Richard A. Mould
The effect of rule (4) on a series or parallel sequence of quantum mechanical steps is to insure that a conscious observer does not skip a step. This rule effectively places the observer in continuous contact with the system. Key Words: brain states, continuous observation, conscious observer, measurement, probability current, state reduction, wave collapse.
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Graphical rule, describing that any single-mode homodyne detection turns a given continuous-variable (CV) graph state into a new one, is presented. Employing two simple graphical rules: local complement operation and vertex deletion (single quadrature-amplitude $\hat{x}$ measurement), the graphical rule for any single-mode quadrature component measurement can be obtained. The shape of CV weighted graph state may be designed and constructed easily from a given larger graph state by applying this graphical rule.
The local complementation rule is applied for continuous-variable (CV) graph states in the paper, which is an elementary graph transformation rule and successive application of which generates the orbit of any graph states. The corresponding local Gaussian transformations of local complementation for four-mode unweighted graph states were found, which do not mirror the form of the local Clifford unitary of qubit exactly. This work is an important step to characterize the local Gaussian equivalence classes of CV graph states.
Simplification Rules for Continuous-Time Quantum Walks on Dynamic Graphs
本文为动态图上的连续时间量子行走提出简化规则，实现标准单量子比特门并演示电路化简，作为电路模型与动态图框架间的转译原语。
In this paper I present a thought experiment that gives different results depending on whether or not the wavefunction collapses. Since the wavefunction does not obey the Schrodinger equation during the collapse, conservation laws are violated. This is the reason why the results are different. Quantities that are conserved if the wavefunction does not collapse might change if it does. I also show that using the Born Rule to derive probabilities of states before a measurement given the state after it (rather than the other way round as it is usually used) leads to the conclusion that the memori…
In orthodox quantum theory, decoherence is presumed to be caused by observation. In this paper, the idea of replacing observation, as the cause of decoherence, with rules derived from the dynamics of the system is addressed. Such rules determine the timing of decoherence and the states in the mixture afterward. For instance, energy conservation during decohenence, for each possible transition, leads to a timing rule. Exponetial decay and ergodic behavior follow directly from the dynamic rules as do Boltzman's postulate of equally probable micro-states and the Pauli rate equations. Ergodic beha…
We examine the role of a conscious observer in a typical quantum mechanical measurement. Four rules are given that govern stochastic choice and state reduction in several cases of continuous and intermittent observation. It is found that consciousness always accompanies a state reduction leading to observation, but its presence is not sufficient to 'cause' a reduction. The distinction is clarified and codified by the rules that are given below. This is the first of several papers that lead to an experimental test of the rules, and of the "parallel principle" that is described elsewhere. Key wo…
The evolution of a quantum system undergoing very frequent measurements takes place in a proper subspace of the total Hilbert space (quantum Zeno effect). When the measuring apparatus is included in the quantum description, the Zeno effect becomes a pure consequence of the dynamics. We show that for continuous measurement processes the quantum Zeno evolution derives from an adiabatic theorem. The system is forced to evolve in a set of orthogonal subspaces of the total Hilbert space and a dynamical superselection rule arises. The dynamical properties of this evolution are investigated and sever…
In a previous paper we examined the role of a conscious observer in a typical quantum mechanical measurement. Four rules were given that were found to govern the stochastic choice and state reduction in several cases of continuous and intermittent observation. It was shown that consciousness always accompanies a state reduction leading to observation, but its presence is not sufficient to 'cause' a reduction. The distinction is clarified and codified by the rules that are repeated below. In this paper, these rules are successfully applied to two different versions of the Schrodinger cat experi…
This paper elaborates on four previously proposed rules of engagement between conscious states and physiological states. A new rule is proposed that applies to a continuous model of conscious brain states that cannot precisely resolve eigenvalues. If two apparatus states are in superposition, and if their eigenvalues are so close together that they cannot be consciously resolved on this model, then it is shown that observation will not generally reduce the superposition to just one of its member eigenstates. In general, the observation of a quantum mechanical superposition results in another s…
A stochastic model for the continuous nondemolition ohservation of the position of a quantum particle in a potential field and a boson reservoir is given. lt is shown that any Gaussian wave function evolving according to the posterior wave equation with a quadratic potential collapses to a Gaussian wave packet given by the stationary solution of this equation.
Born rule: quantum probability as classical probability
本文提出了一种将玻恩法则推导为经典概率的简单方法，证明了在连续基下量子系统可应用与经典系统相同的概率原理，并为整个宇宙存在唯一的本体基提供了可能性。
The main aim of the paper is to present the analytical solution of the Belavkin quantum filtering equation for damped harmonic oscillator being initially in the squeezed coherent state for diffusion observation with complex white noise. The comparison of the a priori and a posteriori mean value of the optical quadrature operators and the photon number operator is given.
We suggest an experimentally realizable scheme to test entanglement of a mixed Gaussian continuous variable state. We find that the entanglement condition is simplified for the family of Gaussian states which are relevant to experimental realization. The entanglement condition is then shown to be directly related to joint homodyne measurements. We show how robust the proposed test of entanglement is against imperfect detection efficiency.
Generically the probabilities of observational results depend upon both the quantum state and the rules for extracting the probabilities from it. It is often argued that inflation may make our observations independent of the quantum state. In a framework in which one considers the state and the rules as logically separate, it is shown how it is possible that the probabilities are indeed independent of the state, but the rules for achieving this seem somewhat implausible.
Time crystals are classified as discrete or continuous depending on whether they spontaneously break discrete or continuous time translation symmetry. While discrete time crystals have been extensively studied in periodically driven systems since their recent discovery, the experimental realization of a continuous time crystal is still pending. Here, we report the observation of a limit cycle phase in a continuously pumped dissipative atom-cavity system, which is characterized by emergent oscillations in the intracavity photon number. We observe that the phase of this oscillation is random for…
Algebra of quantum mechanics via classical phonons. II: Klein-Gordon dynamics, the Heisenberg formalism, the Dirac canonical commutation rule and the Poincare algebra through the continuous Poisson bracket formalism
研究如何从经典声子模型出发，通过经典哈密顿形式主义恢复单无自旋粒子相对论量子力学特征，定义连续泊松括号，建立与量子力学形式的联系并恢复庞加莱群变换及代数。
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