Related papers: On the local unitary equivalence of states of mult…
A new hierarchy of separability conditions for bipartite states is obtained. All the conditions in the hierarchy are necessary for separability. The conditions are expressed in terms of higher powers of the density operator of the bipartite…
Typical quantum computing schemes require transformations (gates) to be targeted at specific elements (qubits). In many physical systems, direct targeting is difficult to achieve; an alternative is to encode local gates into globally…
We address the question of whether or not global entanglement of a quantum state can be inferred from local properties. Specifically, we are interested in genuinely multiparticle entangled states whose two-body marginals are all separable,…
We consider one copy of a quantum system prepared in one of two non-orthogonal pure product states of multipartite distributed among separated parties. We show that there exist protocols which obtain optimal probability in the sense of…
In the first part of this paper we analyze possible quantum computational capacities due to quantum queries associated with equi-partitions of pure orthogonal states. Special emphasis is given to the parity of product states and to…
A necessary and sufficient condition for characterization and quantification of entanglement of any bipartite Gaussian state belonging to a special symmetry class is given in terms of classicality measures of one-party states. For Gaussian…
We consider the transformation of multisystem entangled states by local quantum operations and classical communication. We show that, for any reversible transformation, the relative entropy of entanglement for two parties must remain…
The Schmidt number is a fundamental parameter characterizing the properties of quantum states, and the local projections are a fundamental operation in quantum physics. We investigate the relation between the Schmidt numbers of bipartite…
Entanglement of any pure state of an N times N bi-partite quantum system may be characterized by the vector of coefficients arising by its Schmidt decomposition. We analyze various measures of entanglement derived from the generalized…
After introducing the partially separable concept, we proved the equivalence between the partial separability of a given $m$-partite subsystem with $m$ qubits and the purity of states of this $m$-partite subsystem for a pure state in…
Many protocols of quantum information processing use entangled states. Hence, separability criteria are of great importance. We propose new separability conditions for a bipartite finite-dimensional system. They are derived by using…
Classifying locally equivalent graph states, and stabilizer states more broadly, is a significant problem in the theories of quantum information and multipartite entanglement. A special focus is given to those graph states for which…
We initially consider a quantum system consisting of two qubits, which can be in one of two nonorthogonal states, \Psi_0 or \Psi_1. We distribute the qubits to two parties, Alice and Bob. They each measure their qubit and then compare their…
Every choice of an orthonormal frame in the d-dimensional Hilbert space of a system corresponds to one set of all mutually commuting density matrices or, equivalently, a classical statistical state space of the system; the quantum state…
We study partial coherence and its connections with entanglement. First, we provide a sufficient and necessary condition for bipartite pure state transformation under partial incoherent operations: A bipartite pure state can be transformed…
We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the…
Implementing nonlocal unitary operators is an important and hard question in quantum computing and cryptography. We show that any bipartite nonlocal unitary operator of Schmidt rank three on the $(d_A \times d_B)$-dimensional system is…
Commutators are essential in quantum information theory, influencing quantum state symmetries and information storage robustness. This paper systematically investigates the characteristics of bipartite and multipartite quantum states…
In this letter we have established the physical character of pure bipartite states with the same amount of entanglement in the same Schmidt rank that either they are local unitarily connected or they are incomparable. There exist infinite…
Several entanglement measures are used to define equivalence classes in the set of hypergraph states of three qubits. Our classifications reveal that (i) under local unitary transformations, hypergraph states of three qubits are split into…