Repeatability of measurements: NonHermitian observables and quantum Coriolis force
Abstract
A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of nonHermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that nonHermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems onto nonHermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.
 Authors:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Univ. of Silesia, Katowice (Poland). Inst. of Physics
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Center for Nonlinear Studies
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1414087
 Report Number(s):
 LAUR1621217
Journal ID: ISSN 24699926; PLRAAN
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Journal Article: Accepted Manuscript
 Journal Name:
 Physical Review A
 Additional Journal Information:
 Journal Volume: 94; Journal Issue: 2; Journal ID: ISSN 24699926
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Atomic and Nuclear Physics; Quantum measurement, quantum mechanics
Citation Formats
Gardas, Bartłomiej, Deffner, Sebastian, and Saxena, Avadh. Repeatability of measurements: NonHermitian observables and quantum Coriolis force. United States: N. p., 2016.
Web. doi:10.1103/PhysRevA.94.022121.
Gardas, Bartłomiej, Deffner, Sebastian, & Saxena, Avadh. Repeatability of measurements: NonHermitian observables and quantum Coriolis force. United States. doi:10.1103/PhysRevA.94.022121.
Gardas, Bartłomiej, Deffner, Sebastian, and Saxena, Avadh. 2016.
"Repeatability of measurements: NonHermitian observables and quantum Coriolis force". United States.
doi:10.1103/PhysRevA.94.022121. https://www.osti.gov/servlets/purl/1414087.
@article{osti_1414087,
title = {Repeatability of measurements: NonHermitian observables and quantum Coriolis force},
author = {Gardas, Bartłomiej and Deffner, Sebastian and Saxena, Avadh},
abstractNote = {A noncommuting measurement transfers, via the apparatus, information encoded in a system's state to the external “observer.” Classical measurements determine properties of physical objects. In the quantum realm, the very same notion restricts the recording process to orthogonal states as only those are distinguishable by measurements. Thus, even a possibility to describe physical reality by means of nonHermitian operators should volens nolens be excluded as their eigenstates are not orthogonal. We show that nonHermitian operators with real spectra can be treated within the standard framework of quantum mechanics. Further, we propose a quantum canonical transformation that maps Hermitian systems onto nonHermitian ones. Similar to classical inertial forces this map is accompanied by an energetic cost, pinning the system on the unitary path.},
doi = {10.1103/PhysRevA.94.022121},
journal = {Physical Review A},
number = 2,
volume = 94,
place = {United States},
year = 2016,
month = 8
}
Web of Science

Calculations of timedependent observables in nonHermitian quantum mechanics: The problem and a possible solution
The solutions of the timeindependent Schroedinger equation for nonHermitian (NH) Hamiltonians have been extensively studied and calculated in many different fields of physics by using L{sup 2} methods that originally have been developed for the calculations of bound states. The existing nonHermitian formalism breaks down when dealing with wave packets (WPs). An open question is how timedependent expectation values can be calculated when the Hamiltonian is NH? Using the Fproduct formalism that was recently proposed by Moiseyev and Lein [J. Phys. Chem. 107, 7181 (2003)] we calculate the timedependent expectation values of different observable quantities for a simple wellknown studymore » 
Universal quantum computation using exchange interactions and measurements of single and twospin observables
We show how to construct a universal set of quantum logic gates using control over exchange interactions and single and twospin measurements only. Singlespin unitary operations are teleported between neighboring spins instead of being executed directly, thus potentially eliminating a major difficulty in the construction of several of the most promising proposals for solidstate quantum computation, such as spincoupled quantum dots, donoratom nuclear spins in silicon, and electrons on helium. Contrary to previous proposals dealing with this difficulty, our scheme requires no encoding redundancy. We also discuss an application to superconducting phase qubits.