Decoherence and Quantum-state Measurement in Quantum Optics
Luiz Davidovich
备注：
19 pages, 6 figures in encapsulated postscript format, Springer LNP LaTeX macros. To appear in the Proceedings of the Conference on Decoherence, Information, Complexity, and Entropy (DICE2002), Piombino, Italy, September, 2002 (edited by T.Elze)
This paper discusses work developed in recent years, in the domain of quantum optics, which has led to a better understanding of the classical limit of quantum mechanics. New techniques have been proposed, and experimentally demonstrated, for characterizing and monitoring in real time the quantum state of an electromagnetic field in a cavity. They allow the investigation of the dynamics of the decoherence process by which a quantum-mechanical superposition of coherent states of the field becomes a statistical mixture.
We propose an experiment in which an entangled pair of optical pulses are propagated through non-uniform gravitational fields. A field operator calculation of this situation predicts decoherence of the optical entanglement under experimentally realistic conditions.
We suggest that propagation of nonclassical light in lattices of optical waveguides can provide a laboratory tool to simulate quantum decoherence phenomena with high non-Markovian features. As examples, we study decoherence of optical Schrödinger cats in a lattice that mimics a dissipative quantum harmonic oscillator coupled to a quantum bath, showing fractional decoherence in the strong coupling regime, and Bloch oscillations of optical Schrödinger cats, where damped revivals of the coherence can be observed.
We present a quantum interference approach to preserve coherence in the external states of an atom trapped in an optical lattice. We show that this is possible by suitably choosing the initial state of the atom. We demonstrate this in context of decoherence due to spontaneous emission in an one-dimensional optical double-well lattice.
Photons in cavities have been already used for the realization of simple quantum gates [Q.A. Turchette, Phys. Rev. Lett. 75,4710 (1995)]. We present a method for combatting decoherence in this case.
By using the normal ordering method, we study the state evolution of an optically driven excitons in a quantum well immersed in a leaky cavity, which was introduced by Yu-xi Liu et.al. [Phys. Rev. A {\bf 63}, 033816 (2001)]. The influence of the external laser field on the quantum decoherence of a mesoscopically superposed states of the excitons is investigated. Our result shows that, thought the characteristic time of decoherence does not depend on the external field, the phase of the decoherence factor can be well controlled by adjusting the external parameters.
Taming decoherence is essential in realizing quantum computation and quantum communication. Here we experimentally demonstrate that decoherence due to amplitude damping can be suppressed by exploiting quantum measurement reversal in which a weak measurement and the reversing measurement are introduced before and after the decoherence channel, respectively. We have also investigated the trade-off relation between the degree of decoherence suppression and the channel transmittance.
By virtue of quantum coherence resource measure, we show that the dephasing measurement on a coherence basis can transfer the coherence contained in system into environment totally, which gives a quantification of decoherence.
We study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We find the fidelity for Hadamard gate and compute the purity of the final state when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate that in contradiction to the case of the systematic control errors the stochastic ones lead to decoherence of the final state. In the small errors limit we derive a simple formulae connecting the gate fidelity and the purity of the final state.
A pedagogical and reasonably self-contained introduction to the measurement problems in quantum mechanics and their partial solution by environment-induced decoherence (plus some other important aspects of dcoherence) is given. The point that decoherence does not solve the measurement problems completely is clearly brought out.The relevance of interpretation of quantum mechanics in this context is briefly discussed.
We study decoherence induced by stochastic squeezing control errors considering the particular implementation of Hadamard gate on optical and ion trap holonomic quantum computers. We analytically obtain both the purity of the final state and the fidelity for Hadamard gate when the control noise is modeled by Ornstein-Uhlenbeck stochastic process. We demonstrate the purity and the fidelity oscillations depending on the choice of the initial superimposed state. We derive a linear formulae connecting the gate fidelity and the purity of the final state.
We give an elementary account of quantum measurement and related topics from the modern perspective of decoherence. The discussion should be comprehensible to students who have completed a basic course in quantum mechanics with exposure to concepts such as Hilbert space, density matrices, and von Neumann projection (``wavefunction collapse'').
Various models have been proposed in which the Schrödinger equation is modified to account for a decay of spatial coherences of massive objects. While optomechanical systems and matter-wave interferometry with large clusters are promising candidates to test these models, we here show that using available techniques for atoms in optical lattices, some of these models can be efficiently tested. In particular, we compare unconventional decoherence due to quantum gravity as introduced by Ellis and co-workers [Phys. Lett. B ${\bf 221}$, 113 (1989)] and conventional decoherence due to scattering of …
Quantum enhancement of optical pulse timing accuracy is investigated in the Heisenberg picture. Effects of optical loss, group-velocity dispersion, and Kerr nonlinearity on the position and momentum of an optical pulse are studied via Heisenberg equations of motion. Using the developed formalism, the impact of decoherence by optical loss on the use of adiabatic soliton control for beating the timing standard quantum limit [Tsang, Phys. Rev. Lett. 97, 023902 (2006)] is analyzed theoretically and numerically. The analysis shows that an appreciable enhancement can be achieved using current techno…
We show how to optimally protect quantum states and quantum entanglement under non-zero temperature based on measurement reversal from weak measurement. In particular, we present explicit formulas of the protection.
We analyze the coherence properties of neutron wave packets, after they have interacted with a phase shifter undergoing different kinds of statistical fluctuations. We give a quantitative (and operational) definition of decoherence and compare it to the standard deviation of the distribution of the phase shifts. We find that in some cases the neutron ensemble is more coherent, even though it has interacted with a wider (i.e. more disordered) distribution of shifts. This feature is independent of the particular definition of decoherence: this is shown by proposing and discussing an alternative …
The possible effect of environment on the efficiency of a quantum algorithm is considered explicitely. It is illustrated through the example of Shor's prime factorization algorithm that this effect may be disastrous. The influence of environment on quantum computation is probed on the basis of its analogy to the problem of wave function collapse in quantum measurement.Techniques from the Hepp-Colemen approach and its generalization are used to deal with decoherence problems in quantum computation including dynamic mechanism of decoherence, quantum error avoiding tricks and calculation of decoh…
We present an all-optical implementation of quantum computation using semiconductor quantum dots. Quantum memory is represented by the spin of an excess electron stored in each dot. Two-qubit gates are realized by switching on trion-trion interactions between different dots. State selectivity is achieved via conditional laser excitation exploiting Pauli exclusion principle. Read-out is performed via a quantum-jump technique. We analyze the effect on our scheme's performance of the main imperfections present in real quantum dots: exciton decay, hole mixing and phonon decoherence. We introduce a…
Decoherence for a one-dimensional coupled-resonator waveguide with a two-level system inside one of resonators, induced by their interaction with corresponding environments, is investigated. Each environment is modeled as a continuum of harmonic oscillators. By finding the eigenstates of the hybrid system, which is the dressed state of the hybrid system, we calculate the lifetime of one excitation, which characterizes the existence of quantum coherence in such hybrid system and the basic quantum nature.
Environment-induced decoherence and superselection have been a subject of intensive research over the past two decades, yet their implications for the foundational problems of quantum mechanics, most notably the quantum measurement problem, have remained a matter of great controversy. This paper is intended to clarify key features of the decoherence program, including its more recent results, and to investigate their application and consequences in the context of the main interpretive approaches of quantum mechanics.
Distribution functions defined in accord with the quantum theory of measurement are combined with results obtained from the quantum Langevin equation to discuss decoherence in quantum Brownian motion. Closed form expressions for wave packet spreading and the attenuation of coherence of a pair of wave packets are obtained. The results are exact within the context of linear passive dissipation. It is shown that, contrary to widely accepted current belief, decoherence can occur at high temperature in the absence of dissipation. Expressions for the decoherence time with and without dissipation are…
We study the problem of driving an unknown initial mixed quantum state onto a known pure state without using unitary transformations. This can be achieved, in an efficient manner, with the help of sequential measurements on at least two unbiased bases. However here we found that, when the system is affected by a decoherence mechanism, only one observable is required in order to achieve the same goal. In this way the decoherence can assist the process. We show that, depending on the sort of decoherence, the process can converge faster or slower than the method implemented by means of two comple…
We discuss fluctuations in the measurement process and how these fluctuations are related to the dissipational parameter characterising quantum damping or decoherence. On the example of the measuring current of the variable-barrier or QPC problem we show there is an extra noise or fluctuation connected with the possible different outcomes of a measurement. This noise has an enhanced short time component which could be interpreted as due to ``telegraph noise'' or ``wavefunction collapses''. Furthermore the parameter giving the the strength of this noise is related to the parameter giving the ra…
A quantum system with discrete and continuos evolution spectrum is studied. A final pointer basis is found, that can be defined in a presised mathematical way. This result is use to explain the quantum measurement in the system.
This paper aims to show how adoption of a pragmatist interpretation permits a satisfactory resolution of the quantum measurement problem. The classic measurement problem dissolves once one recognizes that it is not the function of the quantum state to describe or represent the behavior of a quantum system. The residual problem of when, and to what, to apply the Born Rule may then be resolved by judicious appeal to decoherence. This can give sense to talk of measurements of photons and other particles even though quantum field theory does not describe particles.
We apply the influence-functional method of Feynman and Vernon to the study of a single-mode optical field that interacts with an environment at zero temperature. Using the coherent-state formalism of the path integral, we derive a generalized master equation for the single-mode optical field. Our analysis explicitly shows how non-Markovian effects manifest in the exact decoherence dynamics for different environmental correlation time scales. Remarkably, when these are equal to or greater than the time scale for significant change in the system, the interplay between the backaction-induced coh…
The Lindblad approach to continuous quantum measurements is applied to a system composed of a two-level atom interacting with a stationary quantized electromagnetic field through a dispersive coupling fulfilling quantum nondemolition criteria. Two schemes of measurements are examined. The first one consists in measuring the atomic electric dipole, which indirectly allows one to infer the photon distribution inside the cavity. The second one schematizes a measurement of photon momentum, which permits to describe the atomic level distribution. Decoherence of the corresponding reduced density mat…
An alternative approach to decoherence, named non-dynamical decoherence is developed and used to resolve the quantum measurement problem. According to decoherence, the observed system is open to a macroscopic apparatus(together with a possible added environment) in a quantum measurement process. We show that this open system can be well described by an "almost" quotient Hilbert space formed phenomenally according to some stability conditions. A group of random phase unitary operators is introduced further to obtain an exact quotient space for the observed system. In this quotient space, a dens…
Decay parameter of coherence and population inversion are calculated from the master equation of a two level atom tunneling through a squeezed vacuum. Using those parameters, the timescales for decoherence and zeno effect are calculated in the weak measurement scheme. By comparing those timescales, a certain condition has been found for sustainable coherent dynamics.
We propose an efficient method to protect spin squeezing under the action of amplitude-damping, depolarizing and phase-damping channels based on measurement reversal from weak measurement, and consider an ensemble of N independent spin-1/2 particles with exchange symmetry. We find that spin squeezing can be enhanced greatly under three different decoherence channels and spin-squeezing sudden death (SSSD) can be avoided undergoing amplitude damping and phase-damping channels.
By making the second quantization for the Cini Model of quantum measurement without wave function collapse [M. Cini, Nuovo Cimento, B73 27(1983)], the second order quantum decoherence (SOQD) is studied with a two mode boson system interacting with an idealized apparatus composed by two quantum oscillators. In the classical limit that the apparatus is prepared in a Fock state with a very large quantum number, or in a coherent state with average quantum numbers large enough, the SOQD phenomenon appears similar to the first order case of quantum decoherence.
The no-knowledge quantum feedback was proposed by Szigeti et al., Phys. Rev. Lett. 113, 020407 (2014), as a measurement-based feedback protocol for decoherence suppression for an open quantum system. By continuously measuring environmental noises and feeding back controls on the system, the protocol can completely reverse the measurement backaction and therefore suppress the system's decoherence. However, the complete decoherence cancellation was shown only for the instantaneous feedback, which is impractical in real experiments. Therefore, in this work, we generalize the original work and inv…
If a quantum experiment includes random processes, then the results of repeated measurements can appear consistent with irreversible decoherence even if the system's evolution prior to measurement was reversible and unitary. Two thought experiments are constructed as examples.
We illustrate through numerical results a number of features of environment-induced decoherence under a broad class of apparatus-environment interactions in quantum measurements wherein the reduced system-apparatus density matrix evolves towards the nearest separable state and, in addition, there occurs a mixing in relevant groups of apparatus microstates (see below). The resulting final state is unique and correctly embodies the measurement statistics even in the absence of environment-induced superselection because of energy differences between these groups of states. The partial transpose r…
According to our modal-Hamiltonian interpretation (MHI) of quantum mechanics, the Hamiltonian of the closed system defines the set of its definite-valued observables. This definition seems to be incompatible with the pointer basis selected by the environment-induced decoherence (EID) of the open system. In this paper we argue that decoherence can be understood from a closed system perspective which (i) shows that the incompatibility between MHI and EID is only apparent, and (ii) solves certain conceptual challenges that the EID program still has to face.
The effect of introducing measuring devices in a ``quantum pinball'' system is shown to lead to a chaotic evolution for the particle position as defined in Bohm's approach to Quantum Mechanics.
A single Ca+ ion in a Paul trap has been cooled to the ground state of vibration with up to 99.9% probability. Starting from this Fock state |n=0> we have demonstrated coherent quantum state manipulation on an optical transition. Up to 30 Rabi oscillations within 1.4 ms have been observed. We find a similar number of Rabi oscillations after preparation of the ion in the |n=1> Fock state. The coherence of optical state manipulation is only limited by laser and ambient magnetic field fluctuations. Motional heating has been measured to be as low as one vibrational quantum in 190 ms.
We study the problem of measurement-induced decoherence using the phase-space approach employing the Gaussian-smoothed Wigner distribution function. Our investigation is based on the notion that measurement-induced decoherence is represented by the transition from the Wigner distribution to the Gaussian-smoothed Wigner distribution with the widths of the smoothing function identified as measurement errors. We also compare the smoothed Wigner distribution with the corresponding distribution resulting from the classical analysis. The distributions we computed are the phase-space distributions fo…
We consider a universal set of quantum gates encoded within a perturbed decoherence-free subspace of four physical qubits. Using second-order perturbation theory and a measuring device modeled by an infinite set of harmonic oscillators, simply coupled to the system, we show that continuous observation of the coupling agent induces inhibition of the decoherence due to spurious perturbations. We thus advance the idea of protecting or even creating a decoherence-free subspace for processing quantum information.
We analyse the effects of intrinsic decoherence on the probability of generating a tripartite GHZ state using a cool trapped ion coupled to a single mode of the cavity field and interacting with a resonant laser field. Milburn equation is solved for this tripartite system to obtain the time evolution of density matrix as a function of cavity-ion coupling, laser-ion coupling, and the size of unitary time step relative to the time scale determined by system parameters. Starting with the system prepared initially in a separable state, density matrix is used to calculate the probability of tripart…
We exhibit three inequalities involving quantum measurement, all of which are sharp and state independent. The first inequality bounds the performance of joint measurement. The second quantifies the trade-off between the measurement quality and the disturbance caused on the measured system. Finally, the third inequality provides a sharp lower bound on the amount of decoherence in terms of the measurement quality. This gives a unified discription of both the Heisenberg principle and the collapse of the wave function.
Quantum entanglement has been used as an experimental tool to control the state of a quantum subsystem by measurements in its twin subsystem by Kwiat and Chiao 21 year ago, already, with entangled subsystems linked by an auxiliary classical coincidence channel. We propose to extend the idea one significant step further consisting essentially in eliminating the coincidence channel in the reminded experiment. The current availability of bright biphoton sources makes such experiments feasible.
One of the crucial tasks in quantum systems is to reduce the effects of decoherence due to the unavoidable interactions between a system and its environment. Many protection schemes have been proposed recently, among them the weak measurement quantum measurement reversal (WMQMR), weak measurement-based quantum feedback control (QFBC) and quantum feed-forward control (QFFC) are reviewed in this paper. By considering weak measurement, the aim is to find a balance between information gain and disturbance of the system caused by the measurement. We classify different types of measurement and give …
Decoherence is widely felt to have something to do with the quantum measurement problem, but getting clear on just what is made difficult by the fact that the "measurement problem", as traditionally presented in foundational and philosophical discussions, has become somewhat disconnected from the conceptual problems posed by real physics. This, in turn, is because quantum mechanics as discussed in textbooks and in foundational discussions has become somewhat removed from scientific practice, especially where the analysis of measurement is concerned. This paper has two goals: firstly (sections …
A multi-slit interference experiment, with which-way detectors, in the presence of environment induced decoherence, is theoretically analyzed. The effect of environment is modeled via a coupling to a bath of harmonic oscillators. Through an exact analysis, an expression for $\mathcal{C}$, a recently introduced measure of coherence, of the particle at the detecting screen is obtained as a function of the parameters of the environment. It is argued that the effect of decoherence can be quantified using the measured coherence value which lies between zero and one. For the specific case of two sli…
It is difficult to evaluate the precision of quantum measurements because it is not possible to conduct a second reference measurement on the same physical system to compare the measurement outcome with a more accurate value of the measured quantity. Here, I show that a direct evaluation of measurement uncertainties is possible when the measurement outcomes are used to compensate the small amount of decoherence induced in a probe qubit by carefully controlled interactions with the system. Since the original uncertainty of the target observable causes fluctuating phase shifts in the probe qubit…
Marshall et al. gedanken experiment of the quantum superpposition of a mirror (oscilating part of a Michelson interferometer) interacting with single photon is consequently interpreted by relative decoherence.Such relative decoherence (based on the spontaneous superposition breaking (effective hiding)) on the photon (quantum object) caused by mirror (measurement device) is sufficient to model real measurement.
Thermal decoherence is a major obstacle to the realization of quantum coherence for massive mechanical oscillators. Although optical trapping has been used to reduce the thermal decoherence rate for such oscillators, it also increases the rate by subjecting the oscillator to stochastic forces resulting from the frequency fluctuations of the optical field, thereby setting a fundamental limit on the reduction. This is analogous to the noise penalty in an active feedback system. Here, we directly measure the rethermalizaton process for an initially cooled and optically trapped suspended mirror, a…
A parity measurement on two qubits, each consisting of a single atom in a cavity, can be realized by measuring the phase shift of a probe beam, which interacts sequentially with the two qubits, but imperfections lead to decoherence within the subspaces of a given parity. We demonstrate that a different setup, where the probe light interacts repeatedly with the qubits, can reduce the rate of decoherence within the odd or the even parity subspace significantly. We consider both the case of a resonant and the case of a nonresonant light-atom interaction and find that the performance is comparable…
Decoherence of a quantum system induced by the interaction with its environment (measuring medium) may be presented phenomenologically as a continuous (or repeated) fuzzy quantum measurement. The dynamics of the system subject to continuous decoherence (measurement) may be described by the complex-Hamiltonian Schroedinger equation, stochastic Schroedinger equation of a certain type or (nonselectively) by the Lindblad master equation. The formulation of this dynamics with the help of restricted path integrals shows that the dynamics of the measured system depends only on the information recorde…
We study a class of quantum measurement models. A microscopic object is entangled with a macroscopic pointer such that a distinct pointer position is tied to each eigenvalue of the measured object observable. Those different pointer positions mutually decohere under the influence of an environment. Overcoming limitations of previous approaches we (i) cope with initial correlations between pointer and environment by considering them initially in a metastable local thermal equilibrium, (ii) allow for object-pointer entanglement and environment-induced decoherence of distinct pointer readouts to …
Recent experimental results demonstrated the generation of a quantum superpositon (MQS), involving a number of photons in excess of 5x10^4, which showed a high resilience to losses. In order to perform a complete analysis on the effects of de-coherence on this multiphoton fields, obtained through the Quantum Injected Optical Parametric Amplifier (QIOPA), we invesigate theoretically the evolution of the Wigner functions associated to these states in lossy conditions. Recognizing the presence of negative regions in the W-representation as an evidence of non-classicality, we focus our analysis on…
The decoherence times of orthogonally phased components of the optical transition dipole moment in a two-level system have been observed to differ by an order of magnitude. This phase anisotropy is observed in coherent transient experiments where an optical driving field is present during extended periods of decoherence. The decoherence time of the component of the dipole moment in phase with the driving field is extended compared to T_2, obtained from two-pulse photon echoes, in analogy with the spin locking technique of NMR.
Quantum-enhanced measurements use highly non-classical quantum states in order to enhance the precision of the measurement of classical quantities, like the length of an optical cavity. The major goal is to beat the standard quantum limit (SQL), i.e. a precision of order $1/\sqrt{N}$, where $N$ is the number of quantum resources (e.g. the number of photons or atoms used), and to achieve a scaling $1/N$, known as the Heisenberg limit. Doing so would have tremendous impact in many areas, but so far only three experiments have demonstrated a slight improvement over the SQL. The required quantum s…
In this paper, by exploiting the weak measurement and quantum measurement re- versal (WMQMR) procedure, we propose a scheme to show how one can protect the geometric quantum discord (GQD) of a two-qutrit V-type atomic system each of which interacts with a dissipative reservoir independently. We examine the scheme for the GQD of the initial two-qutrit Werner and Horodecki states for different classes of weak mea- surement strengthes. It is found out that the presented protocol enables us to suppress decoherence due to the amplitude damping (AD) channel and preserve the quantum dis- cord of the …
The Schrodinger and Heisenberg pictures are equivalent formulations of quantum mechanics. Here we use the Schrodinger picture to calculate the decoherence that occurs when an optical Schrodinger cat state is passed through a beam splitter. We find that an exponentially large amount of decoherence can occur even when there is a negligible change in the quadrature operator x(t) in the Heisenberg picture. Similar results have been observed in the decoherence produced by an optical amplifier, and we suggest that the usual quadrature operators in the Heisenberg picture do not provide a complete des…
In this work we investigate the relation between quantum measurements and decoherence, in order to formally express the necessity of the latter for obtaining an informative output from the former. To this aim, referring to the Von Neumann scheme for ideal quantum measurements, we first look for the minimal structure that the interaction between principal system and measurement apparatus must have for properly describing the process, beyond the quantum measurement limit, and then analyze the dynamical evolution induced by one such interaction. The analysis is developed by means of a recently in…
We propose a scheme to implement quantum computation in decoherence-free subspace with superconducting devices inside a cavity by unconventional geometric manipulation. Universal single-qubit gates in encoded qubit can be achieved with cavity assisted interaction. A measurement-based two-qubit Controlled-Not gate is produced with parity measurements assisted by an auxiliary superconducting device and followed by prescribed single-qubit gates. The measurement of currents on two parallel devices can realize a projective measurement, which is equivalent to the parity measurement on the involved d…
By considering an exactly solvable model of a two interacting spin-1/2 qubits described by the Heisenberg anisotropic interaction in the presence of intrinsic decoherence, we study the dynamics of entanglement quantified by the concurrence and measurement-induced nonlocality (MIN) based on Hilbert-Schmidt norm and trace distance with different initial conditions. We highlight the relationship between the entanglement and MIN for the pure initial state. For an initial separable state, it is found that the robustness and the generation of the quantum correlations depend on the physical parameter…
