Related papers: Channel-State duality with centers

Channel-State duality with centers

URL: http://arxiv.org/abs/2404.16004v2
Date: Tue, 05 Nov 2024 00:55:03 GMT
Title: Channel-State duality with centers
Authors: Simon Langenscheidt, Eugenia Colafranceschi, Daniele Oriti,
Abstract summary: We study extensions of the mappings arising in usual channel-state duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with constraints. It has many physical applications from quantum many-body theory to holography and quantum gravity.
Score: 0.0
License:
Abstract: We study extensions of the mappings arising in usual channel-state duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with constraints, and it has many physical applications from quantum many-body theory to holography and quantum gravity. We establish that there is a general relationship between non-separability of the state and the isometric properties of the induced channel. We also provide a generalisation of our approach to algebras of trace-class operators on infinite dimensional Hilbert spaces.

Related papers

Entanglement in Algebraic Quantum Field Theories [0.0]
We present the mathematical structures needed for formulating AQFT in terms of the Haag Theory-Araki-Kastler (HAK) axioms and discuss their implications. We provide an extension to general globally hyperbolic spacetimes using the so-called Locally Covariant approach to QFT, which extends the HAK axioms to general spacetimes by means of the Category Theory language.
arXiv Detail & Related papers (2024-10-22T00:53:30Z)
The exponential Orlicz space in quantum information geometry [0.0]
We construct a quantum version of the exponential Orlicz space. We show that the constructed manifold admits a canonical divergence satisfying a Pythagorean relation.
arXiv Detail & Related papers (2023-01-13T09:38:34Z)
Continuous percolation in a Hilbert space for a large system of qubits [58.720142291102135]
The percolation transition is defined through the appearance of the infinite cluster. We show that the exponentially increasing dimensionality of the Hilbert space makes its covering by finite-size hyperspheres inefficient. Our approach to the percolation transition in compact metric spaces may prove useful for its rigorous treatment in other contexts.
arXiv Detail & Related papers (2022-10-15T13:53:21Z)
Trace class operators and states in p-adic quantum mechanics [0.0]
We show that one can define a suitable space of trace class operators in the non-Archimedean setting. The analogies, but also the several (highly non-trivial) differences, with respect to the case of standard quantum mechanics in a complex Hilbert space are analyzed.
arXiv Detail & Related papers (2022-10-04T12:44:22Z)
Self-adjoint extension schemes and modern applications to quantum Hamiltonians [55.2480439325792]
monograph contains revised and enlarged materials from previous lecture notes of undergraduate and graduate courses and seminars delivered by both authors over the last years on a subject that is central both in abstract operator theory and in applications to quantum mechanics. A number of models are discussed, which are receiving today new or renewed interest in mathematical physics, in particular from the point of view of realising certain operators of interests self-adjointly.
arXiv Detail & Related papers (2022-01-25T09:45:16Z)
Semiheaps and Ternary Algebras in Quantum Mechanics Revisited [0.0]
We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. New aspect of this work is a discussion of how symmetries of a quantum system induce homomorphisms of the relevant semiheaps and ternary algebras.
arXiv Detail & Related papers (2021-11-26T09:09:58Z)
Hilbert Space Fragmentation and Commutant Algebras [0.0]
We study the phenomenon of Hilbert space fragmentation in isolated Hamiltonian and Floquet quantum systems. We use the language of commutant algebras, the algebra of all operators that commute with each term of the Hamiltonian or each gate of the circuit.
arXiv Detail & Related papers (2021-08-23T18:00:01Z)
Scaling limits of lattice quantum fields by wavelets [62.997667081978825]
The renormalization group is considered as an inductive system of scaling maps between lattice field algebras. We show that the inductive limit of free lattice ground states exists and the limit state extends to the familiar massive continuum free field.
arXiv Detail & Related papers (2020-10-21T16:30:06Z)
Entanglement and Complexity of Purification in (1+1)-dimensional free Conformal Field Theories [55.53519491066413]
We find pure states in an enlarged Hilbert space that encode the mixed state of a quantum field theory as a partial trace. We analyze these quantities for two intervals in the vacuum of free bosonic and Ising conformal field theories.
arXiv Detail & Related papers (2020-09-24T18:00:13Z)
Preferred basis, decoherence and a quantum state of the Universe [77.34726150561087]
We review a number of issues in foundations of quantum theory and quantum cosmology. These issues can be considered as a part of the scientific legacy of H.D. Zeh.
arXiv Detail & Related papers (2020-06-28T18:07:59Z)
Quantum Geometric Confinement and Dynamical Transmission in Grushin Cylinder [68.8204255655161]
We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder. We retrieve those distinguished extensions previously identified in the recent literature, namely the most confining and the most transmitting.
arXiv Detail & Related papers (2020-03-16T11:37:23Z)

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