Search results for " Statistical"
showing 10 items of 1649 documents
Classical nature of ordered quantum phases and origin of spontaneous symmetry breaking
2016
We analyse the nature of spontaneous symmetry breaking in complex quantum systems by investigating the long-standing conjecture that the maximally symmetry-breaking quantum ground states are the most classical ones corresponding to a globally ordered phase. We make this argument quantitatively precise by comparing different local and global indicators of classicality and quantumness, respectively in symmetry-breaking and symmetry-preserving quantum ground states. We first discuss how naively comparing local, pairwise entanglement and discord apparently leads to the opposite conclusion. Indeed, we show that in symmetry-preserving ground states the two-body entanglement captures only a modest…
Geometric phase kickback in a mesoscopic qubit-oscillator system
2011
We illustrate a reverse Von Neumann measurement scheme in which a geometric phase induced on a quantum harmonic oscillator is measured using a microscopic qubit as a probe. We show how such a phase, generated by a cyclic evolution in the phase space of the harmonic oscillator, can be kicked back on the qubit, which plays the role of a quantum interferometer. We also extend our study to finite-temperature dissipative Markovian dynamics and discuss potential implementations in micro and nano-mechanical devices coupled to an effective two-level system.
Variational Gibbs State Preparation on NISQ devices
2023
The preparation of an equilibrium thermal state of a quantum many-body system on noisy intermediate-scale (NISQ) devices is an important task in order to extend the range of applications of quantum computation. Faithful Gibbs state preparation would pave the way to investigate protocols such as thermalization and out-of-equilibrium thermodynamics, as well as providing useful resources for quantum algorithms, where sampling from Gibbs states constitutes a key subroutine. We propose a variational quantum algorithm (VQA) to prepare Gibbs states of a quantum many-body system. The novelty of our VQA consists in implementing a parameterized quantum circuit acting on two distinct, yet connected, q…
Counting edge modes via dynamics of boundary spin impurities
2021
We study dynamics of the one-dimensional Ising model in the presence of static symmetry-breaking boundary field via the two-time autocorrelation function of the boundary spin. We find that the correlations decay as a power law. We uncover a dynamical phase diagram where, upon tuning the strength of the boundary field, we observe distinct power laws that directly correspond to changes in the number of edge modes as the boundary and bulk magnetic field are varied. We suggest how the universal physics can be demonstrated in current experimental setups, such as Rydberg chains.
Entanglement and quantum correlations in many-body systems: a unified approach via local unitary operations
2014
Local unitary operations allow for a unifying approach to the quantification of quantum correlations among the constituents of a bipartite quantum system. For pure states, the distance between a given state and its image under least-perturbing local unitary operations is a bona fide measure of quantum entanglement, the so-called entanglement of response, which can be extended to mixed states via the convex roof construction. On the other hand, when defined directly on mixed states perturbed by local unitary operations, such a distance turns out to be a bona fide measure of quantum correlations, the so-called discord of response. Exploiting this unified framework, we perform a detailed compa…
Superharmonic double-well systems with zero-energy ground states: Relevance for diffusive relaxation scenarios
2022
Relaxation properties (specifically time-rates) of the Smoluchowski diffusion process on a line, in a confining potential $ U(x) \sim x^m$, $m=2n \geq 2$, can be spectrally quantified by means of the affiliated Schr\"{o}dinger semigroup $\exp (-t\hat{H})$, $t\geq 0$. The inferred (dimensionally rescaled) motion generator $\hat{H}= - \Delta + {\cal{V}}(x)$ involves a potential function ${\cal{V}}(x)= ax^{2m-2} - bx^{m-2}$, $a=a(m), b=b(m) >0$, which for $m>2$ has a conspicuous higher degree (superharmonic) double-well form. For each value of $m>2$, $ \hat{H}$ has the zero-energy ground state eigenfunction $\rho _*^{1/2}(x)$, where $\rho _*(x) \sim \exp -[U(x)]$ stands for the Boltzmann equil…
Dynamics of confined Levy flights in terms of (Levy) semigroups
2011
The master equation for a probability density function (pdf) driven by L\'{e}vy noise, if conditioned to conform with the principle of detailed balance, admits a transformation to a contractive strongly continuous semigroup dynamics. Given a priori a functional form of the semigroup potential, we address the ground-state reconstruction problem for generic L\'{e}vy-stable semigroups, for {\em all} values of the stability index $\mu \in (0,2)$. That is known to resolve an invariant pdf for confined L\'{e}vy flights (e.g. the former jump-type process). Jeopardies of the procedure are discussed, with a focus on: (i) when an invariant pdf actually is an asymptotic one, (ii) subtleties of the pdf…
Indeterminacy relations in random dynamics
2007
We analyze various uncertainty measures for spatial diffusion processes. In this manifestly non-quantum setting, we focus on the existence issue of complementary pairs whose joint dispersion measure has strictly positive lower bound.
Solving fractional Schroedinger-type spectral problems: Cauchy oscillator and Cauchy well
2014
This paper is a direct offspring of Ref. [J. Math. Phys. 54, 072103, (2013)] where basic tenets of the nonlocally induced random and quantum dynamics were analyzed. A number of mentions was maid with respect to various inconsistencies and faulty statements omnipresent in the literature devoted to so-called fractional quantum mechanics spectral problems. Presently, we give a decisive computer-assisted proof, for an exemplary finite and ultimately infinite Cauchy well problem, that spectral solutions proposed so far were plainly wrong. As a constructive input, we provide an explicit spectral solution of the finite Cauchy well. The infinite well emerges as a limiting case in a sequence of deep…
Optical state engineering, quantum communication, and robustness of entanglement promiscuity in three-mode Gaussian states
2006
We present a novel, detailed study on the usefulness of three-mode Gaussian states states for realistic processing of continuous-variable quantum information, with a particular emphasis on the possibilities opened up by their genuine tripartite entanglement. We describe practical schemes to engineer several classes of pure and mixed three-mode states that stand out for their informational and/or entanglement properties. In particular, we introduce a simple procedure -- based on passive optical elements -- to produce pure three-mode Gaussian states with {\em arbitrary} entanglement structure (upon availability of an initial two-mode squeezed state). We analyze in depth the properties of dist…