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

Nonlocal effects in Fock space

If a physical system contains a single particle, and if two distant detectors test the presence of linear superpositions of one-particle and vacuum states, a violation of classical locality can occur. It is due to the creation of a two-particle component by the detecting process itself.Comment: final version in PRL 74 (1995) 4571; 76 (1996) 2205 (erratum

Deep ROSAT-HRI observation of the elliptical galaxy NGC 1399

We present the preliminary results of a deep (167 ks) ROSAT HRI observation of the cD galaxy NGC1399 in the Fornax cluster. We find, in agreement with previous observations, an extended (41 Kpc adopting a distance of 19 Mpc) gaseous halo with a luminosity of L_X=(4.41\pm 0.04)x10^{41} erg/s. The 5 arcsec resolution of the data allows us to detect a very complex and asymmetric structure of the halo with respect to the optical galaxy. Moreover the analysis of the radial structure reveals the presence of a multi-component profile not consistent with a simple King model over the whole 40 Kpc. We do not detect the presence of a central source and pose an upper limit to the luminosity of a possible active nucleus. Due to the length of the observation, comparable to that of a deep survey, we detect a large number of sources within the HRI FOV, in slight excess with respect to the estimates based on previous surveys. We study the flux distribution of the sources, their temporal behaviour and their spatial distribution with respect to the central galaxy.Comment: 15 pages, 10 figures (6 in color), 1 table; uses subfigure.sty, supertabular.sty, lscape.sty, color.sty; To be published in the proceeding of "X-ray Astronomy 2000" (Mondello (Palermo), September 2000

On the generalization of quantum state comparison

We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a set of two pure states with arbitrary a priori probabilities. We show that the optimal coherent measurement is always superior to the optimal incoherent measurement. Second, we develop a strategy for the comparison of two states from a set of N pure states, and find an optimal solution for some parameter range when N=3. In both cases we use the reduction method for the corresponding problem of mixed state discrimination, as introduced by Raynal et al., which reduces the problem to the discrimination of two pure states only for N=2. Finally, we provide a necessary and sufficient condition for unambiguous comparison of mixed states to be possible.Comment: 8 pages, 4 figures, Proposition 1 corrected, appendix adde

From qubits to black holes: entropy, entanglement and all that

Entropy plays a crucial role in characterization of information and entanglement, but it is not a scalar quantity and for many systems it is different for different relativistic observers. Loop quantum gravity predicts the Bekenstein-Hawking term for black hole entropy and logarithmic correction to it. The latter originates in the entanglement between the pieces of spin networks that describe black hole horizon. Entanglement between gravity and matter may restore the unitarity in the black hole evaporation process. If the collapsing matter is assumed to be initially in a pure state, then entropy of the Hawking radiation is exactly the created entanglement between matter and gravity.Comment: Honorable Mention in the 2005 Gravity Research Foundation Essay Competitio

A Schmidt number for density matrices

We introduce the notion of a Schmidt number of a bipartite density matrix, characterizing the minimum Schmidt rank of the pure states that are needed to construct the density matrix. We prove that Schmidt number is nonincreasing under local quantum operations and classical communication. We show that $k$-positive maps witness Schmidt number, in the same way that positive maps witness entanglement. We show that the family of states which is made from mixing the completely mixed state and a maximally entangled state have increasing Schmidt number depending on the amount of maximally entangled state that is mixed in. We show that Schmidt number {\it does not necessarily increase} when taking tensor copies of a density matrix $\rho$; we give an example of a density matrix for which the Schmidt numbers of $\rho$ and $\rho \otimes \rho$ are both 2.Comment: 5 pages RevTex, 1 typo in Proof Lemma 1 correcte