We consider a single copy of a quantum particle moving in a potential and show that it is possible to monitor its complete wave function by only continuously measuring its position. While we assume that the potential is known, no information is available about its state initially. In order to monitor the wave function, an estimate of the wave function is propagated due to the influence of the potential and continuously updated according to the results of the position measurement. We demonstrate by numerical simulations that the estimation reaches arbitrary values of accuracy below 100 percent within a finite time period for the potentials we study. In this way our method grants, a certain time after the beginning of the measurement, an accurate real-time record of the state evolution including the influence of the continuous measurement. Moreover, it is robust against sudden perturbations of the system as for example random momentum kicks from environmental particles, provided they occur not too frequently.
Repeated unbiased measurements cause a continual application of the weak causality principle, leading to an apparent arrow of time for continuously-monitored quantum systems.
A new engineering technique using continuous quantum measurement in conjunction with feed-forward is proposed to improve indistinguishability of a single-photon source. The technique involves continuous monitoring of the state of the emitter, processing the noisy output signal with a simple linear estimation algorithm, and feed forward to control a variable delay at the output. In the weak coupling regime, the information gained by monitoring the state of the emitter is used to reduce the time uncertainty inherent in photon emission from the source, which improves the indistinguishability of t…
An engineering technique using continuous quantum measurement together with a change detection algorithm is proposed to improve the probability of single photon emission for a quantum-dot based single-photon source. The technique involves continuous monitoring of the emitter, integrating the measured signal, and a simple change detection circuit to decide when to stop pumping. The idea is to pump just long enough such that the emitter $+$ cavity system is in a state that can emit at most one photon with high probability. Continuous monitoring provides partial information on the state of the em…
We study the single-photon transport in a single-mode waveguide, in which two-level atoms in spatial superpositions are embedded. We find that the transmission of the photon can be used as a non-destructive probe for coherence of the superposition. The protocol proposed is shown to be independent of the distance between the wells in which the atoms are trapped. Furthermore, we show that by looking at the transmission in a suitable regime, a maximally entangled state can be post-selected from an unknown superposition.
The noise in optical source needs to be characterized for the security of continuous-variable quantum key distribution (CVQKD). Two feasible schemes, based on either active optical switch or passive beamsplitter are proposed to monitor the variance of source noise, through which, Eve's knowledge can be properly estimated. We derive the security bounds for both schemes against collective attacks in the asymptotic case, and find that the passive scheme performs better.
Application of the path-integral approach to continuous measurements leads to effective Lagrangians or Hamiltonians in which the effect of the measurement is taken into account through an imaginary term. We apply these considerations to nonlinear oscillators with use of numerical computations to evaluate quantum limitations for monitoring position in such a class of systems.
We study how non-Markovianity of an open two-level system can be detected when continuously monitoring a part of its bosonic environment. Considering a physical scenario of an atom in a lossy cavity, we demonstrate that the properties of the time-dependent flux of the photons from the cavity allows the detection of memory effects in the atomic dynamics, without requiring state nor process tomography. This framework overlaps with effective descriptions for the memory part of the environment using pseudomode methods. Our central results show how the Markovian measurement record on the environmen…
In a quantum system that is bounded by past and future conditions, weak continuous monitoring forward-evolving and backward-evolving quantum states are usually carried out separately. Therefore, measured signals at a given time t cannot be monitored continuously. Here, we propose an enlarged-quantum-system method to combine these two processes together. Therein, we introduce an enlarged quantum state that contains both the forward- and backward-evolving quantum states. The enlarged state is governed by an enlarged master equation and propagates one-way forward in time. As a result, the measure…
We analyze the problem of estimating past quantum states of a monitored system from a mathematical perspective in order to ensure self-consistency with the principle of quantum non-demolition. Despite several claims of ``measuring noncommuting observables'' in the physics literature, we show that we are always measuring commuting processes. Our main interest is in the notion of quantum smoothing or retrodiction. In particular, we examine proposals to estimate the result of an external measurement made on an open quantum systems during a period where it is also undergoing continuous monitoring.…
We present a continuous monitoring system for intermediate-scale quantum processors that allows extracting estimates of noisy native gate and read-out measurements based on the set of executed quantum circuits and resulting measurement outcomes. In contrast to standard approaches for calibration and benchmarking quantum processors, the executed circuits, which are input to the monitoring system, are assumed to be out of any control. We provide the results of applying our system to the synthetically generated data obtained from a quantum emulator, as well as to the experimental data collected f…
We discuss a model of repeated measurements of position in a quantum system which is monitored for a finite amount of time with a finite instrumental error. In this framework we recover the optimum monitoring of a harmonic oscillator proposed in the case of an instantaneous collapse of the wavefunction into an infinite-accuracy measurement result. We also establish numerically the existence of an optimal measurement strategy in the case of a nonlinear system. This optimal strategy is completely defined by the spectral properties of the nonlinear system.
We illustrate the equivalence between the non-unitary evolution of an open quantum system governed by a Markovian master equation and a process of continuous measurements involving this system. We investigate a system of two coupled modes, only one of them interacting with external degrees of freedom, represented, in the first case, by a finite number of harmonic oscillators, and, in the second, by a sequence of atoms where each one interacts with a single mode during a limited time. Two distinct regimes appear, one of them corresponding to a Zeno-like behavior in the limit of large dissipatio…
We propose a method to continually monitor the energy of a quantum system. We show that by having some previous knowledge of the system's dynamics, but not all of it, one can use the measured energy to determine many other quantities, such as the work performed on the system, the heat exchanged between the system and a thermal reservoir, the time dependence of the Hamiltonian of the system as well as the total entropy produced by its dynamics. We have also analyzed how this method is dependent on the quality factor of the measurements employed.
We analyze the capability of discriminating the statistical nature of a thermal bath by exploiting the interaction with an additional environment. We first shows that, at difference with the standard scenario where the additional environment is not present, the modified evolution induced by the mere presence of the extra bath allows to improve the discrimination task. We then also consider the possibility of continuously monitoring the additional environment and we discuss in detail how to obtain improved performances in the discrimination by considering different kinds of interaction, i.e. di…
Boosting Work Extraction in Quantum Batteries via Continuous Environment Monitoring
Università degli Studi dell’Insubria（因苏布里亚大学）；Istituto Nazionale di Fisica Nucleare, Sezione di Milano（意大利国家核物理研究所米兰分部）；Università di Genova（热那亚大学）；CNR-SPIN（意大利国家研究委员会自旋物理中心）；Università degli Studi di Milano（米兰大学）
We present a comprehensive implementation of the quantum trajectory theory for the description of the entanglement dynamics in a Markovian open quantum system made of two qubits. We introduce the average concurrence to characterize the entanglement in the system and derive a deterministic evolution equation for it that depends on the ways information is read from the environment. This builded in flexibility of the method is used to address two actual issues in quantum information: entanglement protection and entanglement estimation. We identify general physical situations in which an entanglem…
Dynamical Casimir effect (DCE) is the name assigned to the process of generating quanta from vacuum due to an accelerated motion of macroscopic neutral bodies (mirrors) or time-modulation of cavity material properties, as well as the simulation of such processes. Here I review the theoretical results on the detection of DCE using intracavity quantum detectors, such as multi-level atoms, atomic networks and harmonic oscillators. I also stress the mathematical equivalence of this problem to the physics of optical parametric oscillators interacting with atoms or quantum wells, studied in Quantum …
We report on an experimental investigation of the dynamics of entanglement between a single qubit and its environment, as well as for pairs of qubits interacting independently with individual environments, using photons obtained from parametric down-conversion. The qubits are encoded in the polarizations of single photons, while the interaction with the environment is implemented by coupling the polarization of each photon with its momentum. A convenient Sagnac interferometer allows for the implementation of several decoherence channels and for the continuous monitoring of the environment. For…
We consider protocols to generate quantum entanglement between two remote qubits, through joint time-continuous detection of their spontaneous emission. We demonstrate that schemes based on homodyne detection, leading to diffusive quantum trajectories, lead to identical average entanglement yield as comparable photodetection strategies; this is despite substantial differences in the two-qubit state dynamics between these schemes, which we explore in detail. The ability to use different measurements to achieve the same ends may be of practical significance; the less-well-known diffusive scheme …
Entanglement between two quantum systems is a resource in quantum information, but dissipation usually destroys it. In this article we consider two qubits without direct interaction and we show that, even in cases where the open system dynamics destroys any initial entanglement, the mere monitoring of the environment can preserve or create the entanglement, by filtering the state of the qubits. While the systems we study are very simple, we can show examples with entanglement protection or entanglement birth, death, rebirth due to monitoring.
We revisit aspects of monitoring observables with continuous spectrum in a quantum system subject to dissipative (Lindbladian) or conservative (Hamiltonian) evolutions. After recalling some of the salient features of the case of pure monitoring, we deal with the case when monitoring is in competition with a Lindbladian evolution. We show that the strong measurement limit leads to a diffusion on the spectrum of the observable. For the case with competition between observation and Hamiltonian dynamics, we exhibit a scaling limit in which the crossover between the classical regime and a diffusive…
The continuous fuzzy measurement of energy of a single two-level system driven by a resonant external field is studied. An analysis is given in the framework of the phenomenological restricted path integral approach (RPI) (which reduces effectively to a Schrodinger equation with a complex Hamiltonian) as well as with reference to the microphysical details of a class of concrete physical realizations. Within the RPI approach it is demonstrated that for appropriately adjusted fuzziness, information about the evolution of the state of the system can be read off from the measurement readout E(t). …
In ordinary Quantum Mechanics only ideally instantaneous observations of a quantity or a set of compatible quantities are usually considered. In an old paper of our group in Milano a formalism was introduced for the continuous monitoring of a system during a certain interval of time in the framework of a somewhat generalized approach to Q. M. The outcome was a distribution of probability on the space of all the possible continuous histories of a set of quantities to be considered as a kind of coarse grained approximation to some ordinary quantum observables commuting or not. The main aim was t…
An important challenge in non-Markovian open quantum systems is to understand what information we gain from continuous measurement of an output field. For example, atoms in multimode cavity QED systems provide an exciting platform to study many-body phenomena in regimes where the atoms are strongly coupled amongst themselves and with the cavity, but the strong coupling makes it complicated to infer the conditioned state of the atoms from the output light. In this work we address this problem, describing the reduced atomic state via a conditioned hierarchy of equations of motion, which provides…
We study the entanglement entropy of the quantum trajectories of a free fermion chain under continuous monitoring of local occupation numbers. We propose a simple theory for entanglement entropy evolution from disentangled and highly excited initial states. It is based on generalized hydrodynamics and the quasi-particle pair approach to entanglement in integrable systems. We test several quantitative predictions of the theory against extensive numerics and find good agreement. In particular, the volume law entanglement is destroyed by the presence of arbitrarily weak measurement.
Definition of a quantum corridor describing monitoring a quantum observable in the framework of the phenomenological restricted-path-integral (RPI) approach is generalized for the case of a finite resolution of time. The resulting evolution of the continuously measured system cannot be presented by a differential equation. Monitoring of the position of a quantum particle is also considered with the help of a model which takes into account a finite resolution of time. The results based on the model are shown to coincide with those of the phenomenological approach.
Nondemolition filtering of an embedded cluster-state scar under continuous local monitoring
School of Physics and Electronic Engineering, Shanxi University（山西大学物理电子工程学院）；Collaborative Innovation Center of Extreme Optics, Shanxi University（山西大学极端光学协同创新中心）；Department of Physics, University of Science and Technology of China（中国科学技术大学物理系）；School of Instrument Science and Opto-Electronics Engineering, Beijing Information Science and Technology University（北京信息科技大学仪器科学与光电工程学院）；School of Physics, Beihang University（北京航空航天大学物理学院）；School of Applied Science, Beijing Information Science and Technology University（北京信息科技大学应用科学学院）；School of Automation (School of Artificial Intelligence), Beijing Information Science and Technology University（北京信息科技大学自动化学院（人工智能学院））；School of Space and Earth Sciences, Beihang University（北京航空航天大学空间与地球科学学院）
We study a flux qubit in a coplanar waveguide resonator by measuring transmission through the system. In our system with the flux qubit decoupled galvanically from the resonator, the intermediate coupling regime is achieved. In this regime dispersive readout is possible with weak backaction on the qubit. The detailed theoretical analysis and simulations give a good agreement with the experimental data and allow to make the qubit characterization.
Under resonant irradiation, a quantum system can undergo coherent (Rabi) oscillations in time. We report evidence for such oscillations in a _continuously_ observed three-Josephson-junction flux qubit, coupled to a high-quality tank circuit tuned to the Rabi frequency. In addition to simplicity, this method of_Rabi spectroscopy_ enabled a long coherence time of about 2.5 microseconds, corresponding to an effective qubit quality factor \~7000.
The thermodynamics of quantum systems driven out of equilibrium has attracted increasing attention in last the decade, in connection with quantum information and statistical physics, and with a focus on non-classical signatures. While a first approach can deal with average thermodynamics quantities over ensembles, in order to establish the impact of quantum and environmental fluctuations during the evolution, a continuous quantum measurement of the open system is required. Here we provide an introduction to the general theoretical framework to establish and interpret thermodynamics for quantum…
Detecting nonequilibrium phase transitions via continuous monitoring of space-time trajectories and autoencoder-based clustering
Institut für Theoretische Physik, Universität Tübingen（蒂宾根大学理论物理研究所）；Université Paris Cité, CNRS, Matériaux et Phénomènes Quantiques（巴黎西岱大学、法国国家科学研究中心、物质与量子现象）；Centre for Fluid and Complex Systems, Coventry University（考文垂大学流体与复杂系统中心）；The University of Nottingham（诺丁汉大学）
Exact Hilbert-space ergodicity from continuous monitoring
Institute for Advanced Study, Tsinghua University（清华大学高等研究院）；Department of Physics & State Key Laboratory of Surface Physics, Fudan University（复旦大学物理系与表面物理国家重点实验室）
We analyze the dynamics of entanglement in a paradigmatic noninteracting system subject to continuous monitoring of the local excitation densities. Recently, it was conjectured that the evolution of quantum correlations in such system is described by a semi-classical theory, based on entangled pairs of ballistically propagating quasiparticles and inspired by the hydrodynamic approach to unitary (integrable) quantum systems. Here, however, we show that this conjecture does not fully capture the complex behavior of quantum correlations emerging from the interplay between coherent dynamics and co…
