Decoherence in continuous measurements: From models to phenomenology

Decoherence is the name for the complex of phenomena leading to appearance of classical features of quantum systems. In the present paper decoherence in continuous measurements is analyzed with the help of restricted path integrals (RPI) and (equivalently in simple cases) complex Hamiltonians. A continuous measurement results in a readout giving information in the classical form on the evolution of the measured quantum system. The quantum features of the system reveal themselves in the variation of possible measurement readouts. For example, the monitoring energy of a multi-level system may visualize a transition between levels as a process evolving in time but with an unavoidable quantum noise. Decoherence of a continuously measured system is completely determined by the measurement readout, i.e., by the information recorded in its environment. It is shown that the ideology of RPI makes the Feynman version of quantum mechanics closed, contrary to the conventional operator form of quantum mechanics which needs quantum theory of measurement as a necessary additional part.     

Fresnel Type Path Integral for the Stochastic Schrödinger Equation

A path integral representation is obtained for the stochastic partial differential equation of Schrödinger type arising in the theory of open quantum systems subject to continuous nondemolition measurement and filtering, known as the a posteriori or Belavkin equation. The result is established by means of Fresnel-type integrals over paths in configuration space. This is achieved by modifying the classical action functional in the expression for the amplitude along each path by means of a stochastic Itô integral. This modification can be regarded as an extension of Menski's path integral formula for a quantum system subject to continuous measurement to the case of the stochastic Schrödinger equation.     

Diachronic quantum action principle

Classical path and action are diachronic concepts in that they refer to many times instead of just one. The concept of a path is quantized into the concept of a propagation process between the initial preparation of and a measurement on a quantum system. A new quantum action is defined as a linear operator on the space of propagation processes, analogously to representing observables as linear operators on the ket and bra spaces. This quantization of paths and action results in a diachronic action principle: a variation of a dynamical propagation process is generated by the associated variation of the quantum action. The form of this principle is a candidate for the form of a dynamical principle of a theory without a classical time parameter.     

From Quantum Probabilities to Quantum Amplitudes

The task of reconstructing the system’s state from the measurements results, known as the Pauli problem, usually requires repetition of two successive steps. Preparation in an initial state to be determined is followed by an accurate measurement of one of the several chosen operators in order to provide the necessary “Pauli data”. We consider a similar yet more general problem of recovering Feynman’s transition (path) amplitudes from the results of at least three consecutive measurements. The three-step histories of a pre- and post-selected quantum system are subjected to a type of interference not available to their two-step counterparts. We show that this interference can be exploited, and if the intermediate measurement is “fuzzy”, the path amplitudes can be successfully recovered. The simplest case of a two-level system is analysed in detail. The “weak measurement” limit and the usefulness of the path amplitudes are also discussed.     

Entanglement, dephasing, and phase recovery via cross-correlation measurements of electrons

Determination of the path taken by a quantum particle leads to a suppression of interference and to a classical behavior. We employ here a quantum "which path" detector to perform accurate path determination in a two-path Mach-Zehnder electron interferometer, leading to full suppression of the interference. Following the dephasing process we recover the interference by measuring the cross correlation between the interferometer and detector currents. Under our measurement conditions every interfering electron is dephased by approximately a single electron in the detector-leading to mutual entanglement of approximately single pairs of electrons.     

多跳噪声量子纠缠信道特性及最佳中继协议

在量子通信网络中, 最佳中继路径的计算与选择策略是影响网络性能的关键因素. 针对噪声背景下量子隐形传态网络中的中继路径选择问题, 本文首先研究了相位阻尼信道及振幅阻尼信道上的纠缠交换过程, 通过理论推导给出了两种多跳纠缠交换信道上的纠缠保真度与路径等效阻尼系数. 在此基础上提出以路径等效阻尼系数为准则的隐形传态网络最佳中继协议, 并给出了邻居发现、量子链路噪声参数测量、量子链路状态信息传递、中继路径计算与纠缠资源预留等工作的具体过程. 理论分析与性能仿真结果表明, 相比于现有的量子网络路径选择策略, 本文方法能获得更小的路径平均等效阻尼系数及更高的隐形传态保真度. 此外, 通过分析链路纠缠资源数量对协议性能的影响, 说明在进行量子通信网设计时, 可以根据网络的规模及用户的需求合理配置链路纠缠资源.     

Some New Developments in the Theory of Path Integrals,with Applications to Quantum Theory

A survey of recent developments concerning rigorously defined infinite dimensional integrals, mainly of the type of “Feynman path integrals,” is given. Both the theory and its applications, especially in quantum theory, are presented. As for the theory, general results are discussed including the case of polynomially growing phase functions, which are handled by exploiting the connection with probabilistic functional integrals. Also applications to continuous measurement theory and the stochastic Schrödinger equation are given. Other applications of probabilistic methods in non relativistic quantum theory and in quantum field theory, and their relations with statistical mechanics, are discussed.     

Geometric phase of an open double-quantum-dot system detected by a quantum point contact

We study theoretically the geometric phase of a double-quantum-dot(DQD) system measured by a quantum point contact(QPC) in the pure dephasing and dissipative environments, respectively. The results show that in these two environments, the coupling strength between the quantum dots has an enhanced impact on the geometric phase during a quasiperiod. This is due to the fact that the expansion of the width of the tunneling channel connecting the two quantum dots accelerates the oscillations of the electron between the quantum dots and makes the length of the evolution path longer.In addition, there is a notable near-zero region in the geometric phase because the stronger coupling between the system and the QPC freezes the electron in one quantum dot and the solid angle enclosed by the evolution path is approximately zero,which is associated with the quantum Zeno effect. For the pure dephasing environment, the geometric phase is suppressed as the dephasing rate increases which is caused only by the phase damping of the system. In the dissipative environment,the geometric phase is reduced with the increase of the relaxation rate which results from both the energy dissipation and phase damping of the system. Our results are helpful for using the geometric phase to construct the fault-tolerant quantum devices based on quantum dot systems in quantum information.     

Quantum state discrimination and enhancement by noise

Discrimination between two quantum states is addressed as a quantum detection process where a measurement with two outcomes is performed and a conclusive binary decision results about the state. The performance is assessed by the overall probability of decision error. Based on the theory of quantum detection, the optimal measurement and its performance are exhibited in general conditions. An application is realized on the qubit, for which generic models of quantum noise can be investigated for their impact on state discrimination from a noisy qubit. The quantum noise acts through random application of Pauli operators on the qubit prior to its measurement. For discrimination from a noisy qubit, various situations are exhibited where reinforcement of the action of the quantum noise can be associated with enhanced performance. Such implications of the quantum noise are analyzed and interpreted in relation to stochastic resonance and enhancement by noise in information processing.     

Continuous quantum measurement with independent detector cross correlations

We investigate the advantages of using two independent, linear detectors for continuous quantum measurement. For single-shot measurement, the detection process may be quantum limited if the detectors are twins. For weak continuous measurement, cross correlations allow a violation of the Korotkov-Averin bound for the detector's signal-to-noise ratio. The joint weak measurement of noncommuting observables is also investigated, and we find the cross correlation changes sign as a function of frequency, reflecting a crossover from incoherent relaxation to coherent, out of phase oscillations. Our results are applied to a double quantum-dot charge qubit, simultaneously measured by two quantum point contacts.     

Quantum Measurement and Extended Feynman Path Integral

Quantum measurement problem has existed many years and inspired a large of literature in both physics and philosophy, but there is still no conclusion and consensus on it. We show it can be subsumed into the quantum theory if we extend the Feynman path integral by considering the relativistic effect of Feynman paths. According to this extended theory, we deduce not only the Klein--Gordon equation, but also the wave-function-collapse equation. It is shown that the stochastic and instantaneous collapse of the quantum measurement is due to the “potential noise” of the apparatus or environment and “inner correlation” of wave function respectively. Therefore, the definite-status of the macroscopic matter is due to itself and this does not disobey the quantum mechanics. This work will give a new recognition for the measurement problem.     

超短脉冲谐波辐射过程中的量子路径分析

本文数值计算了脉宽为半个光学周期的超短脉冲在不同载波包络相位下的谐波波谱,通过比较谐波波谱截止频率与电子通过主要路径可获得的最大动能的差异,研究了超短脉冲谐波辐射过程中的量子路径。结果显示,超短脉冲谐波辐射过程中电子获得动能的量子路径偏离主要量子路径,而且该偏离效应受载波包络相位的影响。     

Causality, relativity and quantum correlation experiments with moving reference frames

Entanglement, one of the most important features of quantum mechanics, is at the core of the famous Einstein-Bohr philosophical debate [1] and is the principal resource for quantum information processing [2]. We report on new experimental investigations of the properties of entangled photon pairs with emphasis on the tension between quantum mechanics and relativity [3,4]. Entangled photons are sent via an optical fiber network to two villages near Geneva, separated by more than 10 km where they are analyzed by interferometers [5]. The photon pair source is set as precisely as possible in the center so that the two photons arrive at the detectors within a time interval of less than 5 ps (corresponding to a path length difference of less than 1 mm). This sets a lower bound on the ‘speed of quantum information’ to 10⁷ times the speed of light. Next, one detector is set in motion [6] so that both detectors, each in its own inertial reference frame, are first to do the measurement! The data always reproduces the quantum correlations.     

Quantum Computation with Nonlinear Optics

We propose a scheme of quantum computation with nonlinear quantum optics. Polarization states of photons are used for qubits. Photons with different frequencies represent different qubits. Single qubit rotation operation is implemented through optical elements like the Faraday polarization rotator. Photons are separated into different optical paths, or merged into a single optical path using dichromatic mirrors. The controlled-NOT gate between two qubits is implemented by the proper combination of parametric up and down conversions. This scheme has the following features： （1） No auxiliary qubits are required in the controlled-NOT gate operation; （2） No measurement is required in the course of the computation; （3） It is resource efficient and conceptually simple.     

超短脉冲谐波辐射过程中的量子路径分析

本文数值计算了脉宽为半个光学周期的超短脉冲在不同载波包络相位下的谐波波谱,通过比较谐波波谱截止频率与电子通过主要路径可获得的最大动能的差异,研究了超短脉冲谐波辐射过程中的量子路径。结果显示,超短脉冲谐波辐射过程中电子获得动能的量子路径偏离主要量子路径,而且该偏离效应受载波包络相位的影响。     

Stochastic Dynamics of Reduced Wave Functions and Continuous Measurement in Quantum Optics

The stochastic dynamics of open quantum systems interacting with a zero temperature environment is investigated by employing a formulation of quantum statistical ensembles in terms of probability distributions on projective Hilbert space. It is demonstrated that the open system dynamics can consistently be described by a stochastic process on the reduced state space. The physical meaning of reduced probability distributions on projective Hilbert space is derived from a complete, orthogonal measurement of the environment. The elimination of the variables of the environment is shown to lead to a piecewise deterministic process in Hilbert space defined by a differential Chapman-Kolmogorov equation. A Hilbert space path integral representation of the stochastic process is constructed. The general theory is illustrated by means of three examples from quantum optics. For these examples the microscopic derivation of the stochastic process is given and the general solution of the differential Chapman-Kolmogorov equation is constructed by means of the path integral representation.     

Protecting Qutrit-Qutrit Entanglement Under the Generalized Amplitude Decoherence of the Finite Temperature

We investigate the dynamics and protection of quantum entanglement of a qutrit-qutrit system under local amplitude damping channels with finite temperature. We consider two different initial states. We find that the qutrit-qutrit entanglement decays monotonically as the decoherence strength increases, and may go through entanglement sudden death at higher temperature. Special attention is paid to how to protect the quantum entanglement from decoherence by weak measurement and quantum measurement reversal. Our results show that the entanglement increases with the increase of weak measurement strength when the temperature is lower. However, the protections of entanglement by weak measurement and quantum measurement reversal are almost failed and the decays of entanglement goes up with the increase of weak measurement strength for different decoherence strength when the temperature is higher, even entanglement suffers sudden death.

     

No-Cloning Theorem,Kochen-Specker Theorem,and Quantum Measurement Theories

The usual no-cloning theorem implies that two quantum states are identical or orthogonal if we allow a cloning to be on the two quantum states. Here, we investigate a relation between the no-cloning theorem and the projective measurement theory that the results of measurements are either + 1 or − 1. We introduce the Kochen-Specker (KS) theorem with the projective measurement theory. We result in the fact that the two quantum states under consideration cannot be orthogonal if we avoid the KS contradiction. Thus the no-cloning theorem implies that the two quantum states under consideration are identical in that case. It turns out that the KS theorem with the projective measurement theory says a new version of the no-cloning theorem. Next, we investigate a relation between the no-cloning theorem and the measurement theory based on the truth values that the results of measurements are either + 1 or 0. We return to the usual no-cloning theorem that the two quantum states are identical or orthogonal in the case.

     

量子信令交换机模型设计及性能分析

本文提出了量子信令交换机的模型, 该交换机由经典信息控制模块、交换控制模块和量子交换模块三部分组成. 经典控制模块负责将纠缠初态信息传送给纠缠测量及交换单元并更新路由信息. 交换控制模块实现通路选择, 为纠缠对的分发提供通路. 量子交换模块制备纠缠对, 进行Bell态的测量, 完成纠缠交换. 量子信令交换机可以实现多用户间的信令传输及局域网通信. 通过对交换机的性能分析与仿真, 结果表明该交换机结构简单、安全保密、便于扩展、时延小, 对于构建量子通信网有很好的支撑作用. 关键词： 量子通信 量子信令网 量子信令交换机 纠缠交换     

Time-Symmetric Quantum Mechanics

A time-symmetric formulation of nonrelativistic quantum mechanics is developed by applying two consecutive boundary conditions onto solutions of a time- symmetrized wave equation. From known probabilities in ordinary quantum mechanics, a time-symmetric parameter P₀ is then derived that properly weights the likelihood of any complete sequence of measurement outcomes on a quantum system. The results appear to match standard quantum mechanics, but do so without requiring a time-asymmetric collapse of the wavefunction upon measurement, thereby realigning quantum mechanics with an important fundamental symmetry.