Continuous majorization in quantum phase space

• URL: http://arxiv.org/abs/2108.09167v2
• Date: Mon, 15 May 2023 17:09:23 GMT
• Title: Continuous majorization in quantum phase space
• Authors: Zacharie Van Herstraeten, Michael G. Jabbour and Nicolas J. Cerf
• Abstract summary: We show that majorization theory provides an elegant and very natural approach to exploring the information-theoretic properties of Wigner functions in phase space. We conjecture a fundamental majorization relation: any positive Wigner function is majorized by the Wigner function of a Gaussian pure state. Our main result is then to prove this fundamental majorization relation for a relevant subset of Wigner-positive quantum states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We explore the role of majorization theory in quantum phase space. To this purpose, we restrict ourselves to quantum states with positive Wigner functions and show that the continuous version of majorization theory provides an elegant and very natural approach to exploring the information-theoretic properties of Wigner functions in phase space. After identifying all Gaussian pure states as equivalent in the precise sense of continuous majorization, which can be understood in light of Hudson's theorem, we conjecture a fundamental majorization relation: any positive Wigner function is majorized by the Wigner function of a Gaussian pure state (especially, the bosonic vacuum state or ground state of the harmonic oscillator). As a consequence, any Schur-concave function of the Wigner function is lower bounded by the value it takes for the vacuum state. This implies in turn that the Wigner entropy is lower bounded by its value for the vacuum state, while the converse is notably not true. Our main result is then to prove this fundamental majorization relation for a relevant subset of Wigner-positive quantum states which are mixtures of the three lowest eigenstates of the harmonic oscillator. Beyond that, the conjecture is also supported by numerical evidence. We conclude by discussing some implications of this conjecture in the context of entropic uncertainty relations in phase space.

Related papers

• Complex-valued Wigner entropy of a quantum state [0.0]
  We argue the merits of defining a complex-valued entropy associated with any Wigner function. It is anticipated that the complex plane yields a proper framework for analyzing the entropic properties of quasiprobability distributions in phase space.
  arXiv  Detail & Related papers  (2023-10-30T06:30:03Z)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum [77.34726150561087]
  We study phase transitions occurring in the stationary state of the dynamics of integrable many-body non-Hermitian Hamiltonians. We observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian.
  arXiv  Detail & Related papers  (2023-01-18T09:26:02Z)
• Shannon theory for quantum systems and beyond: information compression for fermions [68.8204255655161]
  We show that entanglement fidelity in the fermionic case is capable of evaluating the preservation of correlations. We introduce a fermionic version of the source coding theorem showing that, as in the quantum case, the von Neumann entropy is the minimal rate for which a fermionic compression scheme exists.
  arXiv  Detail & Related papers  (2021-06-09T10:19:18Z)
• Quantum Wigner entropy [0.0]
  We define the Wigner entropy of a quantum state as the differential Shannon entropy of the Wigner function of the state. We conjecture that it is lower bounded by $lnpi +1$ within the convex set of Wigner-positive states. The Wigner entropy is anticipated to be a significant physical quantity, for example, in quantum optics.
  arXiv  Detail & Related papers  (2021-05-26T21:12:50Z)
• In Wigner phase space, convolution explains why the vacuum majorizes mixtures of Fock states [0.0]
  I show that a nonnegative Wigner function that represents a mixture of Fock states is majorized by the Wigner function of the vacuum state. Findings presented in this article might be expanded upon to explain why the Wigner function of the vacuum majorizes.
  arXiv  Detail & Related papers  (2021-04-30T13:28:43Z)
• Interplay between transport and quantum coherences in free fermionic systems [58.720142291102135]
  We study the quench dynamics in free fermionic systems. In particular, we identify a function, that we dub emphtransition map, which takes the value of the stationary current as input and gives the value of correlation as output.
  arXiv  Detail & Related papers  (2021-03-24T17:47:53Z)
• On quantum states with a finite-dimensional approximation property [0.0]
  We consider a class of quantum states containing finite rank states containing infinite rank states with the sufficient rate decreasing of eigenvalues. We show that this property implies finiteness of the entropy von Neumann entropy but unsolved the question concerning the converse implication. We establish the uniform continuity of the above characteristics as functions of a channel w.r.t.
  arXiv  Detail & Related papers  (2021-03-17T13:15:04Z)
• Quantifying Entanglement with Coherence [0.0]
  Entment coherence is essentially the normalized coherence of the entangled state in its Schmidt basis. Entment coherence turns out to be closely related to the unified entropy of the reduced state of one of the subsystems.
  arXiv  Detail & Related papers  (2020-11-25T19:01:04Z)
• 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)
• Probing eigenstate thermalization in quantum simulators via fluctuation-dissipation relations [77.34726150561087]
  The eigenstate thermalization hypothesis (ETH) offers a universal mechanism for the approach to equilibrium of closed quantum many-body systems. Here, we propose a theory-independent route to probe the full ETH in quantum simulators by observing the emergence of fluctuation-dissipation relations. Our work presents a theory-independent way to characterize thermalization in quantum simulators and paves the way to quantum simulate condensed matter pump-probe experiments.
  arXiv  Detail & Related papers  (2020-07-20T18:00:02Z)

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.