Delayed choice for entanglement swapping

Two observers (Alice and Bob) independently prepare two sets of singlets. They test one particle of each singlet along an arbitrarily chosen direction and send the other particle to a third observer, Eve. At a later time, Eve performs joint tests on pairs of particles (one from Alice and one from Bob). According to Eve's choice of test and to her results, Alice and Bob can sort into subsets the samples that they have already tested, and they can verify that each subset behaves as if it consisted of entangled pairs of distant particles, that have never communicated in the past, even indirectly via other particles.Comment: 7 pages, LaTeX, to appear in special issue of J. Modern Optic

Reply to the comment of Y. Aharonov and L. Vaidman on ``Time asymmetry in quantum mechanics: a retrodiction paradox''

In the standard physical interpretation of quantum theory, prediction and retrodiction are not symmetric. The opposite assertion by some authors results from their use of non-standard interpretations of the theory.Comment: final version in Physics Letters A 203 (1995) 15

Depurification by Lorentz boosts

We consider a particle of half-integer spin which is nonrelativistic in the rest frame. Assuming the particle is completely polarized along third axis we calculate the Bloch vector as seen by a moving observer. The result for its length is expressed in terms of dispersion of some vector operator linear in momentum. The relation with the localization properties is discussed.Comment: 5 page

Strategies to measure a quantum state

We consider the problem of determining the mixed quantum state of a large but finite number of identically prepared quantum systems from data obtained in a sequence of ideal (von Neumann) measurements, each performed on an individual copy of the system. In contrast to previous approaches, we do not average over the possible unknown states but work out a ``typical'' probability distribution on the set of states, as implied by the experimental data. As a consequence, any measure of knowledge about the unknown state and thus any notion of ``best strategy'' (i.e. the choice of observables to be measured, and the number of times they are measured) depend on the unknown state. By learning from previously obtained data, the experimentalist re-adjusts the observable to be measured in the next step, eventually approaching an optimal strategy. We consider two measures of knowledge and exhibit all ``best'' strategies for the case of a two-dimensional Hilbert space. Finally, we discuss some features of the problem in higher dimensions and in the infinite dimensional case.Comment: 32 pages, Late