FFLV-type monomial bases for type B

We present a combinatorial monomial basis (or, more precisely, a family of monomial bases) in every finite-dimensional irreducible $\mathfrak{so}_{2n+1}$ -module. These bases are in many ways similar to the FFLV bases for types $A$ and $C$. They are also defined combinatorially via sums over Dyck paths in certain triangular grids. Our sums, however, involve weights depending on the length of the corresponding root. Accordingly, our bases also induce bases in certain degenerations of the modules but these degenerations are obtained not from the filtration by PBW degree but by a weighted version thereof

Dephasing of qubits by transverse low-frequency noise

We analyze the dissipative dynamics of a two-level quantum system subject to low-frequency, e.g. 1/f noise, motivated by recent experiments with superconducting quantum circuits. We show that the effect of transverse linear coupling of the system to low-frequency noise is equivalent to that of quadratic longitudinal coupling. We further find the decay law of quantum coherent oscillations under the influence of both low- and high-frequency fluctuations, in particular, for the case of comparable rates of relaxation and pure dephasing

Search for Squeezed-Pair Correlations at RHIC

Squeezed correlations of particle-antiparticle pairs, also called Back-to-Back Correlations, are predicted to appear if the hadron masses are modified in the hot and dense hadronic medium formed in high energy nucleus-nucleus collisions. Although well-established theoretically, the squeezed-particle correlations have not yet been searched for experimentally in high energy hadronic or heavy ion collisions, clearly requiring optimized forms to experimentally search for this effect. Within a non-relativistic treatment developed earlier we show that one promising way to search for the BBC signal is to look into the squeezed correlation function of pairs of phi-mesons at RHIC energies, plotted in terms of the average momentum of the pair, K12=(k1+k2)/2. This variable's modulus, 2|K12|, is the non-relativistic limit of the variable Q_bbc, introduced herewith. The squeezing effects on the HBT correlation function are also discussed.Comment: 4 pages, 2 figures. To be published in the Proceedings of Quark Matter 2008, Jaipur, Indi

Squeezed Correlations and Spectra for Mass-Shifted Bosons

Huge back-to-back correlations are shown to arise for thermal ensembles of bosonic states with medium-modified masses. The effect is experimentally observable in high energy heavy ion collisions.Comment: 4 pages (RevTex) including 2 eps figures via psfig, published versio

Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton

In a uniform ring-shaped one-dimensional superfluid, quantum fluctuations that unwind the order parameter need to transfer momentum to quasiparticles (phonons). We present a detailed calculation of the leading exponential factor governing the rate of such phonon-assisted tunneling in a weakly-coupled Bose gas at a low temperature $T$. We also estimate the preexponent. We find that for small superfluid velocities the $T$-dependence of the rate is given mainly by $\exp(-c_s P/ 2T)$, where $P$ is the momentum transfer, and $c_s$ is the phonon speed. At low $T$, this represents a strong suppression of the rate, compared to the non-uniform case. As a part of our calculation, we identify a complex instanton, whose analytical continuation to suitable real-time segments is real and describes formation and decay of coherent quasiparticle states with nonzero total momenta.Comment: 15 pages, 3 figures; to be published in Phys. Rev.

Statistics and noise in a quantum measurement process

The quantum measurement process by a single-electron transistor or a quantum point contact coupled to a quantum bit is studied. We find a unified description of the statistics of the monitored quantity, the current, in the regime of strong measurement and expect this description to apply for a wide class of quantum measurements. We derive the probability distributions for the current and charge in different stages of the process. In the parameter regime of the strong measurement the current develops a telegraph-noise behavior which can be detected in the noise spectrum.Comment: 4 pages, 2 figure

Quantum logic operations and creation of entanglement in a scalable superconducting quantum computer with long-range constant interaction between qubits

We consider a one-dimensional chain of many superconducting quantum interference devices (SQUIDs), serving as charge qubits. Each SQUID is coupled to its nearest neighbors through constant capacitances. We study the quantum logic operations and implementation of entanglement in this system. Arrays with two and three qubits are considered in detail. We show that the creation of entanglement with an arbitrary number of qubits can be implemented, without systematic errors, even when the coupling between qubits is not small. A relatively large coupling constant allows one to increase the clock speed of the quantum computer. We analytically and numerically demonstrate the creation of the entanglement for this case, which can be a good test for the experimental implementation of a relatively simple quantum protocol with many qubits. We discuss a possible application of our approach for implementing universal quantum logic for more complex algorithms by decreasing the coupling constant and, correspondingly, decreasing the clock speed. The errors introduced by the long-range interaction for the universal logic gates are estimated analytically and calculated numerically. Our results can be useful for experimental implementation of quantum algorithms using controlled magnetic fluxes and gate voltages applied to the SQUIDs. The algorithms discussed in this paper can be implemented using already existing technologies in superconducting systems with constant inter-qubit coupling.Comment: 24 page

Integrity bases for local invariants of composite quantum systems

Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in $F(q)$ corrected and conclusions modified accordingl

Antiresonance and interaction-induced localization in spin and qubit chains with defects

We study a spin chain with an anisotropic XXZ coupling in an external field. Such a chain models several proposed types of a quantum computer. The chain contains a defect with a different on-site energy. The interaction between excitations is shown to lead to two-excitation states localized next to the defect. In a resonant situation scattering of excitations on each other might cause decay of an excitation localized on the defect. We find that destructive quantum interference suppresses this decay. Numerical results confirm the analytical predictions.Comment: Updated versio