Wigner-Araki-Yanase theorem and the realizability of quantum computing

正直 小澤

Subhash C. Kak, C. J. S. Donald, Elaine T. Delaune

Masanao Ozawa

The Wigner-Araki-Yanase theorem shows that conservation laws limit the accuracy of measurement.Here, we generalize the argument to show that conservation laws limit the accuracy of quantum logic operations.A rigorous lower bound is obtained of the error probability of any physical realization of the controlled-NOT gate under the constraint that the computational basis is represented by a component of spin and that physical implementations obey the angular momentum conservation law.The lower bound is shown to be inversely proportional to the number of ancilla qubits or the strength of the external control field.

Subhash C. Kak, C. J. S. Donald, Elaine T. Delaune

Stephen Parrott

The paper focuses on the fact that quantum projective measurements do not necessarily conserve energy. On the other hand the Wigner-Araki-Yanase (WAY) theorem states that assuming a "standard" von Neumann measurement model and "additivity" of the total energy operator, projective measurements of a system must conserve energy as defined by the system's energy operator. This paper explores the ideas behind the WAY theorem in hopes of uncovering the origin of the contradiction. After Araki and Yanase published their proof of the WAY theorem, Yanase appended a new condition now known as the Yanase condition. Under the simplifying assumption that the observable being measured has discrete and non-degenerate eigenvalues, we prove that the Yanase condition actually follows from the hypotheses of the original WAY theorem. The paper also proves that the hypotheses of the WAY theorem, together with the simplifying assumption, imply that the energy operator for the measuring apparatus must be a multiple of the identity, which seems physically unlikely. It seems probable that this surprising conclusion, along with the Yanase condition, also holds without the simplifying assumption.

Myo Myo Aung