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If X and Y are independent, Y and Z are independent, and so are X and Z, one might be tempted to conclude that X, Y, and Z are independent. But it has long been known in classical probability theory that, intuitive as it may seem, this is…
A 6-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum and the indistinguishable emission produced by a 2-crystal system…
Entanglement is an useful resource because some global operations cannot be locally implemented using classical communication. We prove a number of results about what is and is not locally possible. We focus on orthogonal states, which can…
We claim that the nonlocality without entanglement revealed quite recently by Bennett {\it et al.} [quant-ph/9804053] should be rather interpreted as {\it Einstein-Podolsky-Rosen paradox without entanglement}. It would be true nonlocality…
We report the observation of entanglement between a single trapped atom and a single photon at a wavelength suitable for low-loss communication over large distances, thereby achieving a crucial step towards long range quantum networks. To…
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 study if all maximally entangled states are pure through several entanglement monotones. In the bipartite case, we find that the same conditions which lead to the uniqueness of the entropy of entanglement as a measure of entanglement,…
There is a direct correspondence between two-particle, entangled quantum states, for example, Bell states, and the relative values of the component one-particle states. This leads to a new rationale for quantum computing which makes use of…
A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown…
We show that in the presence of arbitrary catalysts, any pure bipartite entangled state can be converted into any other to unlimited accuracy without the use of any communication, quantum or classical.
A novel approach to entanglement, based on the Gelfand-Naimark-Segal (GNS) construction, is introduced. It considers states as well as algebras of observables on an equal footing. The conventional approach to the emergence of mixed from…
In this paper we consider the notion of quantum entanglement from the perspective of the logos categorical approach [26, 27]. Firstly, we will argue that the widespread distinctions, on the one hand, between pure states and mixed states,…
The behaviour under particle loss of entanglement and nonlocality is investigated in multipartite quantum systems. In particular, we define a notion of persistency of nonlocality, which leads to device-independent tests of persistent…
Nature allows one to explore a manifold of remarkable quantum effects. Most prominently, quantum entanglement can be observed in many-particle systems, between multiple quantized fields, and in hybrid combinations thereof. This diversity,…
This research introduces the concept of the purity number, which represents the number of separable s-particle sub-states within an n-particle state ($s<n$ ). It establishes that, for any , achieving the maximum purity number is both a…
Measuring an entangled state of two particles is crucial to many quantum communication protocols. Yet Bell state distinguishability using a finite apparatus obeying linear evolution and local measurement is theoretically limited. We extend…
The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for…
Recently a quite stimulating paper [1] dealing with the possibility of exploiting the nonlocal aspects of a superposition of states of a single photon appeared. We regard as greatly relevant the results which have been obtained. However we…
We discuss the concept of how entanglement changes with respect to different factorizations of the total algebra which describes the quantum states. Depending on the considered factorization a quantum state appears either entangled or…
These notes are more or less a faithful representation of my talk at the Workshop on ``Quantum Coding and Quantum Computing'' held at the University of Virginia. As such it is an introduction for non-physicists to the topics of the quantum…