Topic
Schmidt decomposition
About: Schmidt decomposition is a research topic. Over the lifetime, 480 publications have been published within this topic receiving 16552 citations.
Papers published on a yearly basis
Papers
TL;DR: Any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.
Abstract: If two separated observers are supplied with entanglement, in the form of n pairs of particles in identical partly entangled pure states, one member of each pair being given to each observer, they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally entangled pairs of particles, for example, Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves entropy of entanglement---the von Neumann entropy of the partial density matrix seen by either observer---with the yield of singlets approaching, for large n, the base-2 entropy of entanglement of the initial partly entangled pure state. Conversely, any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement. \textcopyright{} 1996 The American Physical Society.
3,479 citations
TL;DR: It is proposed that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order and is compared with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions.
Abstract: We study the "entanglement spectrum" (a presentation of the Schmidt decomposition analogous to a set of "energy levels") of a many-body state, and compare the Moore-Read model wave function for the nu=5/2 fractional quantum Hall state with a generic 5/2 state obtained by finite-size diagonalization of the second-Landau-level-projected Coulomb interactions. Their spectra share a common "gapless" structure, related to conformal field theory. In the model state, these are the only levels, while in the "generic" case, they are separated from the rest of the spectrum by a clear "entanglement gap", which appears to remain finite in the thermodynamic limit. We propose that the low-lying entanglement spectrum can be used as a "fingerprint" to identify topological order.
1,975 citations
TL;DR: It is argued that the statistical basis of the measure of entanglement determines an upper bound to the number of singlets that can be obtained by any purification procedure.
Abstract: We improve previously proposed conditions each measure of entanglement has to satisfy. We present a class of entanglement measures that satisfy these conditions and show that the quantum relative entropy and Bures metric generate two measures of this class. We calculate the measures of entanglement for a number of mixed two spin-1/2 systems using the quantum relative entropy, and provide an efficient numerical method to obtain the measures of entanglement in this case. In addition, we prove a number of properties of our entanglement measure that have important physical implications. We briefly explain the statistical basis of our measure of entanglement in the case of the quantum relative entropy. We then argue that our entanglement measure determines an upper bound to the number of singlets that can be obtained by any purification procedure.
1,678 citations
TL;DR: A new entanglement monotone for bipartite quantum states is presented, inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions: it is convex, additive on tensor products, and superadditive in general.
Abstract: In this paper, we present a new entanglement monotone for bipartite quantum states. Its definition is inspired by the so-called intrinsic information of classical cryptography and is given by the halved minimum quantum conditional mutual information over all tripartite state extensions. We derive certain properties of the new measure which we call “squashed entanglement”: it is a lower bound on entanglement of formation and an upper bound on distillable entanglement. Furthermore, it is convex, additive on tensor products, and superadditive in general. Continuity in the state is the only property of our entanglement measure which we cannot provide a proof for. We present some evidence, however, that our quantity has this property, the strongest indication being a conjectured Fannes-type inequality for the conditional von Neumann entropy. This inequality is proved in the classical case.
603 citations
TL;DR: In this paper, the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form.
Abstract: We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.
546 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 19 |
| 2020 | 13 |
| 2019 | 11 |
| 2018 | 17 |
| 2017 | 17 |
| 2016 | 23 |