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There is an argument that accurate sequential measurement of conjugate observables A and B on the same state is possible if the state is an eigenstate of one of the observables. When the state is an eigenstate of A, an accurate measurement of A will not disturb the state, so B can then be accurately measured on the same state.
However, that seems to contradict Eq 15 of http://arxiv.org/abs/quant-ph/0207121:
ε(A)η(B) + ε(A)σ(B) + σ(A)η(B) ≥ |<ψ|[A,B]|ψ>|/2
where ε(A) is the error in the measurement of A, η(B) is the disturbance caused by A to the subsequent measurement of B, and σ(A) and σ(B) are the respective intrinsic uncertainties of the state ψ when A or B are accurately measured separately. For noncommuting observables A and B, ε(A) and η(B) cannot both be zero. So presumably there is a mistake in the argument made at the top. What is the mistake?
However, that seems to contradict Eq 15 of http://arxiv.org/abs/quant-ph/0207121:
ε(A)η(B) + ε(A)σ(B) + σ(A)η(B) ≥ |<ψ|[A,B]|ψ>|/2
where ε(A) is the error in the measurement of A, η(B) is the disturbance caused by A to the subsequent measurement of B, and σ(A) and σ(B) are the respective intrinsic uncertainties of the state ψ when A or B are accurately measured separately. For noncommuting observables A and B, ε(A) and η(B) cannot both be zero. So presumably there is a mistake in the argument made at the top. What is the mistake?
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