Modified Busch-Type Measurements and the Universal Conservation Laws

S. J. van Enk

Paul Busch, PEKKA J. LAHTI, Juha-Pekka Pellonpää +1 more

Masanao Ozawa

Heisenberg’s uncertainty principle, exemplified by the γ ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement contradicts the limit of the accuracy of measurements under conservation laws originally found by Wigner in 1950s, and should be modified to correctly derive the unavoidable noise caused by the conservation law induced decoherence. The obtained accuracy limit leads to an interesting conclusion that a widely accepted, but rather naive, physical encoding of qubits for quantum computing suffers significantly from the decoherence induced by the angular momentum conservation law.

Neil W. MacGill

Ozawa, M

Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement contradicts the limit of the accuracy of measurements under conservation laws originally found by Wigner in 1950s, and should be modified to correctly derive the unavoidable noise caused by the conservation law induced decoherence. The obtained accuracy limit leads to an interesting conclusion that a widely accepted, but rather naive, physical encoding of qubits for quantum computing suffers significantly from the decoherence induced by the angular momentum conservation law.

Ryota Katsube, Masanao Ozawa, Hotta, Masahiro

It is important to improve the accuracy of quantum measurements and operations both in engineering and fundamental physics. It is known, however, that the achievable accuracy of measurements and unitary operations are generally limited by conservation laws according to the Wigner-Araki-Yanase theorem (WAY theorem) and its generalizations. Although many researches have extended the WAY theorem quantitatively, most of them, as well as the original WAY theorem, concern only additive conservation laws like the angular momentum conservation law. In this paper, we explore the limitation incurred by the energy conservation law, which is universal but is one of the non-additive conservation laws. We present a lower bound for the error of a quantum measurement using a scattering process satisfying the energy conservation law. We obtain conditions that a control system Hamiltonian must fulfill in order to implement a controlled unitary gate with zero error when a scattering process is considered. We also show the quantitative relationship between the upper bound of the gate fidelity of a controlled unitary gate and the energy fluctuation of systems when a target system and a control system are both one qubit.