Abstract
We construct quantum coherence resource theories in symmetrized Fock space (QCRTF), thereby providing an information-theoretic framework that connects analyses of quantum coherence in discrete-variable (DV) and continuous variable (CV) bosonic systems. Unlike traditional quantum coherence resource theories, QCRTF can be made independent of the single-particle basis and allow to quantify coherence within and between particle number sectors. For example, QCRTF can be formulated in such a way that neither Bose-Einstein condensates nor Heisenberg-Weyl coherent states are considered as quantum many-body coherence resources, whereas spin-squeezed and quadrature squeezed states are. The QCRTF framework is utilized to calculate the optimal asymptotic distillation rate of maximally correlated bosonic states both for particle number conserving resource states and resource states of indefinite particle number. In particular, we show how to generate a uniform superposition of maximally correlated bosonic states from a state of maximal bosonic coherence with asymptotically unit efficiency using only free operations in the QCRTF.
Highlights
Protocols for transferring quantum coherence from discrete variable (DV) quantum systems to continuous variable (CV) quantum systems, and vice versa, provide vital links between quantum information processing platforms [1]
Other quantum information processing protocols that can be analyzed using the QCRTF framework include the distillation of Gaussian entanglement from non-Gaussian states reported in Ref.[7], which involves only linear optical unitary operations (which are in EM(B,C)) and local vacuum projections (which are in EMA ; vacuum projections on M − 1 modes are in EM(A,B,C))
We have introduced and analyzed three versions of QCRTF that allow a wide variety of DV and CV quantum information processing protocols to be considered within a unified resource theoretic framework
Summary
Protocols for transferring quantum coherence from discrete variable (DV) quantum systems to continuous variable (CV) quantum systems, and vice versa, provide vital links between quantum information processing platforms [1]. We take this idea further to define three interrelated quantum coherence resource theories on bosonic Fock space (QCRTF) that provide a framework to analyze quantum coherence in DV and CV bosonic quantum systems These QCRTF exhibit fundamental differences from traditional QCRTs. For example, the free states in the QCRTFs defined in this work do not necessarily have fixed particle number, and two of the QCRTFs are independent of the single particle basis. This approach yields the asymptotic distillation rate of maximally correlated states from Bose-Einstein condensates, pair correlated states [18], and states of indefinite particle number possessing maximal coherence. M j=1 a∗j aj denotes the particle number operator, and NM (ρ) := trNM ρ denotes the particle number functional
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