Measurement-dependent corrections to work distributions arising from quantum coherences

For a quantum system undergoing a unitary process work is commonly defined based on the Two Projective Measurement (TPM) protocol which measures the energies of the system before and after the process. However, it is well known that projective measurements disregard quantum coherences of the system with respect to the energy basis, thus removing potential quantum signatures in the work distribution. Here we consider weak measurements of the system's energy difference and establish corrections to work averages arising from initial system coherences. We discuss two weak measurement protocols that couple the system to a detector, prepared and measured either in the momentum or the position eigenstates. Work averages are derived for when the system starts in the proper thermal state versus when the initial system state is a pure state with thermal diagonal elements and coherences characterised by a set of phases. We show that by controlling only the phase differences between the energy eigenstate contributions in the system's initial pure state, the average work done during the same unitary process can be controlled. By changing the phases alone one can toggle from regimes where the systems absorbs energy, i.e. a work cost, to the ones where it emits energy, i.e. work can be drawn. This suggests that the coherences are additional resources that can be used to manipulate or store energy in a quantum system.Comment: 9 pages, 3 figure

Theta-frequency resonance at the cerebellum input stage improves spike timing on the millisecond time-scale

The neuronal circuits of the brain are thought to use resonance and oscillations to improve communication over specific frequency bands (Llinas, 1988; Buzsaki, 2006). However, the properties and mechanism of these phenomena in brain circuits remain largely unknown. Here we show that, at the cerebellum input stage, the granular layer (GRL) generates its maximum response at 5\u20137 Hz both in vivo following tactile sensory stimulation of the whisker pad and in acute slices following mossy fiber bundle stimulation. The spatial analysis of GRL activity performed using voltage-sensitive dye (VSD) imaging revealed 5\u20137 Hz resonance covering large GRL areas. In single granule cells, resonance appeared as a reorganization of output spike bursts on the millisecond time-scale, such that the first spike occurred earlier and with higher temporal precision and the probability of spike generation increased. Resonance was independent from circuit inhibition, as it persisted with little variation in the presence of the GABAA receptor blocker, gabazine. However, circuit inhibition reduced the resonance area more markedly at 7 Hz. Simulations with detailed computational models suggested that resonance depended on intrinsic granule cells ionic mechanisms: specifically, Kslow (M-like) and KA currents acted as resonators and the persistent Na current and NMDA current acted as amplifiers. This form of resonance may play an important role for enhancing coherent spike emission from the GRL when theta-frequency bursts are transmitted by the cerebral cortex and peripheral sensory structures during sensory-motor processing, cognition, and learning

Dynamical properties across a quantum phase transition in the Lipkin-Meshkov-Glick model

It is of high interest, in the context of Adiabatic Quantum Computation, to better understand the complex dynamics of a quantum system subject to a time-dependent Hamiltonian, when driven across a quantum phase transition. We present here such a study in the Lipkin-Meshkov-Glick (LMG) model with one variable parameter. We first display numerical results on the dynamical evolution across the LMG quantum phase transition, which clearly shows a pronounced effect of the spectral avoided level crossings. We then derive a phenomenological (classical) transition model, which already shows some closeness to the numerical results. Finally, we show how a simplified quantum transition model can be built which strongly improve the classical approach, and shed light on the physical processes involved in the whole LMG quantum evolution. From our results, we argue that the commonly used description in term of Landau-Zener transitions is not appropriate for our model.Comment: 7 pages, 5 figures; corrected reference

Calorimetric measurement of work in a quantum system

We propose a calorimetric measurement of work in a quantumsystem. As a physical realization, we consider a superconducting two-levelsystem, a Cooper-pair box, driven by a gate voltage past an avoided levelcrossing at charge degeneracy. We demonstrate that, with realistic experimentalparameters, the temperature measurement of a resistor (environment) can detectsingle microwave photons emitted or absorbed by the two-level system. Thismethod would thus be a way to measure the full distribution of work in repeatedmeasurements, and to assess the quantum fluctuation relations.Peer reviewe

On the stability of quantum holonomic gates

We provide a unified geometrical description for analyzing the stability of holonomic quantum gates in the presence of imprecise driving controls (parametric noise). We consider the situation in which these fluctuations do not affect the adiabatic evolution but can reduce the logical gate performance. Using the intrinsic geometric properties of the holonomic gates, we show under which conditions on noise's correlation time and strength, the fluctuations in the driving field cancel out. In this way, we provide theoretical support to previous numerical simulations. We also briefly comment on the error due to the mismatch between real and nominal time of the period of the driving fields and show that it can be reduced by suitably increasing the adiabatic time.Comment: 7 page

New minimal weight representations for left-to-right window methods

Abstract. For an integer w ≥ 2, a radix 2 representation is called a width-w nonadjacent form (w-NAF, for short) if each nonzero digit is an odd integer with absolute value less than 2 w−1, and of any w consecutive digits, at most one is nonzero. In elliptic curve cryptography, the w-NAF window method is used to efficiently compute nP where n is an integer and P is an elliptic curve point. We introduce a new family of radix 2 representations which use the same digits as the w-NAF but have the advantage that they result in a window method which uses less memory. This memory savings results from the fact that these new representations can be deduced using a very simple left-to-right algorithm. Further, we show that like the w-NAF, these new representations have a minimal number of nonzero digits. 1 Window Methods An operation fundamental to elliptic curve cryptography is scalar multiplication; that is, computing nP for an integer, n, and an elliptic curve point, P. A number of different algorithms have been proposed to perform this operation efficiently (see Ch. 3 of [4] for a recent survey). A variety of these algorithms, known as window methods, use the approach described in Algorithm 1.1. For example, suppose D = {0, 1, 3, 5, 7}. Using this digit set, Algorithm 1.1 first computes and stores P, 3P, 5P and 7P. After a D-radix 2 representation of n is computed its digits are read from left to right by the “for ” loop and nP is computed using doubling and addition operations (and no subtractions). One way to compute a D-radix 2 representation of n is to slide a 3-digit window from right to left across the {0, 1}-radix 2 representation of n (see Section 4). Using negative digits takes advantage of the fact that subtracting an elliptic curve point can be done just as efficiently as adding it. Suppose now that D

Universal quantum gates based on both geometric and dynamic phases in quantum dots

A large-scalable quantum computer model, whose qubits are represented by the subspace subtended by the ground state and the single exciton state on semiconductor quantum dots, is proposed. A universal set of quantum gates in this system may be achieved by a mixed approach, composed of dynamic evolution and nonadibatic geometric phase.Comment: 4 pages, to appear in Chin. Phys. Let

Non-adiabatic geometrical quantum gates in semiconductor quantum dots

In this paper we study the implementation of non-adiabatic geometrical quantum gates with in semiconductor quantum dots. Different quantum information enconding/manipulation schemes exploiting excitonic degrees of freedom are discussed. By means of the Aharanov-Anandan geometrical phase one can avoid the limitations of adiabatic schemes relying on adiabatic Berry phase; fast geometrical quantum gates can be in principle implementedComment: 5 Pages LaTeX, 10 Figures include