Nonseparability of continuously measured quantum systems in the classical limit

2007 ◽  
Vol 85 (6) ◽  
pp. 633-640
Author(s):  
S Ghose ◽  
B C Sanders ◽  
P M Alsing ◽  
I H Deutsch
Keyword(s):  
Quantum System ◽  
Classical Limit ◽  
Quantum Systems ◽  
Classical Dynamics ◽  
Nonclassical States ◽  
Classical Transition ◽  
Measured System ◽  
Nonseparable States ◽  
03.65 Ud ◽  
03.67 Mn

We analyze the question of separability in a continuously measured quantum system as it approaches the classical limit. We show that the record of position measurements can approach the classical limit even when the system is described by highly nonseparable states. In particular, in systems with a chaotic classical limit, chaos can work to enhance the entanglement in the system in the classical regime. This coexistence of nonclassical states and classical dynamics can be understood by analyzing the conditioned evolution of the measured system and the conditions for the quantum-to-classical transition. PACS Nos.: 03.65.Ta, 03.65.Ud, 03.67.Mn, 05.45.Mt, 03.67.–a

The geometric phase for chaotic systems

1992 ◽  
Vol 436 (1898) ◽  
pp. 631-661 ◽  
Keyword(s):  
Periodic Orbits ◽  
Parameter Space ◽  
Integrable Systems ◽  
Geometric Phase ◽  
Classical Limit ◽  
Chaotic Systems ◽  
Quantum Systems ◽  
Classical Dynamics

The geometric phase acquired by the eigenstates of cycled quantum systems is given by the flux of a two-form through a surface in the system’s parameter space. We obtain the classical limit of this two-form in a form applicable to systems whose classical dynamics is chaotic. For integrable systems the expression is equivalent to the Hannay two-form. We discuss various properties of the classical two-form, derive semiclassical corrections to it (associated with classical periodic orbits), and consider implications for the semiclassical density of degeneracies.

scholarly journals Simulating molecules on a cloud-based 5-qubit IBM-Q universal quantum computer

2021 ◽  
Vol 4 (1) ◽  
Author(s):  
S. Leontica ◽  
F. Tennie ◽  
T. Farrow
Keyword(s):  
Quantum System ◽  
Energy Transport ◽  
Quantum Computer ◽  
Complex Molecule ◽  
Dissipative System ◽  
Quantum Simulation ◽  
Quantum Systems ◽  
Molecular Structures ◽  
Unitary Evolution ◽  
Universal Quantum

AbstractSimulating the behaviour of complex quantum systems is impossible on classical supercomputers due to the exponential scaling of the number of quantum states with the number of particles in the simulated system. Quantum computers aim to break through this limit by using one quantum system to simulate another quantum system. Although in their infancy, they are a promising tool for applied fields seeking to simulate quantum interactions in complex atomic and molecular structures. Here, we show an efficient technique for transpiling the unitary evolution of quantum systems into the language of universal quantum computation using the IBM quantum computer and show that it is a viable tool for compiling near-term quantum simulation algorithms. We develop code that decomposes arbitrary 3-qubit gates and implement it in a quantum simulation first for a linear ordered chain to highlight the generality of the approach, and second, for a complex molecule. We choose the Fenna-Matthews-Olsen (FMO) photosynthetic protein because it has a well characterised Hamiltonian and presents a complex dissipative system coupled to a noisy environment that helps to improve the efficiency of energy transport. The method can be implemented in a broad range of molecular and other simulation settings.

CLASSICAL DIFFUSION AND QUANTAL LOCALIZATION OF A KICKED PARTICLE IN A WELL

1988 ◽  
Vol 02 (01) ◽  
pp. 103-120 ◽  
Author(s):  
AVRAHAM COHEN ◽  
SHMUEL FISHMAN
Keyword(s):  
Diffusion Coefficient ◽  
Classical Limit ◽  
Approximate Formula ◽  
Quantum Systems ◽  
Potential Well ◽  
Diffusive Growth ◽  
Classical Chaos ◽  
The One ◽  
Short Time ◽  
Infinite Potential Well

The classical and quantal behavior of a particle in an infinite potential well, that is periodically kicked is studied. The kicking potential is K|q|α, where q is the coordinate, while K and α are constants. Classically, it is found that for α > 2 the energy of the particle increases diffusively, for α < 2 it is bounded and for α = 2 the result depends on K. An approximate formula for the diffusion coefficient is presented and compared with numerical results. For quantum systems that are chaotic in the classical limit, diffusive growth of energy takes place for a short time and then it is suppressed by quantal effects. For the systems that are studied in this work the origin of the quantal localization in energy is related to the one of classical chaos.

THE TRAPPED-ION QUBIT: COHERENT CONTROL IN INFINITE-DIMENSIONAL QUANTUM SYSTEMS

2009 ◽  
Vol 24 (32) ◽  
pp. 2565-2578
Author(s):  
C. RANGAN
Keyword(s):  
Quantum Computing ◽  
Quantum System ◽  
Quantum Control ◽  
Coherent Control ◽  
Quantum Information Processing ◽  
Quantum Systems ◽  
Infinite Dimensional ◽  
Trapped Ion ◽  
Rich Variety ◽  
Control Research

Theories of quantum control have, until recently, made the assumption that the Hilbert space of a quantum system can be truncated to finite dimensions. Such truncations, which can be achieved for most quantum systems via bandwidth restrictions, have enabled the development of a rich variety of quantum control and optimal control schemes. Recent studies in quantum information processing have addressed the control of infinite-dimensional quantum systems such as the quantum states of a trapped-ion. Controllability in an infinite-dimensional quantum system is hard to prove with conventional methods, and infinite-dimensional systems provide unique challenges in designing control fields. In this paper, we will discuss the control of a popular system for quantum computing the trapped-ion qubit. This system, modeled by a spin-half particle coupled to a quantized harmonic oscillator, is an example for a surprisingly rich variety of control problems. We will show how this infinite-dimensional quantum system can be examined via the lens of the Finite Controllability Theorem, two-color STIRAP, the generalized Heisenberg system, etc. These results are important from the viewpoint of developing more efficient quantum control protocols, particularly in quantum computing systems. This work shows how one can expand the scope of quantum control research to beyond that of finite-dimensional quantum systems.

scholarly journals Quasi-Lie Brackets and the Breaking of Time-Translation Symmetry for Quantum Systems Embedded in Classical Baths

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 518 ◽  
Author(s):  
Alessandro Sergi ◽  
Gabriel Hanna ◽  
Roberto Grimaudo ◽  
Antonino Messina
Keyword(s):  
Constant Temperature ◽  
Degrees Of Freedom ◽  
Open Quantum Systems ◽  
Hamiltonian Dynamics ◽  
Quantum Systems ◽  
Classical Dynamics ◽  
Open Quantum ◽  
Time Translation ◽  
Translation Symmetry ◽  
Lie Brackets

Many open quantum systems encountered in both natural and synthetic situations are embedded in classical-like baths. Often, the bath degrees of freedom may be represented in terms of canonically conjugate coordinates, but in some cases they may require a non-canonical or non-Hamiltonian representation. Herein, we review an approach to the dynamics and statistical mechanics of quantum subsystems embedded in either non-canonical or non-Hamiltonian classical-like baths which is based on operator-valued quasi-probability functions. These functions typically evolve through the action of quasi-Lie brackets and their associated Quantum-Classical Liouville Equations, or through quasi-Lie brackets augmented by dissipative terms. Quasi-Lie brackets possess the unique feature that, while conserving the energy (which the Noether theorem links to time-translation symmetry), they violate the time-translation symmetry of their algebra. This fact can be heuristically understood in terms of the dynamics of the open quantum subsystem. We then describe an example in which a quantum subsystem is embedded in a bath of classical spins, which are described by non-canonical coordinates. In this case, it has been shown that an off-diagonal open-bath geometric phase enters into the propagation of the quantum-classical dynamics. Next, we discuss how non-Hamiltonian dynamics may be employed to generate the constant-temperature evolution of phase space degrees of freedom coupled to the quantum subsystem. Constant-temperature dynamics may be generated by either a classical Langevin stochastic process or a Nosé–Hoover deterministic thermostat. These two approaches are not equivalent but have different advantages and drawbacks. In all cases, the calculation of the operator-valued quasi-probability function allows one to compute time-dependent statistical averages of observables. This may be accomplished in practice using a hybrid Molecular Dynamics/Monte Carlo algorithms, which we outline herein.

scholarly journals USE OF THE WHIRLIGIG PRINCIPLE FOR STABILIZING THE INITIAL STATES OF SOME CLASSIC AND QUANTUM SYSTEMS

2020 ◽  
pp. 78-81
Author(s):  
V.A. Buts
Keyword(s):  
Quantum System ◽  
Excited States ◽  
Quantum Systems ◽  
Nuclear Systems ◽  
Initial States

It is shown that the whirligig principle can be used for stabilization of the initial states of some classical and quantum systems. This feature of the whirligig principle is demonstrated by simple examples. The most important result of this work is the proof of the fact that the stabilization of the excited states of quantum systems can be realized by acting not on the quantum system itself, but by acting on the states into which the system must go. Potentially, this result can be used to stabilize excited nuclear systems.

scholarly journals Quantum Filtering Equations for a System Driven by Nonclassical Fields

2018 ◽  
Vol 25 (02) ◽  
pp. 1850007 ◽  
Author(s):  
Anita Da̧browska
Keyword(s):  
Quantum System ◽  
Coherent States ◽  
Single Photon ◽  
Photon Counting ◽  
Stochastic Evolution ◽  
Input Output ◽  
Nonclassical States ◽  
Cascade System ◽  
Unitary Evolution ◽  
Photon States

Using Gardiner and Collet’s input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by light in some specific nonclassical states. The quantum system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the nonclassical states of field: a combination of vacuum and single photon states and a mixture of two coherent states. The stochastic evolution conditioned on the results of the photon counting and quadrature measurements is described.

TEMPORAL QUANTUM CHAOS

1999 ◽  
Vol 13 (18) ◽  
pp. 2361-2369 ◽  
Author(s):  
R. AURICH ◽  
F. STEINER
Keyword(s):  
Quantum Chaos ◽  
Chaotic Systems ◽  
Quantum Systems ◽  
Time Behavior ◽  
Classical Dynamics ◽  
Long Time Behavior ◽  
Initial State ◽  
Numerical Tests ◽  
Weyl Sum ◽  
Long Time

We study the long-time behavior of bound quantum systems whose classical dynamics is chaotic and put forward two conjectures. Conjecture A states that the autocorrelation function C(t)=<Ψ(0)|Ψ(t)> of a delocalized initial state |Ψ(0)> shows characteristic fluctuations, which we identify with a universal signature of temporal quantum chaos. For example, for the (appropriately normalized) value distribution of S~|C(t)| we predict the distribution P(S)=(π/2)Se-πS2/4. Conjecture B gives the best possible upper bound for a generalized Weyl sum and is related to the extremely large recurrence times in temporal quantum chaos. Numerical tests carried out for numerous chaotic systems confirm nicely the two conjectures and thus provide strong evidence for temporal quantum chaos.

scholarly journals Probing Rényi entanglement entropy via randomized measurements

Science ◽  
2019 ◽  
Vol 364 (6437) ◽  
pp. 260-263 ◽  
Author(s):  
Tiff Brydges ◽  
Andreas Elben ◽  
Petar Jurcevic ◽  
Benoît Vermersch ◽  
Christine Maier ◽  
...  
Keyword(s):  
Quantum System ◽  
Entanglement Entropy ◽  
Quantum Systems ◽  
Quantum States ◽  
Many Body ◽  
Trapped Ion ◽  
Statistical Correlations ◽  
Quantum Simulator ◽  
Entanglement Structure ◽  
Arbitrary Quantum

Entanglement is a key feature of many-body quantum systems. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a protocol for measuring the second-order Rényi entropy based on statistical correlations between randomized measurements. Our experiments, carried out with a trapped-ion quantum simulator with partition sizes of up to 10 qubits, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts, in both the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, which is applicable to arbitrary quantum states of up to several tens of qubits.

scholarly journals Semi-classical bounds on scattering cross sections in two dimensional magnetic fields

1997 ◽  
Vol 147 ◽  
pp. 25-61
Author(s):  
Hideo Tamura
Keyword(s):  
Magnetic Fields ◽  
Energy Range ◽  
Cross Sections ◽  
Classical Limit ◽  
Uniform Boundedness ◽  
Classical Dynamics ◽  
Two Dimensional ◽  
Total Cross Sections ◽  
Scattering Cross ◽  
Scattering Cross Sections

AbstractWe prove the uniform boundedness of averaged total cross sections or of quantities related to scattering into cones in the semi-classical limit for scattering by two dimensional magnetic fields. We do not necessarily assume that the energy under consideration is in a non-trapping energy range in the sense of classical dynamics.

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