arXiv:2106.14680

Comment on "When the Quantum Energy Teleportation is Observable? "

Masahiro Hotta

Published Jun 25, 2021• 1 citation

Abstract

Recently authors of a paper (arXiv:2105.04407) claim that quantum energy teleportation is unobservable due to a time-energy uncertainty relation. In this short note, I will point out that their argument is wrong. They misuse the uncertainty relation.

DOI: 10.48550/arxiv.2106.14680

Related papers

When the Quantum Energy Teleportation is Observable?

H. Razmi, A. MohammadKazemi

We want to investigate when the quantum energy teleportation is observable. The condition for observability is based on the minimum time value determined by the fundamental energy-time uncertainty relation.

arXiv:2105.04407May 7, 20211 citation

Answer to Fock Concerning the Time Energy Indeterminacy Relation

Yakir Aharonov, David Böhm

An answer is given to a recent criticizm by Fock, concerning our paper "Time in the Quantum Theory and the Uncertainty Relation for Time and Energy." It is proved that Fock's criticizm is wrong, and that our previous conclusion that energy can be measured in an arbitrarily short period of time is valid.

Physical ReviewJun 22, 196448 citations

Time in the Quantum Theory and the Uncertainty Relation for Time and Energy

Yakir Aharonov, David Böhm

Physical ReviewJun 1, 1961481 citations

Comment on "Reply to Comment on Time-dependent Quasi-Hermitian Hamiltonians and the Unitary Quantum Evolution"

Mostafazadeh, Ali

arXiv:0711.1078Nov 7, 20074 citations

Comment on Energy-Time Uncertainty Relations in Quantum Measurements

Yasuda, Koji

The measurement apparatus proposed in the titled paper, "Energy-Time Uncertainty Relations in Quantum Measurements" [Found. Phys. 46, 1522-1550 (2016)] was examined. A simple proof was presented for the non-existence of the apparatus.

arXiv:1809.06539Sep 18, 20180 citations

Remarks on Time-Energy Uncertainty Relations

Romeo Brunetti, Klaus Fredenhagen

Dedicated to Huzihiro Araki on the occasion of his seventieth birthday Using a recent construction of observables characterizing the time of occurence of an effect in quantum theory, we present a rigorous derivation of the standard time-energy uncertainty relation. In addition, we prove an uncertainty relation for time meaurements alone. 1

Jan 1, 200215 citations

arXiv:2106.14680

Comment on "When the Quantum Energy Teleportation is Observable? "

Masahiro Hotta

Published Jun 25, 2021• 1 citation

arXiv HTML PDF

Abstract

DOI: 10.48550/arxiv.2106.14680

Related papers

When the Quantum Energy Teleportation is Observable?

H. Razmi, A. MohammadKazemi

arXiv:2105.04407May 7, 20211 citation

Answer to Fock Concerning the Time Energy Indeterminacy Relation

Yakir Aharonov, David Böhm

Physical ReviewJun 22, 196448 citations

Time in the Quantum Theory and the Uncertainty Relation for Time and Energy

Yakir Aharonov, David Böhm

Because time does not appear in Schr\"odinger's equation as an operator but only as a parameter, the time-energy uncertainty relation must be formulated in a special way. This problem has in fact been studied by many authors and we give a summary of their treatments. We then criticize the main conclusion of these treatments; viz., that in a measurement of energy carried out in a time interval, $\ensuremath{\Delta}t$, there must be a minimum uncertainty in the transfer of energy to the observed system, given by $\ensuremath{\Delta}({E}^{\ensuremath{'}}\ensuremath{-}E)>~\frac{h}{\ensuremath{\Delta}t}$. We show that this conclusion is erroneous in two respects. First, it is not consistent with the general principles of the quantum theory, which require that all uncertainty relations be expressible in terms of the mathematical formalism, i.e., by means of operators, wave functions, etc. Secondly, the examples of measurement processes that were used to derive the above uncertainty relation are not general enough. We then develop a systematic presentation of our own point of view, with regard to the role of time in the quantum theory, and give a concrete example of a measurement process not satisfying the above uncertainty relation.Because time does not appear in Schr\"odinger's equation as an operator but only as a parameter, the time-energy uncertainty relation must be formulated in a special way. This problem has in fact been studied by many authors and we give a summary of their treatments. We then criticize the main conclusion of these treatments; viz., that in a measurement of energy carried out in a time interval, $\ensuremath{\Delta}t$, there must be a minimum uncertainty in the transfer of energy to the observed system, given by $\ensuremath{\Delta}({E}^{\ensuremath{'}}\ensuremath{-}E)>~\frac{h}{\ensuremath{\Delta}t}$. We show that this conclusion is erroneous in two respects. First, it is not consistent with the general principles of the quantum theory, which require that all uncertainty relations be expressible in terms of the mathematical formalism, i.e., by means of operators, wave functions, etc. Secondly, the examples of measurement processes that were used to derive the above uncertainty relation are not general enough. We then develop a systematic presentation of our own point of view, with regard to the role of time in the quantum theory, and give a concrete example of a measurement process not satisfying the above uncertainty relation.

Physical ReviewJun 1, 1961481 citations

Comment on "Reply to Comment on Time-dependent Quasi-Hermitian Hamiltonians and the Unitary Quantum Evolution"

Mostafazadeh, Ali

I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper [arXiv:0710.5653v1], one finds that the time-evolution of the associated quantum system is not governed by the Schrödinger equation for the Hamiltonian operator $H$ but an operator $H'$ which differs from $H$ if the metric operator is time-dependent. In the latter case this effective Hamiltonian $H'$ is not observable. This is consistent with the conclusions of my paper [Phys. Lett. B 650, 208 (2007), arXiv:0706.1872v2] which allow for unitary time-evolution generated by unobservable Hamiltonians.I point out that if one defines the operator $U_R(t)$ as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of $U_R(t)$ as given in his paper [arXiv:0710.5653v1], one finds that the time-evolution of the associated quantum system is not governed by the Schrödinger equation for the Hamiltonian operator $H$ but an operator $H'$ which differs from $H$ if the metric operator is time-dependent. In the latter case this effective Hamiltonian $H'$ is not observable. This is consistent with the conclusions of my paper [Phys. Lett. B 650, 208 (2007), arXiv:0706.1872v2] which allow for unitary time-evolution generated by unobservable Hamiltonians.

arXiv:0711.1078Nov 7, 20074 citations

Comment on Energy-Time Uncertainty Relations in Quantum Measurements

Yasuda, Koji

arXiv:1809.06539Sep 18, 20180 citations

Remarks on Time-Energy Uncertainty Relations

Romeo Brunetti, Klaus Fredenhagen

Jan 1, 200215 citations

I point out that if one defines the operator

U_R(t)

as done by M. Znojil in his reply [arXiv:0711.0514v1] to my comment [arXiv:0711.0137v1] and also accepts the validity of the defining relation of

U_R(t)

as given in his paper [arXiv:0710.5653v1], one finds that the time-evolution of the associated quantum system is not governed by the Schrödinger equation for the Hamiltonian operator

H

but an operator

H'

which differs from

H

if the metric operator is time-dependent. In the latter case this effective Hamiltonian

H'

is not observable. This is consistent with the conclusions of my paper [Phys. Lett. B 650, 208 (2007), arXiv:0706.1872v2] which allow for unitary time-evolution generated by unobservable Hamiltonians.