"Commutator formalism" for pairs correlated through Schmidt decomposition as used in Quantum Information

Abstract

To easily calculate statistical properties of pairs correlated through Schmidt decomposition, as commonly used in Quantum Information, we propose a "commutator formalism" for these single-index pairs, somewhat simpler than the one we developed for double-index Wannier excitons. We use it here to get the pair number threshold for bosonic behavior of $N$ pairs through the requirement that their number operator mean value must stay close to $N$. While the main term of this mean value is controlled by the second moment of the Schmidt distribution, so that to increase this threshold, we must increase the Schmidt number, higher momenta appearing at higher orders lead to choosing a distribution as flat as possible.

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• Criteria for two distinguishable fermions to behave like a boson
• Composite boson many-body theory for Frenkel excitons
• "Moth-eaten effect" driven by Pauli blocking, revealed for Cooper pairs
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Cited by in corpus (18)

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• Two-boson composites
• Quantum information approach to Bose-Einstein condensation of composite bosons
• Coherent states of composite bosons
• Statistical signatures of states orthogonal to the Fock-state ladder of composite bosons
• Influence of the Pauli exclusion principle on scattering properties of cobosons
• On the description of composite bosons in discrete models
• Assembly of 2N entangled fermions into multipartite composite bosons
• Strongly bound fermion pairs on a ring: a composite-boson approach
• On dynamical stability of composite quantum particles: when entanglement is enough and when interaction is needed
• Ground state of composite bosons in low-dimensional graphs
• Partition function of N composite bosons
• Effect of Pauli blocking on coherent states of composite bosons
• Nonlocal bunching of composite bosons