Definite quantum measurements

Lawrence S. Schulman

Muxi Liu

We investigated the possibility that a single measurement run with a definite outcome is a joint unitary evolution of all the participating systems, and measurement runs with different definite outcomes correspond to different unitary maps. With reasonable assumptions, we derived a lower bound of the dependence of the environment after measurement on the state of the system before measurement, conditioned on the same measurement outcome. An experimental test of this dependence relation can either serve as evidence that the unitary dynamics and the definite outcome in the orthodox sense cannot be true together or suggest a deviation from the von Neumann measurement model plus a "conditioning" interpretational step.

Michael Dickson

Consider the general form of the state of a quantum system, (eq. 1), where the are (non-degenerate) eigenvectors of an operator, A, corresponding to an observable, A. According to the standard interpretation of quantum mechanics (the precise details of which do not concern me here), A does not have a definite value on the system in the state . But now suppose we measure A by coupling the system to a measuring apparatus. The composite system is then (eq. 2) where the are the indicator-states of the apparatus. Again, the standard interpretation tells us that the apparatus is not in a definite indicator-state. But how can this be? Measurements do have definite results. The apparatus is always in a definite state. I have just reviewed one version of the measurement problem. The modal interpretation of quantum mechanics proposes a solution.

Lawrence S. Schulman

Art Hobson

The heart of the measurement puzzle, namely the problem of definite outcomes, remains unresolved. This paper shows that Josef Jauch's 1968 reduced density operator approach is the solution, even though many question it: The entangled "Measurement State" implies local mixtures of definite but indeterminate eigenvalues even though the MS continues evolving unitarily. A second, independent, argument based on the quantum's nonlocal entanglement with its measuring apparatus shows that the outcomes must be definite eigenvalues because of relativity's ban on instant signaling. Experiments with entangled photon pairs show the MS to be a non-paradoxical superposition of correlations between states rather than a "Schrodinger's cat" superposition of states. Nature's measurement strategy is to shift the superposition--the coherence--from the detected quantum to the correlations between the quantum and its detector, allowing both subsystems to collapse locally to mixtures of definite eigenvalues. This solution implies an innocuous revision of the standard eigenvalue-eigenstate link. Three frequent objections to this solution are rebutted.

Art Hobson