H. Kröger
We have previously proposed a conjecture stating that quantum mechanical transition amplitudes can be parametrized in terms of a quantum action. Here we give a proof of the conjecture and establish the existance of a local quantum action in the case of imaginary time in the Feynman-Kac limit (when temperature goes to zero). Moreover we discuss some symmetry properties of the quantum action.
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A general formulation of discrete-time quantum mechanics, restrictions on the action and the relation of unitarity to the existence theorem for initial-value problems
基于普通量子力学中的Feynman方法，给出了离散时间量子力学的一般公式。它表明，在普通的量子力学（由于非交换性的运营商），目前的模糊性，不再存在于这里。然后研究了演化算子的么正性准则。结果表明，发展算子的幺正性限制了作用的形式，也暗示了经典初值问题解的存在性。
A quantum version of the action principle is considered in the case of a free relativistic particle. The classical limit of the quantum action is obtained.
A quantum version of the action principle is formulated in terms of real parameters of a wave functional. The classical limit of the quantum action of a harmonic oscillator is obtained.
We discuss the concept of the quantum action with the purpose to characterize and quantitatively compute quantum chaos. As an example we consider in quantum mechanics a 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling - which is classically a chaotic system. We compare Poincaré sections obtained from the quantum action with those from the classical action.
We use the quantum action to study the dynamics of quantum system at finite temperature. We construct the quantum action non-perturbatively and find temperature dependent action parameters. Here we apply the quantum action to study quantum chaos. We present a numerical study of a classically chaotic 2-D Hamiltonian system - harmonic oscillators with anharmonic coupling. We compare Poincaré sections for the quantum action at finite temperature with those of classical action.
Quantum State Group Actions
本文探索群作用于量子态集合的量子态群作用，证明其安全性限制与计算问题，并展示其在统一现有量子货币方案及密钥分发协议方面的作用。
The traditional approach to feedback control is to apply forces to a system by modifying the Hamiltonian. Here we show that quantum systems can be controlled without any Hamiltonian feedback, purely by exploiting the random quantum back-action of a continuous weak measurement. We demonstrate that, quite remarkably, the quantum back-action of such an adaptive measurement is just as effective at controlling quantum systems as traditional feedback.
We consider a mixed chaotic Hamiltonian system and compare classical with quantum chaos. As alternative to the methods of enegy level spacing statistics and trace formulas, we construct a quantum action and a quantum analogue phase space to analyse quantum chaos.
A discrete action principle for general quantum automata is proposed. This action principle is particularized to Discrete Time Quantum Walks (DTQWs) and then extended into an energy and momentum preserving, manifestly covariant formulation. Space-time coordinates are introduced as new variables of the action and their equations of motion enforce energy and momentum conservation. This guarantees that the proposed action can be used to build future, DTQW-based self-consistent models of spinors interacting with gauge fields. A discrete stress-energy tensor for the DTQW is also obtained by functio…
The existence of quantum time crystals is investigated and shown to be possible in pure phases defined by a state invariant under a group of space translations, as displayed by explicit examples.
We calculate the quantum corrections to the classical action of a particle with coordinate-dependent mass. The result is made self-consistent by a variational approach, thus making it applicable to strong-couplings and singular potentials. By including thermal fluctuations, the we obtain an effective action whose classical Euler-Lagrange equation describes the motion of a particle including quantum and thermal effects.
In this letter we establish the impossibility of existence of self replicating machine in the quantum world. We establish this result by three different but consistent approaches of linearity of quantum mechanics, no signalling condition and conservation of entanglement under local unitary operations.
In the framework quotient algebra partition, a general methodology is introduced to construct fault tolerant encodes for an arbitrary action in an error-correcting code.
An alternative interpretation of the quantum adiabatic approximation is presented. This interpretation is based on the ideas originally advocated by David Bohm in his quest for establishing a hidden variable alternative to quantum mechanics. It indicates that the validity of the quantum adiabatic approximation is a sufficient condition for the separability of the quantum action function in the time variable. The implications of this interpretation for Berry's adiabatic phase and its semi-classical limit are also discussed.
We investigate the question if quantum algorithms exist that compute the maximum of a set of conjugated elements of a given number field in quantum polynomial time. We will relate the existence of these algorithms for a certain family of number fields to an open conjecture from elementary number theory.
We study the back action on a coupled multiple-qubit system induced by a quantum cavity probe in a non-demolition quantum measurement scheme. The exact quantum state stochastic Schrödinger equation is derived to systematically investigate the dynamics of quantum entanglement of the multiple-qubit system inside the cavity probe. Although quantum entanglement cannot be directly measured through experiments, the back action on quantum entanglement in the multi-qubit system is witnessed by applying the exact quantum state stochastic equations. Our results demonstrate that the analysis on the sensi…
We have recently suggested a quantum action, which has the form of a classical action and takes into account quantum effects via renormalized action parameters. Here we apply it to quantum chaos. We study a system in 2-D with weak anharmonic coupling ($V_{coupl} \propto x^{2}y^{2}$) being classically chaotic. We construct the quantum action at finite temperature. We compute Poincaré sections of the quantum action at that temperature and compare it with those of the classical action. We observe chaotic behavior in both cases.
A new form of covariant quantum theory based on a quantum version of the action principle is considered for the case of a free bosonic string. The central idea of the new approach is to delay conditions of stationarity of the classical action with respect to Lagrangian multipliers up to the quantum level where delayed conditions of stationarity are imposed on a quantum action. Physical states of the ordinary covariant quantum theory are replaced by well defined stationary states as those which obey quantum action principle. The stationary states have well defined energies.
We propose a new method to overcome quantum back-action in a measurement process using oscillators. An optical oscillator is used as a meter to measure the parameters of another open oscillator. The optical oscillator is synthesized such that the optical restoring force counters any perturbations induced by the quantum back-action phenomena. As a result, it is shown that the quantum back-action in continuous measurement is suppressed in the low frequency regime i.e., for frequencies much smaller than the resonance frequency of the open oscillator. As the meter plays the role of measuring param…
In this paper we derive various identities involving the {\it action} functional which enters the path-integral formulation of quantum mechanics. They provide some kind of generalisations of the Ehrenfest theorem giving correlations between powers of the action and its functional derivatives.
Quantum Action Principle formulated earlier is used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics. In this new approach the probability "flows" in the Minkowsky space being dependent on an inner time parameter which we interpret as a particle life time. The life time is determined as a function of observable parameters of the real experiment by means of an additional condition of stationarity for the quantum action.
Quantum Money from Abelian Group Actions
本文基于阿贝尔群作用构造公钥量子货币及量子闪电，通过椭圆曲线同源实现群作用，在通用群模型中证明安全性并开发量子安全证明工具包，还揭示了量子环境下相关假设/模型的局限性。
We propose that the dispersion management of coherent atomic matter waves can be exploited to overcome quantum back-action in condensate-based optomechanical sensors. The effective mass of an atomic Bose-Einstein condensate modulated by an optical lattice can become negative, resulting in a negative-frequency optomechanical oscillator, a negative environment temperature, and optomechanical properties opposite to those of a positive-mass system. This enables a quantum-mechanics-free subsystem insulated from quantum back-action.
We solve one of the oldest problems in the theory of quantum stabilizer codes by proving the non-existence of quantum [[13,5,4]]-codes.
Recently, Lloyd and Montangero have made a brief research proposal on universal quantum computation in integrable systems. The main idea is to encode qubits into quantum action variables and build up quantum gates by the method of resonant control. We study this proposal to argue quantum computation using action variables as fault-tolerant quantum computation, whose fault-tolerance is guaranteed by the quantum KAM theorem. Besides, we view the Birkhoff norm form as a mathematical framework of the extended harmonic oscillator quantum computation.
Co-existence of different states is a profound concept, which possibly underlies the phase transition and the symmetry breaking. Because of a property inherent to quantum mechanics (cf. uncertainty), the co-existence is expected to appear more naturally in quantum-microscopic systems than in macroscopic systems. In this paper a mathematical theory describing co-existence of states in quantum systems is presented, and the co-existence is classified into 9 types.
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