相关论文: Ranks of quantum states with prescribed reduced st…
For a quantum state represented as an $n\times n$ density matrix $\sigma \in M_n$, let ${\cal S}(\sigma)$ be the compact convex set of quantum states $\rho = (\rho_{ij}) \in M_{m\cdot n}$ with the first partial trace equal to $\sigma$,…
We study the concurrence of arbitrary-dimensional multipartite quantum states. Analytical lower bounds of concurrence for tripartite quantum states are derived by projecting high-dimensional states to $2\otimes 2\otimes 2$ substates. The…
We present a necessary and sufficient product criterion for bipartite quantum states based on the rank of realignment matrix of density matrix. Then, this approach is generalized to multipartite systems. We first introduce the concept of…
Quantification of quantum entanglement plays a crucial role in the study of quantum information tasks. We present analytical lower bounds for both concurrence and 2-concurrence based on the correlation matrices of bipartite quantum states.…
Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we…
We report here on the results of numerical searches for PPT states with specified ranks for density matrices and their partial transpose. The study includes several bipartite quantum systems of low dimensions. For a series of ranks extremal…
We investigate relations between the ranks of marginals of multipartite quantum states. These are the Schmidt ranks across all possible bipartitions and constitute a natural quantification of multipartite entanglement dimensionality. We…
We propose a technique to investigate multipartite entanglement in the symmetric subspace. Our approach is to map an $N$-qubit symmetric state onto a bipartite symmetric state of higher local dimension. We show that this mapping preserves…
We consider an arbitrary d_{1}\otimes d_{2}\otimes ... \otimes d_{N} composite quantum system and find necessary conditions for general m-party subsystem states to be the reduced states of a common N-party state. These conditions will lead…
Subsystems of composite quantum systems are described by reduced density matrices, or quantum marginals. Important physical properties often do not depend on the whole wave function but rather only on the marginals. Not every collection of…
In many quantum information processing protocols, entangled states shared among parties are an important resource. In this article, we study how bipartite states may be distributed in the context of a quantum network limited by timing…
We extend the matrix decomposition method(MDM) in classifying the $2\times N\times N$ truly entangled states to $2\times M\times N$ system under the condition of stochastic local operations and classical communication. It is found that the…
Explicit sufficient and necessary conditions for separability of $N$-dimensional rank two multiparty quantum mixed states are presented. A nonseparability inequality is also given, for the case where one of the eigenvectors corresponding to…
States on coupled quantum system whose restrictions to each subsystems are normalized traces are called marginal tracial states. We investigate extremal marginal tracial states and maximal rank of such states. Diagonal marginal tracial…
We propose a method to detect genuine quantum correlation for arbitrary quantum state in terms of the rank of coefficient matrices associated with the pure state. We then derive a necessary and sufficient condition for a quantum state to…
It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is…
We investigate the differential geometry of bipartite quantum states. In particular the manifold structures of pure bipartite states are studied in detail. The manifolds with respect to all normalized pure states of arbitrarily given…
We quantify the usefulness of a bipartite quantum state in the ancilla-assisted channel discrimination of arbitrary quantum channels, formally defining a worst-case-scenario channel discrimination power for bipartite quantum states. We show…
One way to diagnose chaos in bipartite unitary channels is via the tripartite information of the corresponding Choi state, which for certain choices of the subsystems reduces to the negative conditional mutual information (CMI). We study…
We study the invariants of arbitrary dimensional multipartite quantum states under local unitary transformations. For multipartite pure states, we give a set of invariants in terms of singular values of coefficient matrices. For…