Universal Separability and Entanglement in Identical Particle Systems (original) (raw)

Entanglement of indistinguishable particles

Physical Review A, 2011

We present a general criterion for entanglement of N indistinguishable particles decomposed into arbitrary s subsystems based on the unambiguous measurability of correlation. Our argument provides a unified viewpoint on the entanglement of indistinguishable particles, which is still unsettled despite various proposals made mainly for the s = 2 case. Even though entanglement is defined only with reference to the measurement setup, we find that the so-called i.i.d. states form a special class of bosonic states which are universally separable.

Entanglement of Identical Particles

Open Systems & Information Dynamics, 2014

Unlike for bipartite states consisting of distinguishable particles, in the case of identical parties the notion of entanglement is still under debate. In the following, we review two different approaches to the entanglement of systems consisting of two bosons or fermions; the first approach is based on the particle aspect typical of first quantization and identifies separable pure states as those that allow to assign two orthogonal single particle vector states to both parties. The second approach makes full use of the mode aspect of second quantization whereby separability can be formulated as absence of nonlocal correlation among two different sets of modes. While the first approach applies to pure states only, the second one is more general and characterizes generic entangled states. In the following, we shall show that the mode-based approach indeed contains the particle-based one.

Spatial separation and entanglement of identical particles

International Journal of Quantum Information, 2014

We reconsider the effect of indistinguishability on the reduced density operator of the internal degrees of freedom (tracing out the spatial degrees of freedom) for a quantum system composed of identical particles located in different spatial regions. We explicitly show that if the spin measurements are performed in disjoint spatial regions then there are no constraints on the structure of the reduced state of the system. This implies that the statistics of identical particles has no role from the point of view of separability and entanglement when the measurements are spatially separated. We extend the treatment to the case of n particles and show the connection with some recent criteria for separability based on subalgebras of observables.

Compatibility and Separability for Classical and Quantum Entanglement

We study the concepts of compatibility and separability and their implications for quantum and classical systems. These concepts are illustrated on a macroscopic model for the singlet state of a quantum system of two entangled spin 1/2 with a parameter reflecting indeterminism in the measurement procedure. By varying this parameter we describe situations from quantum, intermediate to classical and study which tests are compatible or separated. We prove that for classical deterministic systems the concepts of separability and compatibility coincide, but for quantum systems and intermediate systems these concepts are generally different.

Entanglement of indistinguishable particles in condensed-matter physics

Physical Review A, 2006

Using an operational definition we quantify the entanglement, EP, between two parties who share an arbitrary pure state of N indistinguishable particles. We show that EP ≤ EM, where EM is the bipartite entanglement calculated from the mode-occupation representation. Unlike EM, EP is super-additive. For example, EP = 0 for any single-particle state, but the state |1 |1 , where both modes are split between the two parties, has EP = 1/2. We discuss how this relates to quantum correlations between particles, for both fermions and bosons. PACS numbers: 03.65.Ta, 03.67.-a, 03.75.-b, 05.30.-d Entanglement lies at the heart of quantum mechanics, and is profoundly important in quantum information (QI) [1]. It might be thought that there is nothing new to be said about bipartite entanglement if the shared state |Ψ AB is pure. In ebits, the entanglement is simply [2]

Criteria for particle entanglement in many-body systems of bosons

Cornell University - arXiv, 2015

Basing on the analogy between the coherent states of light and separable states of N bosons, we demonstrate that the violation Cauchy-Schwarz inequality for any-order correlation function signals the entanglement among the constituent particles. Rather than restricting to the correlations between the positions of particles, we consider the broadest set of measurements allowed by quantum mechanics. Our result is general-it applies to any quantum system of bosons, even when the number of particles is not fixed, provided that there is no coherence between different number states. We also demonstrate that the compact expression for the separable state of bosons can be used to relate some known metrological quantities to the particle entanglement in a very simple way.

On Entanglement and Separability

We propose two necessary sufficient (NS) criteria to decide the separability of quantum states. They follow from two independent ideas: i) the Bloch-sphere-like-representation of states and ii) the proportionality of lines (rows, columns etc.) of certain multimatrix [1] associated with states. The second criterion proposes a natural way to determine the possible partial (or total, when possible) factorization of given multipartite state and in a sense can be used to determine the structure of the entanglement. We also introduce three entanglement measures based on the proposed new characterizations of entanglement. At last we discuss the second criterion mentioned above in the language of density matrix which is an inevitable language especially for mixed states.

Entanglement or Separability an introduction

2012

Quantum entanglement is a huge and active research field these days. Not only the philosophical aspects of these ’spooky’ features in quantum mechanics are quite interesting, but also the possibilities to make use of it in our everyday life is thrilling. In the last few years many possible applications, mostly within the ’Quantum Information’ field, have been developed. Of course to make use of this feature one demands tools to control entanglement in a certain sense. How can one define entanglement? How can one identify an entangled quantum system? Can entanglement be measured? These are questions one desires an answer for and indeed many answers have been found. However today entanglement is not yet fully in control by mathematics; many problems are still not solved. This paper aims to provide a theoretical introduction to get a feeling for the mathematical problems concerning entanglement and presents approaches to handle entanglement identification or entanglement measures for s...

Entangled identical particles and noise

2011

For systems of identical Bosons, it is necessary to reformulate the notions of separability and entanglement in algebraic terms shifting the emphasis from the particle aspect of first quantization to the mode description typical of second quantization. Within this new framework, we show that, unlike for systems consisting of distinguishable qubits, negativity is an exhaustive bipartite entanglement witness for systems with fixed number of Bosons; further, we investigate the impact of dephasing noise in relation to the use of such many-body Bosonic systems in metrological applications.

Separable and entangled states of composite quantum systems; Rigorous description

arXiv (Cornell University), 1997

We present a general description of separable states in Quantum Mechanics. In particular, our result gives an easy proof that inseparabitity (or entanglement) is a pure quantum (noncommutative) notion. This implies that distinction between separability and inseparabitity has sense only for composite systems consisting of pure quantum subsystems. Moreover, we provide the unified characterization of pure-state entanglement and mixed-state entanglement.