Positivity and complete positivity of differentiab…
The partial separability of multipartite qubit density matrixes is strictly defined. We give a reduction way from N-partite qubit density matrixes to bipartite qubit density matrixes, and prove a necessary condition that a N-partite qubit…
Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, especially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that…
Let H be a positive semidefinite matrix partitioned into Hermitian blocks. Then, up to a direct sum operation, H is the average of matrices isometrically congruent to its partial trace. A few corollaries are given, related to important…
In quantum information and computation, the generation of entanglement through unitary gates remains a significant and active area of research. However, there are states termed as absolutely separable, from which entanglement cannot be…
We apply random matrix and free probability techniques to the study of linear maps of interest in quantum information theory. Random quantum channels have already been widely investigated with spectacular success. Here, we are interested in…
We extend the classification of mixed states of quantum systems composed of arbitrary number of subsystems of arbitrary dimensions. This extended classification is complete in the sense of partial separability and gives 1+18+1 partial…
The stochastic--quantum correspondence reinterprets quantum dynamics as arising from an underlying stochastic process on a configuration space. We generalize the correspondence by lifting an arbitrary stochastic kernel $\Gamma$ in finite…
It is known that the dynamical evolution of a system, from an initial tensor product state of system and environment, to any two later times, t1,t2 (t2>t1), are both completely positive (CP) but in the intermediate times between t1 and t2…
We give a separability criterion for three qubit states in terms of diagonal and anti-diagonal entries. This gives us a complete characterization of separability when all the entries are zero except for diagonal and anti-diagonals. The…
Using Godement mean on the Fourier-Stieltjes algebra of a locally compact quantum group we obtain strong separation results for quantum positive-definite functions associated to a subclass of representations, strengthening for example the…
Positive maps are useful for detecting entanglement in quantum information theory. Any entangled state can be detected by some positive map. In this paper, the relation between positive block matrices and completely positive…
Quantum simulation is a powerful tool to study the properties of quantum systems. The dynamics of open quantum systems are often described by Completely Positive (CP) maps, for which several quantum simulation schemes exist. We present a…
Discrimination between unknown processes chosen from a finite set is experimentally shown to be possible even in the case of non-orthogonal processes. We demonstrate unambiguous deterministic quantum process discrimination (QPD) of…
Multiplicativity of certain maximal p -> q norms of a tensor product of linear maps on matrix algebras is proved in situations in which the condition of complete positivity (CP) is either augmented by, or replaced by, the requirement that…
Many insights into the quantum world can be found by studying it from amongst more general operational theories of physics. In this thesis, we develop an approach to the study of such theories purely in terms of the behaviour of their…
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…
We propose a categorical foundation for the connection between pure and mixed states in quantum information and quantum computation. The foundation is based on distributive monoidal categories. First, we prove that the category of all…
Quantum process tomography is a procedure by which the unknown dynamical evolution of an open quantum system can be fully experimentally characterized. We demonstrate explicitly how this procedure can be implemented with a nuclear magnetic…
This article introduces PnCP, a MATLAB toolbox for constructing positive maps which are not completely positive. We survey optimization and sum of squares relaxation techniques to find the most numerically efficient methods for this…
A family of separability criteria based on correlation matrix (tensor) is provided. Interestingly, it unifies several criteria known before like e.g. CCNR or realignment criterion, de Vicente criterion and derived recently separability…