Fermionic mode entanglement in quantum information

Abstract

We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped with a notion of subsystems in the absence of a global tensor product structure. We argue that any apparent similarities between fermionic modes and qubits are superficial and can only be applied in limited situations. In particular, we discuss the ambiguities that arise from different treatments of this subject. Our results are independent of the specific context of the fermionic fields as long as the canonical anti-commutation relations are satisfied, e.g., in relativistic quantum fields, or fermionic trapped ions.

v2: 9 pages, published version, minor format changes w.r.t. v1

References in corpus (32)

• Mixed State Entanglement and Quantum Error Correction
• A computable measure of entanglement
• Entanglement of Dirac fields in non-inertial frames
• Quantum Entanglement in Fermionic Lattices
• Quantum Correlations in Systems of Indistinguishable Particles
• Quantum Correlations in Two-Fermion Systems
• The entanglement of indistinguishable particles shared between two parties
• The Unruh effect in quantum information beyond the single-mode approximation
• General criterion for the entanglement of two indistinguishable particles
• Double-Occupancy Errors, Adiabaticity, and Entanglement of Spin-Qubits in Quantum Dots
• Quantum Correlations in Two-Boson Wavefunctions
• Gaussian measures of entanglement versus negativities: the ordering of two-mode Gaussian states
• A comparison of the entanglement measures negativity and concurrence
• Entanglement in a two-identical-particle system
• Entanglement in fermionic systems
• Entanglement of Dirac fields in an expanding spacetime
• Quantum Entanglement of Identical Particles
• Redistribution of particle and anti-particle entanglement in non-inertial frames
• Fermionic entanglement ambiguity in non-inertial frames
• Motion generates entanglement
• Entanglement in Relativistic Quantum Field Theory
• Residual entanglement of accelerated fermions is not nonlocal
• BCS-like Modewise Entanglement of Fermion Gaussian States
• Kinematic entanglement degradation of fermionic cavity modes
• Entanglement and Tensor Product Decomposition for Two Fermions
• Persistence of Tripartite Nonlocality for Non-inertial Observers
• Quantum gates and multipartite entanglement resonances realized by non-uniform cavity motion
• Natural mode entanglement as a resource for quantum communication
• Convergence of fermionic field entanglement at infinite acceleration in relativistic quantum information
• Comment on "Fermionic entanglement ambiguity in noninertial frames"
• Comment on "On two misconceptions in current relativistic quantum information"
• Ferreting out the Fluffy Bunnies: Entanglement constrained by Generalized superselection rules

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• Interference of Identical Particles from Entanglement to Boson-Sampling
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• Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories
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• Two-orbital quantum discord in fermion systems
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• From entanglement certification with quench dynamics to multipartite entanglement of interacting fermions
• Fermionic Entanglement in Superconducting Systems
• Quantum Operations in an Information Theory for Fermions
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• One-body information loss in fermion systems
• Fermionic state discrimination by local operations and classical communication
• Information-theoretical formulation of anyonic entanglement
• Nonlocal Entanglement of 1D Thermal States Induced by Fermion Exchange Statistics
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Degradability of Fermionic Gaussian Channels
• Classical and Quantum Orbital Correlations in the Molecular Electronic States
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• Tunable mode entanglement: topological Su-Schrieffer-Heeger (SSH) chain with an embedded Aharonov-Bohm quantum ring
• Multiple uncertainty relation for accelerated quantum information
• Probing Planckian physics in de Sitter space with quantum correlations
• A classification of Markovian fermionic Gaussian master equations
• Unambiguous discrimination of Fermionic states through local operations and classical communication
• Entropic distinguishability of quantum fields in phase space
• Renormalized entropy of entanglement in relativistic field theory
• Entanglement Witnessing for Lattice Gauge Theories
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• Exterior calculus and fermionic quantum computation
• Bipartite representations and many-body entanglement of pure states of $N$ indistinguishable particles
• Relativistic quantum information theory and quantum reference frames
• Photonic entanglement during a zero-g flight
• Decoherence of Dirac-particle quantumness for fermionic fields in a dilatonic black hole
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• Localised Systems in Relativistic Quantum Information
• Correlation energy and quantum correlations in a solvable model
• Decoherence of charge density waves in beam splitters for interacting quantum wires
• Information and majorization theory for fermionic phase-space distributions
• Spins extracted from fermionic states and their entanglement properties
• Non-local spin entanglement in a fermionic chain
• Quantum Statistical Mechanics of Electronically Open Molecules: Reduced Density Operators
• Analysis of quantum correlations within the ground state of a three level Lipkin model