相关论文: On the local unitary equivalence of states of mult…

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…

We study the power of local test for bipartite quantum states. Our central result is that, for properties of bipartite pure states, unitary invariance on one part implies an optimal (over all global testers) local tester acting only on the…

We consider a bipartite mixed state of the form, $\rho =\sum_{\alpha, \beta =1}^{l}a_{\alpha \beta} | \psi_{\alpha}> < \psi_ \beta}| $, where $| \psi_{\alpha}>$ are normalized bipartite state vectors, and matrix $(a_{\alpha \beta})$ is…

We introduce algebraic sets in the complex projective spaces for the mixed states in bipartite quantum systems as their invariants under local unitary operations. The algebraic sets of the mixed state have to be the union of the linear…

Multipartite quantum entanglement serves as a resource for spatially separated parties performing distributed quantum information processing. Any multipartite entangled state can be generated from appropriately distributed bipartite…

We present that the local unitary equivalence of n-party pure states is consistent with the one of their (n-1)-party reduced density matrices. As an application, we obtain the local invariants for a class of tripartite pure qudits.

Unitary operations are physically implementable. We further the understanding of such operations by studying the possible forms of nonlocal unitary operators, which are bipartite or multipartite unitary operators that are not tensor product…

For two qubits and for general bipartite quantum systems, we give a simple spectral condition in terms of the ordered eigenvalues of the density matrix which guarantees that the corresponding state is separable.

We study the relation between local unitary (LU) equivalence and local Clifford (LC) equivalence of stabilizer states. We introduce a large subclass of stabilizer states, such that every two LU equivalent states in this class are…

A method is presented to obtain local unitary invariants for multipartite quantum systems consisting of fermions or distinguishable particles. The invariants are organized into infinite families, in particular, the generalization to higher…

Understanding multipartite entanglement is vital, as it underpins a wide range of phenomena across physics. The study of transformations of states via Local Operations assisted by Classical Communication (LOCC) allows one to quantitatively…

Research on quantum states often focuses on the correlation between nonlocal effects and local unitary invariants, among which local unitary equivalence plays a significant role in quantum state classification and resource theories. This…

We find that a bipartite quantum state is entangled if and only if it is quantum coherent with respect to complete bases of states in the corresponding system that are distinguishable under local quantum operations and classical…

Given a set of multipartite entangled states, can we find a common state to prepare them by local operations and classical communication? Such a state, if exists, will be a common resource for the given set of states. We completely solve…

We investigate whether pure entangled states can be associated to a measurement basis in which all vectors are local unitary transformations of the original state. We prove that for bipartite states with a local dimension that is either $2,…

For a general multipartite quantum state, we formulate a locally checkable condition, under which the expectation values of certain nonlocal observables are completely determined by the expectation values of some local observables. The…

We study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An…

We prove that every unitary acting on any multipartite system and having operator Schmidt rank equal to 2 can be diagonalized by local unitaries. This then implies that every such multipartite unitary is locally equivalent to a controlled…

In previous work the authors introduced a notion of generic states and obtained criteria for local equivalence of them. Here they introduce the concept of CHG states maintaining the criteria of local equivalence. This fact allows the…

We analyze the distinguishability norm on the states of a multi-partite system, defined by local measurements. Concretely, we show that the norm associated to a tensor product of sufficiently symmetric measurements is essentially equivalent…