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arXiv:quant-ph/0101093 · Physical Review Letters

Generic Entanglement Generation, Quantum Statistics, and Complementarity

Sougato Bose, Dipankar Home

Published Jan 23, 2002• 111 citations
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Abstract

A general and an arbitrarily efficient scheme for entangling the spins (or any spinlike degree of freedom) of two independent uncorrelated identical particles by a combination of two particle interferometry and which way detection is formulated. It is shown that the same setup could be used to identify the quantum statistics of the incident particles from either the sign or the magnitude of measured spin correlations. Our setup also exhibits a curious complementarity between particle distinguishability and the amount of generated entanglement.

DOI
10.1103/physrevlett.88.050401

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A general and an arbitrarily efficient scheme for entangling the spins (or any spinlike degree of freedom) of two independent uncorrelated identical particles by a combination of two particle interferometry and which way detection is formulated. It is shown that the same setup could be used to identify the quantum statistics of the incident particles from either the sign or the magnitude of measured spin correlations. Our setup also exhibits a curious complementarity between particle distinguishability and the amount of generated entanglement.
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Significance Entanglement as a fundamental concept of quantum physics is manifested in correlations between particles. The correlation between two particles is usually measured by detecting both of them. Here, we present the results of an experiment based on a unique concept, where the momentum correlation between two photons is measured by detecting only one of them. This measurement is possible by exploiting the quantum mechanical complementarity between path-distinguishability and interference. Our approach can potentially be generalized to measure other higher-order correlations in lower order, which would enable experimental access to a broader class of correlated quantum systems, particularly in situations in which technical limitations make it impossible to efficiently detect one of the correlated particles.
The controlled generation and identification of quantum correlations, usually encoded in either qubits or continuous degrees of freedom, builds the foundation of quantum information science. Recently, more sophisticated approaches, involving a combination of two distinct degrees of freedom, have been proposed to improve on the traditional strategies. Hyperentanglement describes simultaneous entanglement in more than one distinct degree of freedom, whereas hybrid entanglement refers to entanglement shared between a discrete and a continuous degree of freedom. In this work we propose a scheme that allows us to combine the two approaches, and to extend them to the strongest form of quantum correlations. Specifically, we show how two identical, initially separated particles can be manipulated to produce Bell nonlocality among their spins, among their momenta, as well as across their spins and momenta. We discuss possible experimental realizations with atomic and photonic systems.
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.
Identical particles have dynamically invariant labels in all setups where their degrees of freedom can be partitioned into two parts, which we call internal and visible, with the visible part subject to unitary evolution, while the dynamically invariant internal part accounts for the partial distinguishability of particles. We give the explicit form of the visible state in terms of the indistinguishability function, generalizing the standard symmetrization/antisymmetrization postulate for bosons/fermions with internal modes. The indistinguishability function on the symmetric group accounts for the permutation symmetry of the dynamically invariant label state and gives a self-contained description of the symmetry spectrum of the visible state. It is shown that the indistinguishability of single particles emitted independently from a stable source is completely characterized by the projective measures on the symmetry spectrum. We reveal a hierarchy of successive upper bounds on the projective measure of indistinguishability in terms of marginal projective measures. We point out an experimentally feasible way to get the upper bounds on the indistinguishability of an arbitrarily large number of single photons by direct experimental readout of their marginal projective measures. We also analyze the indistinguishability of coherent superpositions and convex mixtures and resolve a recently posed problem.
All identical particles are inherently correlated from the outset, regardless of how far apart their creation took place. In this paper, this fact is used for extraction of entanglement from independent particles unaffected by any interactions. Specifically, we are concerned with operational schemes for generation of all tripartite entangled states, essentially the GHZ state and the W state, which prevent the particles from touching one another over the entire evolution. The protocols discussed in the paper require only three particles in linear optical setups with equal efficiency for boson, fermion or anyon statistics. Within this framework indistinguishability of particles presents itself as a useful resource of entanglement accessible for practical applications.