TY - JOUR

T1 - Measuring energy, estimating Hamiltonians, and the time-energy uncertainty relation

AU - Aharonov, Y.

AU - Massar, S.

AU - Popescu, S.

PY - 2002

Y1 - 2002

N2 - Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine which is the Hamiltonian. We show that, in general, this requires a time [Formula Presented] that obeys the uncertainty relation [Formula Presented] where [Formula Presented] is a measure of how accurately the unknown Hamiltonian must be estimated. We apply this result to the problem of measuring the energy of an unknown quantum state. It has been previously shown that if the Hamiltonian is known, then the energy can, in principle, be measured with arbitrarily large precision in an arbitrarily short time. On the other hand, we show that if the Hamiltonian is not known then an energy measurement necessarily takes a minimum time [Formula Presented] which obeys the uncertainty relation [Formula Presented] where [Formula Presented] is the precision of the energy measurement. Several examples are studied to address the question of whether it is possible to saturate these uncertainty relations. Their interpretation is discussed in detail.

AB - Suppose that the Hamiltonian acting on a quantum system is unknown and one wants to determine which is the Hamiltonian. We show that, in general, this requires a time [Formula Presented] that obeys the uncertainty relation [Formula Presented] where [Formula Presented] is a measure of how accurately the unknown Hamiltonian must be estimated. We apply this result to the problem of measuring the energy of an unknown quantum state. It has been previously shown that if the Hamiltonian is known, then the energy can, in principle, be measured with arbitrarily large precision in an arbitrarily short time. On the other hand, we show that if the Hamiltonian is not known then an energy measurement necessarily takes a minimum time [Formula Presented] which obeys the uncertainty relation [Formula Presented] where [Formula Presented] is the precision of the energy measurement. Several examples are studied to address the question of whether it is possible to saturate these uncertainty relations. Their interpretation is discussed in detail.

UR - http://www.scopus.com/inward/record.url?scp=84881129486&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.66.052107

DO - 10.1103/PhysRevA.66.052107

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AN - SCOPUS:84881129486

SN - 2469-9926

VL - 66

SP - 11

JO - Physical Review A

JF - Physical Review A

IS - 5

ER -