Narrow Results

We obtain an almost complete description of the structure of the p-spin interaction model down to temperatures that decrease exponentially with p. We prove in particular the spontaneous creation of pure states, and we describe the distribution of their weights. This confirms the picture of "one step of symmetry breaking" predicted by the physicists. Similar results are obtained when a small external field is added, provided one accepts to add a lower order "generic" perturbation to the Hamiltonian.

This paper is the continuation of a study into the information paradox problem started by the author in his earlier works. As before, the key instrument is a deformed density matrix in quantum mechanics of the early universe. It is assumed that the latter represents quantum mechanics with fundamental length. It is demonstrated that the obtained results agree well with the canonical viewpoint that in the processes involving black holes pure states go to the mixed ones in the assumption that all measurements are performed by the observer in a well-known quantum mechanics. Also it is shown that high entropy for Planck's remnants of black holes appearing in the assumption of the generalized uncertainty relations may be explained within the scope of the density matrix entropy introduced by the author previously. It is noted that the suggested paradigm is consistent with the holographic principle. Because of this, a conjecture is made about the possibility for obtaining the generalized uncertainty relations from the covariant entropy bound at high energies in the same way as Bousso has derived Heisenberg's uncertainty principle for the flat space.

The relationship between quantum entanglement and non-locality is studied in a two-qubit system for pure states and Werner states. It is found that Werner states are more entangled than pure states if one compares the negativity for a given degree of non-locality. Furthermore, we also find that the entanglement produces sudden death for pure states but reaches to a fixed value for Werner states if the non-locality is not satisfied.

The purpose of this article is to review the literature for pure and mixed state geometric phase and also the experimental measurement of the phase using NMR.

This note is devoted to some foundational aspects of quantum mechanics (QM) related to quantum information (QI), especially quantum teleportation and "one way quantum computing." We emphasize the role of the projection postulate (determining post-measurement states) in QI and the difference between its Lüders and von Neumann versions. As is well-known, these postulates differ in the case of observables with degenerate spectra. Such observables are important in operations with entangled states: any measurement on one subsystem is represented by an observable with degenerate spectrum in the Hilbert space of a composite system. Some QI schemes (e.g. quantum teleportation and "one way quantum computing") are based on the use of Lüders postulate. The formal application of von Neumann postulate can block these QI schemes. In this note, we present a list of natural conditions under which von Neumann's description of measurements via refinement implies Lüders projection postulate.