Wigner function for a particle in an infinite lattice

We study the Wigner function for a quantum system with a discrete, infinite dimensional Hilbert space, such as a spinless particle moving on a one dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase space construction, propose a meaningful definition of the Wigner function in this case, and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states, and to their superpositions.Comment: 19 pages (single column), 7 figure

How much entanglement is needed to reduce the energy variance?

We explore the relation between the entanglement of a pure state and its energy variance for a local one dimensional Hamiltonian, as the system size increases. In particular, we introduce a construction which creates a matrix product state of arbitrarily small energy variance $\delta^2$ for $N$ spins, with bond dimension scaling as $\sqrt{N} D_0^{1/\delta}$, where $D_0>1$ is a constant. This implies that a polynomially increasing bond dimension is enough to construct states with energy variance that vanishes with the inverse of the logarithm of the system size. We run numerical simulations to probe the construction on two different models, and compare the local reduced density matrices of the resulting states to the corresponding thermal equilibrium. Our results suggest that the spatially homogeneous states with logarithmically decreasing variance, which can be constructed efficiently, do converge to the thermal equilibrium in the thermodynamic limit, while the same is not true if the variance remains constant.Comment: small changes to fix typos and bibliographic reference

Time Reversal Violation from the entangled B0-antiB0 system

We discuss the concepts and methodology to implement an experiment probing directly Time Reversal (T) non-invariance, without any experimental connection to CP violation, by the exchange of "in" and "out" states. The idea relies on the B0-antiB0 entanglement and decay time information available at B factories. The flavor or CP tag of the state of the still living neutral meson by the first decay of its orthogonal partner overcomes the problem of irreversibility for unstable systems, which prevents direct tests of T with incoherent particle states. T violation in the time evolution between the two decays means experimentally a difference between the intensities for the time-ordered (l^+ X, J/psi K_S) and (J/psi K_L, l^- X) decays, and three other independent asymmetries. The proposed strategy has been applied to simulated data samples of similar size and features to those currently available, from which we estimate the significance of the expected discovery to reach many standard deviations.Comment: 17 pages, 2 figures, 6 table

Simulation of many-qubit quantum computation with matrix product states

Matrix product states provide a natural entanglement basis to represent a quantum register and operate quantum gates on it. This scheme can be materialized to simulate a quantum adiabatic algorithm solving hard instances of a NP-Complete problem. Errors inherent to truncations of the exact action of interacting gates are controlled by the size of the matrices in the representation. The property of finding the right solution for an instance and the expected value of the energy are found to be remarkably robust against these errors. As a symbolic example, we simulate the algorithm solving a 100-qubit hard instance, that is, finding the correct product state out of ~ 10^30 possibilities. Accumulated statistics for up to 60 qubits point at a slow growth of the average minimum time to solve hard instances with highly-truncated simulations of adiabatic quantum evolution.Comment: 5 pages, 4 figures, final versio

Limit theorem for a time-dependent coined quantum walk on the line

We study time-dependent discrete-time quantum walks on the one-dimensional lattice. We compute the limit distribution of a two-period quantum walk defined by two orthogonal matrices. For the symmetric case, the distribution is determined by one of two matrices. Moreover, limit theorems for two special cases are presented

Effects of dissipation in an adiabatic quantum search algorithm

We consider the effect of two different environments on the performance of the quantum adiabatic search algorithm, a thermal bath at finite temperature, and a structured environment similar to the one encountered in systems coupled to the electromagnetic field that exists within a photonic crystal. While for all the parameter regimes explored here, the algorithm performance is worsened by the contact with a thermal environment, the picture appears to be different when considering a structured environment. In this case we show that, by tuning the environment parameters to certain regimes, the algorithm performance can actually be improved with respect to the closed system case. Additionally, the relevance of considering the dissipation rates as complex quantities is discussed in both cases. More particularly, we find that the imaginary part of the rates can not be neglected with the usual argument that it simply amounts to an energy shift, and in fact influences crucially the system dynamics.Comment: 18 pages, 9 figure

Anomalous diffusion in the resonant quantum kicked rotor

We study the resonances of the quantum kicked rotor subjected to an excitation that follows a deterministic time-dependent prescription. For the primary resonances we find an analytical relation between the long-time behavior of the standard deviation and the external kick strength. For the secondary resonances we obtain essentially the same result numerically. Selecting the time sequence of the kick allows to obtain a variety of asymptotic wave-function spreadings: super-ballistic, ballistic, sub-ballistic, diffusive, sub-diffusive and localized.Comment: 5 pages, 3 figures To appear in Physica A

T and CPT Symmetries in Entangled Neutral Meson Systems

Genuine tests of an asymmetry under T and/or CPT transformations imply the interchange between in-states and out-states. I explain a methodology to perform model-indepedent separate measurements of the three CP, T and CPT symmetry violations for transitions involving the decay of the neutral meson systems in B- and {\Phi}-factories. It makes use of the quantum-mechanical entanglement only, for which the individual state of each neutral meson is not defined before the decay of its orthogonal partner. The final proof of the independence of the three asymmetries is that no other theoretical ingredient is involved and that the event sample corresponding to each case is different from the other two. The experimental analysis for the measurements of these three asymmetries as function of the time interval {\Delta}t > 0 between the first and second decays is discussed, as well as the significance of the expected results. In particular, one may advance a first observation of true, direct, evidence of Time-Reserval-Violation in B-factories by many standard deviations from zero, without any reference to, and independent of, CP-Violation. In some quantum gravity framework the CPT-transformation is ill-defined, so there is a resulting loss of particle-antiparticle identity. This mechanism induces a breaking of the EPR correlation in the entanglement imposed by Bose statistics to the neutral meson system, the so-called {\omega}-effect. I present results and prospects for the {\omega}-parameter in the correlated neutral meson-antimeson states.Comment: Proc. DISCRETE 2010, Symposium on Prospects in the Physics of Discrete Symmetries, December 2010, Rom

Slowest local operators in quantum spin chains

We numerically construct slowly relaxing local operators in a nonintegrable spin-1/2 chain. Restricting the support of the operator to $M$ consecutive spins along the chain, we exhaustively search for the operator that minimizes the Frobenius norm of the commutator with the Hamiltonian. We first show that the Frobenius norm bounds the time scale of relaxation of the operator at high temperatures. We find operators with significantly slower relaxation than the slowest simple "hydrodynamic" mode due to energy diffusion. Then, we examine some properties of the nontrivial slow operators. Using both exhaustive search and tensor network techniques, we find similar slowly relaxing operators for a Floquet spin chain; this system is hydrodynamically "trivial", with no conservation laws restricting their dynamics. We argue that such slow relaxation may be a generic feature following from locality and unitarity.Comment: 14 pages, 12 figures, published versio