The curious quantum statistics in the interval between measurements

David Z. Albert, Yakir Aharonov, Susan S. D’Amato

Whether quantum mechanical systems, within the interval between two measurements, can be assigned definite, simultaneous values of noncommuting observables has been the subject of a very old dispute. A certain widely held assumption about such systems has been crucial to that dispute. That assumption turns out to be wrong: A previously unknown prediction of quantum mechanics, which fails to satisfy that assumption, is described here, and the consequences of that failure are considered.

Alexander Semenovich Holevo

Sougato Bose, Dipankar Home

A general and an arbitrarily efficient scheme for entangling the spins (or any spinlike degree of freedom) of two independent uncorrelated identical particles by a combination of two particle interferometry and which way detection is formulated. It is shown that the same setup could be used to identify the quantum statistics of the incident particles from either the sign or the magnitude of measured spin correlations. Our setup also exhibits a curious complementarity between particle distinguishability and the amount of generated entanglement.

Michael B. Mensky

Vladimir V. Ulyanov

Vasil Dinev Penchev

Quantum invariance designates the relation of any quantum coherent state to the corresponding statistical ensemble of measured results. The adequate generalization of ‘measurement’ is discussed to involve the discrepancy, due to the fundamental Planck constant, between any quantum coherent state and its statistical representation as a statistical ensemble after measurement.A set-theory corollary is the curious invariance to the axiom of choice: Any coherent state excludes any well-ordering and thus excludes also the axiom of choice. It should be equated to a well-ordered set after measurement and thus requires the axiom of choice.Quantum invariance underlies quantum information and reveals it as the relation of an unordered quantum “much” (i.e. a coherent state) and a well-ordered “many” of the measured results (i.e. a statistical ensemble). It opens up to a new horizon, in which all physical processes and phenomena can be interpreted as quantum computations realizing relevant operations and algorithms on quantum information. All phenomena of entanglement can be described in terms of the so defined quantum information.Quantum invariance elucidates the link between general relativity and quantum mechanics and thus, the problem of quantum gravity.