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.
Highlights
In quantum mechanics, name-labels are assigned to identical particles making them distinguishable
In this work we aim at providing an advancement towards the straightforward description of quantum correlations in identical particle systems grounded on simple physical arguments which can unambiguously answer the general question: when and at which extent quantum particle indistinguishability assumes physical relevance in determining the entanglement among the particles? We present here a treatment of identical particles which, like the second quantization, does not resort to name labels yet adopting a particle-based formalism in terms of states
Indistinguishability requires that the identical particles cannot be individually addressed and, in accordance to quantum mechanics, introduction of unphysical quantities to treat them is unneeded
Summary
Name-labels are assigned to identical particles making them distinguishable. We present here a treatment of identical particles which, like the second quantization, does not resort to name labels yet adopting a particle-based (first quantization) formalism in terms of states This approach assumes that a many-particle state is a whole single object, characterized by a complete set of commuting observables, and quantifies the physical entanglement of bosons and fermions on the same footing by the same notions used for distinguishable particles such as the von Neumann entropy of partial trace. It allows the study of identical particle entanglement under arbitrary conditions of wave function overlap at the same complexity level required for nonidentical particles and, albeit presented here for two particles, it is straightforwardly generalizable to many-particle systems for scalability. Our approach quantitatively establishes the role of local measurements, particle nature and spatial overlap in assessing identical particle entanglement, supplying theoretical support to very recent experimental observations of entangling operations for identical atoms
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