Quantum entanglement of identical particles by standard information-theoretic notions

Abstract

Quantum entanglement of identical particles is essential in quantum information theory. Yet, its correct determination remains an open issue hindering the general understanding and exploitation of many-particle systems. Operator-based methods have been developed that attempt to overcome the issue. Here we introduce a state-based method which, as second quantization, does not label identical particles and presents conceptual and technical advances compared to the previous ones. It establishes the quantitative role played by arbitrary wave function overlaps, local measurements and particle nature (bosons or fermions) in assessing entanglement by notions commonly used in quantum information theory for distinguishable particles, like partial trace. Our approach furthermore shows that bringing identical particles into the same spatial location functions as an entangling gate, providing fundamental theoretical support to recent experimental observations with ultracold atoms. These results pave the way to set and interpret experiments for utilizing quantum correlations in realistic scenarios where overlap of particles can count, as in Bose-Einstein condensates, quantum dots and biological molecular aggregates.

Universality of Schmidt decomposition and particle identity

“…40. Hereafter, we mean by “symmetric states” (or “symmetric Hilbert space”) the symmetric or antisymmetric behavior of the system states depending on the bosonic or fermionic nature of the particles, respectively.…”

“…Analogously, we have (this wedge product will be crucial in demonstrating the theorem below). The probability amplitude of finding the two particles in if they are in | ϕ, ψ 〉, is obtained by the symmetric two-particle scalar product defined in terms of one-particle amplitudes as40…”

“…The state | ϕ, ψ 〉 spans a linear symmetric two-particle Hilbert space . A symmetric inner product between state spaces of different dimensionality (one-particle projective measurement) can also be introduced as40…”

“…Using a recent non-standard particle-based approach40, here we develop a SD valid for both bosons and fermions, which allows the direct characterization of the physical entanglement of the particles. Differently from previous viewpoints, application of this method to the paradigmatic example exposed above allows, without resorting to extraction, to demonstrate that entanglement is zero for separated particles and nonzero when they overlap.…”

Generation and protection of steady-state quantum correlations due to quantum channels with memory

“…Entanglement is a special type of quantum correlations, and it has been proven to be very important for quantum communication networks and quantum computations [2,3]. On the other hand, quantum discord which captures more general quantum correlations than entanglement, has initially been introduced by Olliver and Zurek [4].…”