Canonical Quantum Coarse-Graining and Surfaces of Ignorance
- URL: http://arxiv.org/abs/2111.07836v1
- Date: Mon, 15 Nov 2021 15:23:38 GMT
- Title: Canonical Quantum Coarse-Graining and Surfaces of Ignorance
- Authors: Shannon Ray, Paul M. Alsing, Carlo Cafaro, and Shelton Jacinto
- Abstract summary: We use negentropy to connect ignorance as measured by quantum information entropy and ignorance related to quantum coarse-graining.
Our procedure reproduces features of Boltzmann's original coarse-graining by showing that the majority of phase space consists of states near or at equilibrium.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper we introduce a canonical quantum coarse-graining and use
negentropy to connect ignorance as measured by quantum information entropy and
ignorance related to quantum coarse-graining. For our procedure, macro-states
are the set of purifications $\{|\bar{\Gamma}^{\rho}\rangle\}$ associated with
density operator $\rho$ and micro-states are elements of
$\{|\bar{\Gamma}^{\rho}\rangle\}$. Unlike other quantum coarse-graining
procedures, ours always gives a well-defined unique coarse-graining of phase
space. Our coarse-graining is also unique in that the volumes of phase space
associated with macro-states are computed from differential manifolds whose
metric components are constructed from the Lie group symmetries that generate
$\{|\bar{\Gamma}^{\rho}\rangle\}$. We call these manifolds surfaces of
ignorance, and their volumes quantify the lack of information in $\rho$ as
measured by quantum information entropies. To show that these volumes behave
like information entropies, we compare them to the von Neumann and linear
entropies for states whose symmetries are given by $SO(3)$, $SU(2)$, and
$SO(N)$. We also show that our procedure reproduces features of Boltzmann's
original coarse-graining by showing that the majority of phase space consists
of states near or at equilibrium. As a consequence of this coarse-graining, it
is shown that an inherent flag variety structure underlies composite Hilbert
spaces.
Related papers
- Measurement-induced Lévy flights of quantum information [38.68022950138448]
We explore a model of free fermions in one dimension subject to frustrated local measurements across adjacent sites.
For maximal misalignment, superdiffusive behavior emerges from the vanishing of the measurement-induced quasiparticle decay rate.
Our findings show how intricate fractal-scaling entanglement can be produced for local Hamiltonians.
arXiv Detail & Related papers (2025-01-22T14:29:13Z) - Exact path integrals on half-line in quantum cosmology with a fluid clock and aspects of operator ordering ambiguity [0.0]
We perform $textitexact$ half-line path integral quantization of flat, homogeneous cosmological models containing a perfect fluid acting as an internal clock.
We argue that a particular ordering prescription in the quantum theory can preserve two symmetries.
arXiv Detail & Related papers (2025-01-20T19:00:02Z) - Quantum Homogenization as a Quantum Steady State Protocol on NISQ Hardware [42.52549987351643]
Quantum homogenization is a reservoir-based quantum state approximation protocol.
We extend the standard quantum homogenization protocol to the dynamically-equivalent ($mathttSWAP$)$alpha$ formulation.
We show that our proposed protocol yields a completely positive, trace preserving (CPTP) map under which the code subspace is correctable.
arXiv Detail & Related papers (2024-12-19T05:50:54Z) - Geometry of degenerate quantum states, configurations of $m$-planes and invariants on complex Grassmannians [55.2480439325792]
We show how to reduce the geometry of degenerate states to the non-abelian connection $A$.
We find independent invariants associated with each triple of subspaces.
Some of them generalize the Berry-Pancharatnam phase, and some do not have analogues for 1-dimensional subspaces.
arXiv Detail & Related papers (2024-04-04T06:39:28Z) - Mixed-state quantum anomaly and multipartite entanglement [8.070164241593814]
We show a surprising connection between mixed state entanglement and 't Hooft anomaly.
We generate simple examples of mixed states with nontrivial long-ranged multipartite entanglement.
We also analyze mixed anomaly involving both strong and weak symmetries.
arXiv Detail & Related papers (2024-01-30T19:00:02Z) - Topological Quantum Computation on Supersymmetric Spin Chains [0.0]
Quantum gates built out of braid group elements form the building blocks of topological quantum computation.
We show that the fusion spaces of anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains.
arXiv Detail & Related papers (2022-09-08T13:52:10Z) - A Differential-Geometric Approach to Quantum Ignorance Consistent with
Entropic Properties of Statistical Mechanics [0.0]
We show that the volume behaves like the von Neumann entropy in that it is zero for pure states, maximal for maximally mixed states, and is a concave function w.r.t the purity of $rho_S$.
arXiv Detail & Related papers (2022-08-08T13:43:50Z) - Geometric relative entropies and barycentric Rényi divergences [16.385815610837167]
monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
We show that monotone quantum relative entropies define monotone R'enyi quantities whenever $P$ is a probability measure.
arXiv Detail & Related papers (2022-07-28T17:58:59Z) - Annihilating Entanglement Between Cones [77.34726150561087]
We show that Lorentz cones are the only cones with a symmetric base for which a certain stronger version of the resilience property is satisfied.
Our proof exploits the symmetries of the Lorentz cones and applies two constructions resembling protocols for entanglement distillation.
arXiv Detail & Related papers (2021-10-22T15:02:39Z) - Anomalous Quantum Information Scrambling for $\mathbb{Z}_3$ Parafermion
Chains [0.0]
Parafermions are exotic quasiparticles with non-Abelian fractional statistics.
We study the scrambling of quantum information in one-dimensional parafermionic chains.
arXiv Detail & Related papers (2021-03-24T19:00:04Z) - Complete entropic inequalities for quantum Markov chains [17.21921346541951]
We prove that every GNS-symmetric quantum Markov semigroup on a finite dimensional algebra satisfies a modified log-Sobolev inequality.
We also establish the first general approximateization property of relative entropy.
arXiv Detail & Related papers (2021-02-08T11:47:37Z)
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.