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

Comment on "Classical interventions in quantum systems II. Relativistic invariance"

In a recent paper [Phys. Rev. A 61, 022117 (2000)], quant-ph/9906034, A. Peres argued that quantum mechanics is consistent with special relativity by proposing that the operators that describe time evolution do not need to transform covariantly, although the measurable quantities need to transform covariantly. We discuss the weaknesses of this proposal.Comment: 4 pages, to appear in Phys. Rev.

Infinite matrices may violate the associative law

The momentum operator for a particle in a box is represented by an infinite order Hermitian matrix $P$. Its square $P^2$ is well defined (and diagonal), but its cube $P^3$ is ill defined, because $P P^2\neq P^2 P$. Truncating these matrices to a finite order restores the associative law, but leads to other curious results.Comment: final version in J. Phys. A28 (1995) 1765-177

Understanding Popper's Experiment

An experiment proposed by Karl Popper is considered by many to be a crucial test of quantum mechanics. Although many loopholes in the original proposal have been pointed out, they are not crucial to the test. We use only the standard interpretation of quantum mechanics to point out what is fundamentally wrong with the proposal, and demonstrate that Popper's basic premise was faulty.Comment: Edited version, to appear in Am. J. Phy

The Effects of Symmetries on Quantum Fidelity Decay

We explore the effect of a system's symmetries on fidelity decay behavior. Chaos-like exponential fidelity decay behavior occurs in non-chaotic systems when the system possesses symmetries and the applied perturbation is not tied to a classical parameter. Similar systems without symmetries exhibit faster-than-exponential decay under the same type of perturbation. This counter-intuitive result, that extra symmetries cause the system to behave in a chaotic fashion, may have important ramifications for quantum error correction.Comment: 5 pages, 3 figures, to be published Phys. Rev. E Rapid Communicatio

Bell's inequality with Dirac particles

We study Bell's inequality using the Bell states constructed from four component Dirac spinors. Spin operator is related to the Pauli-Lubanski pseudo vector which is relativistic invariant operator. By using Lorentz transformation, in both Bell states and spin operator, we obtain an observer independent Bell's inequality, so that it is maximally violated as long as it is violated maximally in the rest frame.Comment: 7 pages. arXiv admin note: text overlap with arXiv:quant-ph/0308156 by other author

Optimal distinction between non-orthogonal quantum states

Given a finite set of linearly independent quantum states, an observer who examines a single quantum system may sometimes identify its state with certainty. However, unless these quantum states are orthogonal, there is a finite probability of failure. A complete solution is given to the problem of optimal distinction of three states, having arbitrary prior probabilities and arbitrary detection values. A generalization to more than three states is outlined.Comment: 9 pages LaTeX, one PostScript figure on separate pag

Quantum mechanics explained

The physical motivation for the mathematical formalism of quantum mechanics is made clear and compelling by starting from an obvious fact - essentially, the stability of matter - and inquiring into its preconditions: what does it take to make this fact possible?Comment: 29 pages, 5 figures. v2: revised in response to referee comment

Maximally-Disordered Distillable Quantum States

We explore classical to quantum transition of correlations by studying the quantum states located just outside of the classically-correlated-states-only neighborhood of the maximally mixed state (the largest separable ball (LSB)). We show that a natural candidate for such states raises the possibility of a layered transition, i.e., an annular region comprising only classical and the classical-like bound entangled states, followed by free or distillable entanglement. Surprisingly, we find the transition to be abrupt for bipartite systems: distillable states emerge arbitrarily close to the LSB. For multipartite systems, while the radius of the LSB remains unknown, we determine the radius of the largest undistillable ball. Our results also provide an upper bound on how noisy shared entangled states can be for executing quantum information processing protocols.Comment: Published Version, 7 pages, Late