Robustness of quantum Markov chains

If the conditional information of a classical probability distribution of three random variables is zero, then it obeys a Markov chain condition. If the conditional information is close to zero, then it is known that the distance (minimum relative entropy) of the distribution to the nearest Markov chain distribution is precisely the conditional information. We prove here that this simple situation does not obtain for quantum conditional information. We show that for tri-partite quantum states the quantum conditional information is always a lower bound for the minimum relative entropy distance to a quantum Markov chain state, but the distance can be much greater; indeed the two quantities can be of different asymptotic order and may even differ by a dimensional factor.Comment: 14 pages, no figures; not for the feeble-minde

Thermodynamic Potential for Superfluid 3He in Aerogel

We present a free energy functional for superfluid 3He in the presence of homogeneously distributed impurity disorder which extends the Ginzburg-Landau free energy functional to all temperatures. We use the new free energy functional to calculate the thermodynamic potential, entropy, heat capacity and density of states for the B-phase of superfluid 3He in homogeneous, isotropic aerogel.Comment: 10 pages, 4 figure

Radiative production of invisible charginos in photon photon collision

If in a supersymmetric model, the lightest chargino is nearly degenerate with the lightest neutralino, the former can decay into the latter alongwith a soft pion (or a lepton-neutrino pair). Near degeneracy of the chargino and neutralino masses can cause the other decay products (the pion or the lepton) to be almost invisible. Photon-photon colliders offer a possibility of clean detection of such an event through a hard photon tag.Comment: 12 pages, 5 postscript figure

B_c meson rare decays in the light-cone quark model

We investigate the rare decays $B_c \rightarrow D_s(1968) \ell \bar{\ell}$ and $B_c\rightarrow D_s^*(2317) \ell \bar{\ell}$ in the framework of the light-cone quark model (LCQM). The transition form factors are calculated in the space-like region and then analytically continued to the time-like region via exponential parametrization. The branching ratios and longitudinal lepton polarization asymmetries (LPAs) for the two decays are given and compared with each other. The results are helpful to investigating the structure of $B_c$ meson and to testing the unitarity of CKM quark mixing matrix. All these results can be tested in the future experiments at the LHC.Comment: 9 pages, 11 figures, version accepted for publication in EPJ

Scattering by impurity-induced order parameter ``holes'' in d-wave superconductors

Nonmagnetic impurities in d-wave superconductors cause strong local suppressions of the order parameter. We investigate the observable effects of the scatterigng off such suppressions in bulk samples by treating the order parameter "hole" as a pointlike off-diagonal scatterer treated within a self-consistent t-matrix approximation. Strong scattering potentials lead to a finite-energy spectral feature in the d-wave "impurity band", the observable effects of which include enhanced low-temperature microwave power absorption and a stronger sensitivity of the London penetration depth to disorder than found previously in simpler ``dirty'' d-wave models.Comment: 5 pp. Revtex including 4 postscript figures, submitted to Phys. Rev.

Exponential lower bound on the highest fidelity achievable by quantum error-correcting codes

On a class of memoryless quantum channels which includes the depolarizing channel, the highest fidelity of quantum error-correcting codes of length n and rate R is proven to be lower bounded by 1-exp[-nE(R)+o(n)] for some function E(R). The E(R) is positive below some threshold R', which implies R' is a lower bound on the quantum capacity.Comment: Ver.4. In vers.1--3, I claimed Theorem 1 for general quantum channels. Now I claim this only for a slight generalization of depolarizing channel in this paper because Lemma 2 in vers.1--3 was wrong; the original general statement is proved in quant-ph/0112103. Ver.5. Text sectionalized. Appeared in PRA. The PRA article is typographically slightly crude: The LaTeX symbol star, used as superscripts, was capriciously replaced by the asterisk in several places after my proof readin

Optimization of entanglement witnesses

An entanglement witness (EW) is an operator that allows to detect entangled states. We give necessary and sufficient conditions for such operators to be optimal, i.e. to detect entangled states in an optimal way. We show how to optimize general EW, and then we particularize our results to the non-decomposable ones; the latter are those that can detect positive partial transpose entangled states (PPTES). We also present a method to systematically construct and optimize this last class of operators based on the existence of ``edge'' PPTES, i.e. states that violate the range separability criterion [Phys. Lett. A{\bf 232}, 333 (1997)] in an extreme manner. This method also permits the systematic construction of non-decomposable positive maps (PM). Our results lead to a novel sufficient condition for entanglement in terms of non-decomposable EW and PM. Finally, we illustrate our results by constructing optimal EW acting on H=\C^2\otimes \C^4. The corresponding PM constitute the first examples of PM with minimal ``qubit'' domain, or - equivalently - minimal hermitian conjugate codomain.Comment: 18 pages, two figures, minor change

Test for entanglement using physically observable witness operators and positive maps

Motivated by the Peres-Horodecki criterion and the realignment criterion we develop a more powerful method to identify entangled states for any bipartite system through a universal construction of the witness operator. The method also gives a new family of positive but non-completely positive maps of arbitrary high dimensions which provide a much better test than the witness operators themselves. Moreover, we find there are two types of positive maps that can detect 2xN and 4xN bound entangled states. Since entanglement witnesses are physical observables and may be measured locally our construction could be of great significance for future experiments.Comment: 6 pages, 1 figure, revtex4 styl

Retrodiction of Generalised Measurement Outcomes

If a generalised measurement is performed on a quantum system and we do not know the outcome, are we able to retrodict it with a second measurement? We obtain a necessary and sufficient condition for perfect retrodiction of the outcome of a known generalised measurement, given the final state, for an arbitrary initial state. From this, we deduce that, when the input and output Hilbert spaces have equal (finite) dimension, it is impossible to perfectly retrodict the outcome of any fine-grained measurement (where each POVM element corresponds to a single Kraus operator) for all initial states unless the measurement is unitarily equivalent to a projective measurement. It also enables us to show that every POVM can be realised in such a way that perfect outcome retrodiction is possible for an arbitrary initial state when the number of outcomes does not exceed the output Hilbert space dimension. We then consider the situation where the initial state is not arbitrary, though it may be entangled, and describe the conditions under which unambiguous outcome retrodiction is possible for a fine-grained generalised measurement. We find that this is possible for some state if the Kraus operators are linearly independent. This condition is also necessary when the Kraus operators are non-singular. From this, we deduce that every trace-preserving quantum operation is associated with a generalised measurement whose outcome is unambiguously retrodictable for some initial state, and also that a set of unitary operators can be unambiguously discriminated iff they are linearly independent. We then examine the issue of unambiguous outcome retrodiction without entanglement. This has important connections with the theory of locally linearly dependent and locally linearly independent operators.Comment: To appear in Physical Review

Using Heavy Quark Spin Symmetry in Semileptonic BcB_c Decays

The form factors parameterizing the B_c semileptonic matrix elements can be related to a few invariant functions if the decoupling of the spin of the heavy quarks in B_c and in the mesons produced in the semileptonic decays is exploited. We compute the form factors as overlap integral of the meson wave-functions obtained using a QCD relativistic potential model, and give predictions for semileptonic and non-leptonic B_c decay modes. We also discuss possible experimental tests of the heavy quark spin symmetry in B_c decays.Comment: RevTex, 22 pages, 2 figure