Related papers: Subnormalized states and trace-nonincreasing maps
Linear maps of matrices describing evolution of density matrices for a quantum system initially entangled with another are identified and found to be not always completely positive. They can even map a positive matrix to a matrix that is…
We study completely positive and trace-preserving equivariant maps between operators on irreducible representations of $\mathrm{SU}(2)$. We find asymptotic approximations of channels in the limit of large output representation and we…
We quantify the representational power of matrix product states (MPS) for entangled qubit systems by giving polynomial expressions in a pure quantum state's amplitudes which hold if and only if the state is a translation invariant matrix…
Quantum supermaps are a higher-order generalization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive, trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By…
In this paper, we present a thought experiment that demonstrates that the equivalence of quantum reduced states and statistical mixed states of ensembles is not merely a simple mathematical formulation in quantum mechanics, but rather…
We consider to treat the usual probabilistic cloning, state separation, unambiguous state discrimination, \emph{etc} in a uniform framework. All these transformations can be regarded as special examples of generalized completely positive…
We study methods of inducing metrics on unital completely positive maps by employing seminorms arising in noncommutative geometry. Our main approach relies on the development of an infinite-dimensional $C^*$-algebraic analogue of the…
For a given set of input-output pairs of quantum states or observables, we ask the question whether there exists a physically implementable transformation that maps each of the inputs to the corresponding output. The physical maps on…
We report a study of a disorder-dependent real-space representation of the quantum geometry in topological systems. Thanks to the development of an efficient linear-scaling numerical methodology based on the kernel polynomial method, we can…
We introduce a class of intrinsic symmetry-protected topological mixed-state(mSPT) in open quantum systems that feature modulated symmetries, such as dipole and subsystem symmetries. Intriguingly, these mSPT phases cannot be realized as the…
Let $H$ and $K$ be (finite or infinite dimensional) complex Hilbert spaces. A characterization of positive completely bounded normal linear maps from ${\mathcal B}(H)$ into ${\mathcal B}(K)$ is given, which particularly gives a…
Mixed state ensembles such as the Bures-Hall and Hilbert-Schmidt measure are probability distributions that characterise the statistical properties of random density matrices and can be used to determine the typical features of mixed…
We introduce an entanglement measure, the Modified Bloch Norm (MBN), for finite-dimensional bipartite mixed states, based on the improved Bloch matrix criteria. MBN is demonstrated to be effective in analyzing the dynamics of bound…
We present a generic study of unambiguous discrimination between two mixed quantum states. We derive operational optimality conditions and show that the optimal measurements can be classified according to their rank. In Hilbert space…
Generalized measurement schemes on one part of bipartite states, which would leave the set of all separable states insensitive are explored here to understand quantumness of correlations in a more general perspecitve. This is done by…
Microscopic Schr{\"o}dinger cat states are generated from quantum correlated fields using a probabilistic heralding photon subtraction event. Subsequent quantum state tomography provides complete information about the state with typical…
In these notes we prove that the $s$ or $u$-states of cocycles over partially hyperbolic maps are closed in the space of invariant measures.
The nonlinear positive map of density matrix of two-qubit Werner state called nonlinear channel is studied. The map of density matrix is realized by rational function. The influence of the map onto the entanglement properties of the…
Given a bipartite quantum system represented by a tensor product of two Hilbert spaces, we give an elementary argument showing that if either component space is infinite-dimensional, then the set of nonseparable density operators is…
We show that only those composite quantum systems possessing nonvanishing quantum correlations have the property that any nontrivial local unitary evolution changes their global state. We derive the exact relation between the global state…