Fermionic systems for quantum information people

• URL: http://arxiv.org/abs/2006.03087v4
• Date: Fri, 10 Dec 2021 10:56:20 GMT
• Title: Fermionic systems for quantum information people
• Authors: Szil\'ard Szalay, Zolt\'an Zimbor\'as, Mih\'aly M\'at\'e, Gergely Barcza, Christian Schilling, \"Ors Legeza
• Abstract summary: We develop new tools for the treatment of fermionic systems. We consider variants of the notions of fermionic mode correlation and entanglement.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity superselection in the fermionic case on the other. We discuss these two fundamental differences extensively, and illustrate these through the Jordan--Wigner representation in a coherent, self-contained, pedagogical way, from the point of view of quantum information theory. Our perspective leads us to develop useful new tools for the treatment of fermionic systems, such as the fermionic (quasi-)tensor product, fermionic canonical embedding, fermionic partial trace, fermionic products of maps and fermionic embeddings of maps. We formulate these by direct, easily applicable formulas, without mode permutations, for arbitrary partitionings of the modes. It is also shown that fermionic reduced states can be calculated by the fermionic partial trace, containing the proper phase factors. We also consider variants of the notions of fermionic mode correlation and entanglement, which can be endowed with the usual, local operation based motivation, if the parity superselection rule is imposed. We also elucidate some other fundamental points, related to joint map extensions, which make the parity superselection inevitable in the description of fermionic systems.

Related papers

• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose [0.0]
  Entanglement of mixed quantum states can be quantified using the partial transpose and its corresponding entanglement measure, the logarithmic negativity. Recently, the notion of partial transpose has been extended to systems of anyons, which are exotic quasiparticles whose exchange statistics go beyond the bosonic and fermionic case.
  arXiv  Detail & Related papers  (2024-03-18T18:00:00Z)
• Fermionic anyons: entanglement and quantum computation from a resource-theoretic perspective [39.58317527488534]
  We develop a framework to characterize the separability of a specific type of one-dimensional quasiparticle known as a fermionic anyon. We map this notion of fermionic-anyon separability to the free resources of matchgate circuits. We also identify how entanglement between two qubits encoded in a dual-rail manner, as standard for matchgate circuits, corresponds to the notion of entanglement between fermionic anyons.
  arXiv  Detail & Related papers  (2023-06-01T15:25:19Z)
• Third quantization of open quantum systems: new dissipative symmetries and connections to phase-space and Keldysh field theory formulations [77.34726150561087]
  We reformulate the technique of third quantization in a way that explicitly connects all three methods. We first show that our formulation reveals a fundamental dissipative symmetry present in all quadratic bosonic or fermionic Lindbladians. For bosons, we then show that the Wigner function and the characteristic function can be thought of as ''wavefunctions'' of the density matrix.
  arXiv  Detail & Related papers  (2023-02-27T18:56:40Z)
• Fermionic Entanglement and Correlation [0.0]
  Entanglement plays a central role in numerous fields of quantum science. We show two natural pictures of defining fermionic entanglement: the particle picture and the mode picture. Both pictures reveal essential and interconnected aspects of fermionic entanglement.
  arXiv  Detail & Related papers  (2022-07-08T12:00:09Z)
• Topological transitions with continuously monitored free fermions [68.8204255655161]
  We show the presence of a topological phase transition that is of a different universality class than that observed in stroboscopic projective circuits. We find that this entanglement transition is well identified by a combination of the bipartite entanglement entropy and the topological entanglement entropy.
  arXiv  Detail & Related papers  (2021-12-17T22:01:54Z)
• Spectrum of localized states in fermionic chains with defect and adiabatic charge pumping [68.8204255655161]
  We study the localized states of a generic quadratic fermionic chain with finite-range couplings. We analyze the robustness of the connection between bands against perturbations of the Hamiltonian.
  arXiv  Detail & Related papers  (2021-07-20T18:44:06Z)
• Jordan-Wigner transformation and qubits with nontrivial exchange rule [91.3755431537592]
  Well-known (spinless) fermionic qubits may need more subtle consideration in comparison with usual (spinful) fermions. considered method has some relation with construction of super-spaces, but it has some differences with standard definition of supersymmety sometimes used for generalizations of qubit model.
  arXiv  Detail & Related papers  (2021-03-08T09:31:03Z)
• Quantum Operations in an Information Theory for Fermions [0.0]
  We introduce the physically allowed quantum operations, in congruence with the parity super-selection rule, that map the set of allowed fermionic states onto itself. We explicitly show the equivalence between these three representations of fermionic quantum operations.
  arXiv  Detail & Related papers  (2021-02-17T23:41:05Z)
• Linear-optical dynamics of one-dimensional anyons [0.0]
  We study the dynamics of bosonic and fermionic anyons defined on a one-dimensional lattice. We show how to exploit the Aharonov-Bohm effect exhibited by these particles to build a deterministic, entangling two-qubit gate. In particular we prove that, for a specific value of the exchange factor, an anyonic mirror can generate cat states.
  arXiv  Detail & Related papers  (2020-12-23T20:48:52Z)
• Models of zero-range interaction for the bosonic trimer at unitarity [91.3755431537592]
  We present the construction of quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered.
  arXiv  Detail & Related papers  (2020-06-03T17:54:43Z)
• Radiative topological biphoton states in modulated qubit arrays [105.54048699217668]
  We study topological properties of bound pairs of photons in spatially-modulated qubit arrays coupled to a waveguide. For open boundary condition, we find exotic topological bound-pair edge states with radiative losses. By joining two structures with different spatial modulations, we find long-lived interface states which may have applications in storage and quantum information processing.
  arXiv  Detail & Related papers  (2020-02-24T04:44:12Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.