Dealing with indistinguishable particles and their entanglement

Abstract

Here, we discuss a particle-based approach to deal with systems of many identical quantum objects (particles) that never employs labels to mark them. We show that it avoids both methodological problems and drawbacks in the study of quantum correlations associated with the standard quantum mechanical treatment of identical particles. The core of this approach is represented by the multiparticle probability amplitude, whose structure in terms of single-particle amplitudes we derive here by first principles. To characterize entanglement among the identical particles, this new method uses the same notions, such as partial trace, adopted for non-identical ones. We highlight the connection between our approach and second quantization. We also define spin-exchanged multipartite states which contain a generalization of W states to identical particles. We prove that particle spatial overlap plays a role in the distributed entanglement within multipartite systems and is responsible for the appearance of non-local quantum correlations.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.

Effects of Indistinguishability in a System of Three Identical Qubits

“…Let us consider three identical qubits, each in the state |ϕ k σ k ≡ |ϕ k ⊗ |σ k (k = 1, 2, 3), where ϕ k is the k-th spatial wavefunction and σ k is the corresponding pseudospin ↑, ↓ (e.g., components of a spin-1/2 fermion, two energy levels of a boson, horizontal H and vertical V polarizations of a photon). Using the NSA [9], the three-qubit elementary state is |Φ (3) = |ϕ 1 σ 1 , ϕ 2 σ 2 , ϕ 3 σ 3 , which cannot be separated in terms of tensor products of single-qubit states: it must be meant as an overall object representing a list of the single-particle states.…”

“…1(a). Considering all the possible bipartitions (AB)-C, (CA)-B, (BC)-A of the three-particle system, by performing localized projective measurements and partial traces [9] one finds that all the three bipartitions give pure one-particle and two-particle reduced density matrices. Following conventional wisdom this state is, as expected, fully uncorrelated [11].…”

Quantum entanglement in one-dimensional anyons

“…We can recast the above idea in the language of second quantization. If |Φ is an N -particle state, its inner product with a single-particle state |ψ k is [15] a ψ k |Φ ≡ ψ k | · |Φ Note that since a ψ k is an annihilation operator, the left hand side of the above equation represents an (N − 1)-particle state which, by definition, is the inner product on the right hand side. As mentioned earlier, this simple expedient allows us to go beyond bosons and fermions by suitably generalising the operator algebra.…”

Indistinguishability-enabled coherence for quantum metrology

“…In this Letter, we generalize the resource theory of coherence to systems of identical particles, using a particle-based approach that only allows physical labels to address the particles in the system [19,20]. Our aim is to show how indistinguishability may be a source of operational coherence.…”

“…Coherence of identical particle states. -Let us consider, in the no-label formalism [19][20][21], two identical spins (that is particles with a two-level internal state space) in the mixed state…”