Mutual compatibility/incompatibility of quasi-Hermitian quantum observables

• URL: http://arxiv.org/abs/2505.00791v1
• Date: Thu, 01 May 2025 18:41:27 GMT
• Title: Mutual compatibility/incompatibility of quasi-Hermitian quantum observables
• Authors: Miloslav Znojil,
• Abstract summary: In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_jneq A_jdagger$, $j=1,2, ldots,K$.<n>In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $Thetaneq I$.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In the framework of quasi-Hermitian quantum mechanics the eligible operators of observables may be non-Hermitian, $A_j\neq A_j^\dagger$, $j=1,2, \ldots,K$. In principle, the standard probabilistic interpretation of the theory can be re-established via a reconstruction of physical inner-product metric $\Theta\neq I$ guaranteeing the quasi-Hermiticity $A_j^\dagger \,\Theta=\Theta\,A_j$. The task is easy at $K=1$ because there are many eligible metrics $\Theta=\Theta(A_1)$. In our paper the next case with $K=2$ is analyzed. The criteria of the existence of a shared metric $\Theta=\Theta(A_1,A_2)$ are presented and discussed.

Related papers

• Measuring quantum relative entropy with finite-size effect [53.64687146666141]
  We study the estimation of relative entropy $D(rho|sigma)$ when $sigma$ is known.<n>Our estimator attains the Cram'er-Rao type bound when the dimension $d$ is fixed.
  arXiv  Detail & Related papers  (2024-06-25T06:07:20Z)
• Quantum connection, charges and virtual particles [65.268245109828]
  A quantum bundle $L_hbar$ is endowed with a connection $A_hbar$ and its sections are standard wave functions $psi$ obeying the Schr"odinger equation. We will lift the bundles $L_Cpm$ and connection $A_hbar$ on them to the relativistic phase space $T*R3,1$ and couple them to the Dirac spinor bundle describing both particles and antiparticles.
  arXiv  Detail & Related papers  (2023-10-10T10:27:09Z)
• Three alternative model-building strategies using quasi-Hermitian time-dependent observables [0.0]
  The theory is called non-Hermitian interaction-picture, NIP. In our paper the key role played by identity $H(t)=G(t)+Sigma(t)$ is shown to imply that there exist just three alternative meaningful implementations of the NIP approach.
  arXiv  Detail & Related papers  (2023-08-15T07:35:42Z)
• Systematics of quasi-Hermitian representations of non-Hermitian quantum models [0.0]
  This paper introduces and describes a set of constructive returns of the description to one of the correct and eligible physical Hilbert spaces $cal R_N(0)$. In the extreme of the theory the construction is currently well known and involves solely the inner product metric $Theta=Theta(H)$. At $j=N$ the inner-product metric remains trivial and only the Hamiltonian must be Hermitized, $H to mathfrakh = Omega,H,Omega-1=mathfrak
  arXiv  Detail & Related papers  (2022-12-07T20:10:58Z)
• Enlarging the notion of additivity of resource quantifiers [62.997667081978825]
  Given a quantum state $varrho$ and a quantifier $cal E(varrho), it is a hard task to determine $cal E(varrhootimes N)$. We show that the one shot distillable entanglement of certain spherically symmetric states can be quantitatively approximated by such an augmented additivity.
  arXiv  Detail & Related papers  (2022-07-31T00:23:10Z)
• Factorized Hilbert-space metrics and non-commutative quasi-Hermitian observables [0.0]
  It is well known that an (in general, non-commutative) set of non-Hermitian operators $Lambda_j$ with real eigenvalues need not necessarily represent observables. We describe a specific class of quantum models in which these operators plus the underlying physical Hilbert-space metric $Theta$ are all represented.
  arXiv  Detail & Related papers  (2022-06-27T18:33:03Z)
• Monogamy of entanglement between cones [68.8204255655161]
  We show that monogamy is not only a feature of quantum theory, but that it characterizes the minimal tensor product of general pairs of convex cones. Our proof makes use of a new characterization of products of simplices up to affine equivalence.
  arXiv  Detail & Related papers  (2022-06-23T16:23:59Z)
• Feasibility and method of multi-step Hermitization of crypto-Hermitian quantum Hamiltonians [0.0]
  We build unitary models using non-Hermitian Hamiltonians (i.e., $H neq Hdagger$) which are Hermitizable. The necessary Hermiticity of the Hamiltonian $H = Hddagger$ can be achieved by the mere metric-mediated amendment $langle psi_a|psi_brangle$ to the inner product.
  arXiv  Detail & Related papers  (2022-03-05T07:24:51Z)
• Uncertainties in Quantum Measurements: A Quantum Tomography [52.77024349608834]
  The observables associated with a quantum system $S$ form a non-commutative algebra $mathcal A_S$. It is assumed that a density matrix $rho$ can be determined from the expectation values of observables. Abelian algebras do not have inner automorphisms, so the measurement apparatus can determine mean values of observables.
  arXiv  Detail & Related papers  (2021-12-14T16:29:53Z)
• Simplest non-additive measures of quantum resources [77.34726150561087]
  We study measures that can be described by $cal E(rhootimes N) =E(e;N) ne Ne$.
  arXiv  Detail & Related papers  (2021-06-23T20:27:04Z)
• Anisotropy and asymptotic degeneracy of the physical-Hilbert-space inner-product metrics in an exactly solvable crypto-unitary quantum model [0.0]
  In quantum mechanics only the knowledge of a complete set of observables $Lambda_j$ enables us to declare the related physical inner product. In our present paper we describe a strictly non-numerical $N$ by $N$ matrix model in which such a restriction is replaced by another.
  arXiv  Detail & Related papers  (2012-12-04T14:22:48Z)

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.