Structure of canonical variables in the theory of quantum systems with finitely and infinitely many degrees of freedom

1974 ◽  
Vol 19 (1) ◽  
pp. 325-331
Author(s):  
N. V. Borisov
Keyword(s):  
Degrees Of Freedom ◽  
Quantum Systems ◽  
Canonical Variables

scholarly journals Multiparticle quantum plasmonics

Nanophotonics ◽  
2020 ◽  
Vol 9 (6) ◽  
pp. 1243-1269 ◽  
Author(s):  
Chenglong You ◽  
Apurv Chaitanya Nellikka ◽  
Israel De Leon ◽  
Omar S. Magaña-Loaiza
Keyword(s):  
Quantum Dynamics ◽  
Degrees Of Freedom ◽  
Single Photon ◽  
Quantum Systems ◽  
Many Body ◽  
Statistical Fluctuations ◽  
Quantum Plasmonics ◽  
Control Of Quantum Systems ◽  
Multiparticle Systems ◽  
Quantum Photonics

AbstractA single photon can be coupled to collective charge oscillations at the interfaces between metals and dielectrics forming a single surface plasmon. The electromagnetic near-fields induced by single surface plasmons offer new degrees of freedom to perform an exquisite control of complex quantum dynamics. Remarkably, the control of quantum systems represents one of the most significant challenges in the field of quantum photonics. Recently, there has been an enormous interest in using plasmonic systems to control multiphoton dynamics in complex photonic circuits. In this review, we discuss recent advances that unveil novel routes to control multiparticle quantum systems composed of multiple photons and plasmons. We describe important properties that characterize optical multiparticle systems such as their statistical quantum fluctuations and correlations. In this regard, we discuss the role that photon-plasmon interactions play in the manipulation of these fundamental properties for multiparticle systems. We also review recent works that show novel platforms to manipulate many-body light-matter interactions. In this spirit, the foundations that will allow nonexperts to understand new perspectives in multiparticle quantum plasmonics are described. First, we discuss the quantum statistical fluctuations of the electromagnetic field as well as the fundamentals of plasmonics and its quantum properties. This discussion is followed by a brief treatment of the dynamics that characterize complex multiparticle interactions. We apply these ideas to describe quantum interactions in photonic-plasmonic multiparticle quantum systems. We summarize the state-of-the-art in quantum devices that rely on plasmonic interactions. The review is concluded with our perspective on the future applications and challenges in this burgeoning field.

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.

Cluster state quantum computation for many-level systems

2007 ◽  
Vol 7 (3) ◽  
pp. 184-208
Author(s):  
W. Hall
Keyword(s):  
Quantum Computation ◽  
Degrees Of Freedom ◽  
Cluster State ◽  
Quantum Systems ◽  
Explicit Description ◽  
State Model ◽  
Mutually Unbiased Bases ◽  
Large Set ◽  
Adaptive Computation ◽  
Complete Framework

The cluster state model for quantum computation [Phys. Rev. Lett. \textbf{86}, 5188] outlines a scheme that allows one to use measurement on a large set of entangled quantum systems in what is known as a cluster state to undertake quantum computations. The model itself and many works dedicated to it involve using entangled qubits. In this paper we consider the issue of using entangled qudits instead. We present a complete framework for cluster state quantum computation using qudits, which not only contains the features of the original qubit model but also contains the new idea of adaptive computation: via a change in the classical computation that helps to correct the errors that are inherent in the model, the implemented quantum computation can be changed. This feature arises through the extra degrees of freedom that appear when using qudits. Finally, for prime dimensions, we give a very explicit description of the model, making use of mutually unbiased bases.

scholarly journals On the Hamiltonian approach: Applications to geophysical flows

1998 ◽  
Vol 5 (4) ◽  
pp. 219-240 ◽  
Author(s):  
V. Goncharov ◽  
V. Pavlov
Keyword(s):  
Degrees Of Freedom ◽  
Fluid Motion ◽  
Gauge Transformations ◽  
Motion Models ◽  
Canonical Variables ◽  
Long Time ◽  
Minimum Number ◽  
Nonlinear Gauge ◽  
Hydrodynamical System ◽  
General Method

Abstract. This paper presents developments of the Harniltonian Approach to problems of fluid dynamics, and also considers some specific applications of the general method to hydrodynamical models. Nonlinear gauge transformations are found to result in a reduction to a minimum number of degrees of freedom, i.e. the number of pairs of canonically conjugated variables used in a given hydrodynamical system. It is shown that any conservative hydrodynamic model with additional fields which are in involution may be always reduced to the canonical Hamiltonian system with three degrees of freedom only. These gauge transformations are associated with the law of helicity conservation. Constraints imposed on the corresponding Clebsch representation are determined for some particular cases, such as, for example. when fluid motions develop in the absence of helicity. For a long time the process of the introduction of canonical variables into hydrodynamics has remained more of an intuitive foresight than a logical finding. The special attention is allocated to the problem of the elaboration of the corresponding regular procedure. The Harniltonian Approach is applied to geophysical models including incompressible (3D and 2D) fluid motion models in curvilinear and lagrangian coordinates. The problems of the canonical description of the Rossby waves on a rotating sphere and of the evolution of a system consisting of N singular vortices are investigated.

scholarly journals State-independent contextuality in classical light

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Tao Li ◽  
Qiang Zeng ◽  
Xiong Zhang ◽  
Tian Chen ◽  
Xiangdong Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Information Science ◽  
Quantum Systems ◽  
Optical Systems ◽  
Quantum Information Science ◽  
Independent Manner ◽  
Classical Counterpart ◽  
Information Processes ◽  
Fundamental Phenomenon ◽  
Application Prospects

AbstractState-independent contextuality is a fundamental phenomenon in quantum mechanics, which has been demonstrated experimentally in different systems in recent years. Here we show that such contextuality can also be simulated in classical optical systems. Using path and polarization degrees of freedom of classical optics fields, we have constructed the classical trit (cetrit), here the term ‘cetrit’ is the classical counterpart of a qutrit in quantum systems. Furthermore, in classical optical systems we have simulated the violations of several Yu-Oh-like noncontextual inequalities in a state-independent manner by implementing the projection measurements. Our results not only provide new physical insights into the contextuality and also show the application prospects of the concepts developed recently in quantum information science to classical optical systems and optical information processes.

scholarly journals QUANTUM ESTIMATION OF RELATIVE INFORMATION

2006 ◽  
Vol 04 (01) ◽  
pp. 131-149 ◽  
Author(s):  
NETANEL H. LINDNER ◽  
PETRA F. SCUDO ◽  
DAGMAR BRUß
Keyword(s):  
Symmetry Group ◽  
Prior Knowledge ◽  
Reference Frame ◽  
Spatial Orientation ◽  
Degrees Of Freedom ◽  
Estimation Procedure ◽  
Quantum Systems ◽  
Relative Information ◽  
Rotation Parameters ◽  
Require Information

We derive optimal schemes for preparation and estimation of relational degrees of freedom between two quantum systems. We specifically analyze the case of rotation parameters representing relative angles between elements of the SU(2) symmetry group. Our estimation procedure does not assume prior knowledge of the absolute spatial orientation of the systems and as such does not require information on the underlying classical reference frame in which the states are prepared.

scholarly journals The cost of quantum locality

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200602
Author(s):  
C. A. Bédard
Keyword(s):  
Wave Function ◽  
Degrees Of Freedom ◽  
Quantum Systems ◽  
Bell’S Theorem ◽  
Bell's Theorem ◽  
Global System ◽  
Small System ◽  
Local Description ◽  
Quantum Locality ◽  
The Cost

It has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally—notwithstanding Bell’s theorem. More recently, Raymond-Robichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the dimensionality of their underlining space. The number of degrees of freedom of a single qubit’s local description is shown to grow exponentially with the total number of qubits considered as a global system. This apparently unreasonable cost to describe such a small system in a large Universe is nonetheless shown to be expected. Finally, structures that supplement the universal wave function are investigated.

scholarly journals Accurate Truncations of Chain Mapping Models for Open Quantum Systems

Nanomaterials ◽  
2021 ◽  
Vol 11 (8) ◽  
pp. 2104
Author(s):  
Mónica Sánchez-Barquilla ◽  
Johannes Feist
Keyword(s):  
Degrees Of Freedom ◽  
Nearest Neighbor ◽  
Open Quantum Systems ◽  
Quantum Systems ◽  
Open Quantum ◽  
Research Fields ◽  
A Chain ◽  
Chain Lengths ◽  
Mapping Models ◽  
Nearest Neighbor Coupling

The dynamics of open quantum systems are of great interest in many research fields, such as for the interaction of a quantum emitter with the electromagnetic modes of a nanophotonic structure. A powerful approach for treating such setups in the non-Markovian limit is given by the chain mapping where an arbitrary environment can be transformed to a chain of modes with only nearest-neighbor coupling. However, when long propagation times are desired, the required long chain lengths limit the utility of this approach. We study various approaches for truncating the chains at manageable lengths while still preserving an accurate description of the dynamics. We achieve this by introducing losses to the chain modes in such a way that the effective environment acting on the system remains unchanged, using a number of different strategies. Furthermore, we demonstrate that extending the chain mapping to allow next-nearest neighbor coupling permits the reproduction of an arbitrary environment, and adding longer-range interactions does not further increase the effective number of degrees of freedom in the environment.

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