Optimal reference states for maximum accessible entanglement under the local particle number superselection rule

Abstract

Global conservation laws imply superselection rules (SSR) which restrict the operations that are possible on any given state. Imposing the additional constraint of local operations and classical communication (LOCC) forbids the transfer of quantum systems between spatially separated sites. In the case of particle conservation this imposes a SSR for local particle number. That is, the coherences between subspaces of fixed particle number at each site are not accessible and any state is therefore equivalent to its projection onto these subspaces. The accessible entanglement under the SSR is less than (or equal to) that available in the absence of the SSR. An ancilla can be used as a reference system to increase the amount of accessible entanglement. We examine the relationship between local particle number uncertainty and the accessible entanglement and consider the optimal reference states for recovering entanglement from certain systems. In particular we derive the optimal ancilla state for extracting entanglement for a single shared particle and make steps towards the optimum for general systems.

arXiv comment14 pages, 6 figures, clarified a key result but otherwise mostly minor changes

References in corpus (18)

• Reference frames, superselection rules, and quantum information
• The entanglement of indistinguishable particles shared between two parties
• Optimal states and almost optimal adaptive measurements for quantum interferometry
• Classical and quantum communication without a shared reference frame
• Tradeoff between extractable mechanical work, accessible entanglement, and ability to act as a reference system, under arbitrary superselection rules
• Entanglement constrained by superselection rules
• Uncertainty Relations for Joint Measurements of Noncommuting Observables
• Entanglement of indistinguishable particles in condensed matter physics
• Decoherence-full subsystems and the cryptographic power of a private shared reference frame
• Optimal measurements for relative quantum information
• Quantifying the resource of sharing a reference frame
• Quantum reference frames and deformed symmetries
• Comment on "Some implications of the quantum nature of laser fields for quantum computations"
• Entanglement of identical particles and reference phase uncertainty
• Entanglement and Symmetry: A Case Study in Superselection Rules, Reference Frames, and Beyond
• Constraints for quantum logic arising from conservation laws and field fluctuations
• Decoherence of a two-state atom driven by coherent light
• Relative states, quantum axes and quantum references

Cited by in corpus (6)

• Relating the Resource Theories of Entanglement and Quantum Coherence
• Essential entanglement for atomic and molecular physics
• Entanglement in indistinguishable particle systems
• Quantum entanglement from random measurements
• New Spin Squeezing and Other Entanglement Tests for Two Mode Systems of Identical Bosons
• Reference frames for Bell inequality violation in the presence of superselection rules