Experimental results stated in quant-ph/0612031 are seminal: The authors have realized nondemolition measurements of the photon number. As to the interpretation of the results, it seems to be less than convincing: The treatment of the system state and of the role of measurement is not compatible with the conventional point of view. We propose an adequate treatment, in which the experimental results are a manifestation of a partial Zeno effect (a slowdown of relaxation).
We propose a theoretical scheme of quantum nondemolition measurement of two-qubit Werner state. We discuss our scheme with the two qubits restricted in a local place and then extend the scheme to the case in which two qubits are separated. We also consider the experimental realization of our scheme based on cavity quantum electrodynamics. It is very interesting that our scheme is robust against the dissipative effects introduced by the probe process. We also give a brief interpretation of our scheme finally.
We propose a technique to control the macroscopic collective nuclear spin of a Helium-3 vapor in the quantum regime using light. The scheme relies on metastability exchange collisions to mediate interactions between optically accessible metastable states and the ground-state nuclear spin, giving rise to an effective nuclear spin-light quantum nondemolition interaction of the Faraday form. Our technique enables measurement-based quantum control of nuclear spins, such as the preparation of spin-squeezed states. This, combined with the day-long coherence time of nuclear spin states in Helium-3, o…
We show that frequent nondemolition measurements of a quantum system immersed in a thermal bath allow the extraction of work in a closed cycle from the system-bath interaction (correlation) energy, a hitherto unexploited work resource. It allows for work even if no information is gathered or the bath is at zero temperature, provided the cycle is within the bath memory time. The predicted work resource may be the basis of quantum engines embedded in a bath with long memory time, such as the electromagnetic bath of a high-Q cavity coupled to two-level systems.
We demonstrate an optical quantum nondemolition (QND) interaction gate with a bandwidth of about 100 MHz. Employing this gate, we are able to perform QND measurements in real time on randomly fluctuating signals. Our QND gate relies upon linear optics and offline-prepared squeezed states. In contrast to previous demonstrations on narrow sideband modes, our gate is compatible with non-Gaussian quantum states temporally localized in a wave-packet mode, and thus opens the way for universal gate operations and realization of quantum error correction.
Considering ultracold atoms traversing a high-Q Fabry-Perot cavity, we theoretically demonstrate a quantum nondemolition measurement of the photon number. This fully quantum mechanical approach may be understood utilizing concepts as effective mass and group velocity of the atom. The various photon numbers induce a splitting of the atomic wave packet, and a time-of-flight measurement of the atom thereby reveals the photon number. While repeated atomic measurements increase the efficiency of the protocol, it is shown that by considering long interaction times only a few atoms are needed to reso…
We derive a measurement operator corresponding to a quantum nondemolition (QND) measurement of an atomic ensemble. The quantum measurement operator takes the form of a positive operator valued measure (POVM) and is valid for arbitrary interaction times, initial coherent state amplitudes, and final photon measurement outcomes. We analyze the dependence on various parameters and show that the effect of the QND measurement for short interaction times is to apply a Gaussian modulation of the initial state wavefunction. We derive approximate expressions for the POVM in various limits, such as the s…
We study the quantitative characterization of the performance of qubit measurements in this paper. In particular, the back-action evading nature of quantum nondemolition (QND) readout of qubits is fully quantified by quantum trace distance. Only computational basis states are necessary to be taken into consideration. Most importantly, we propose an experimentally efficient method to evaluate the QND fidelity based on the classical trace distance, which uses an experimental scheme with two consecutive measurements. The three key quantifiers of a measurement, i.e., QND fidelity, readout fidelity…
We theoretically study the measurement-induced dephasing caused by back action noise in quantum nondemolition measurements of a superconducting flux qubit which is coupled to a superconducting quantum interference device (SQUID). Our analytical results indicate that information on qubit flows from qubit to detector, while quantum fluctuations which may cause dephasing of the qubit also inject to qubit. Furthermore, the measurement probability is frequency dependent in a short time scale and has a close relationship with the measurement-induced dephasing. When the detuning between driven and ba…
Projective quantum nondemolition (QND) measurement is important for quantum technologies. Here we propose a method for constructing projective QND measurement on a nuclear spin via the measurement of an axillary electron spin in generic electron-nuclear spin systems coupled through weak hyperfine interaction. The key idea is to apply suitable quantum control on the electron to construct a weak QND measurement on the nuclear spin and then cascade a sequence of such measurements into a projective one. We identify a set of tunable parameters to select the QND observables and control the strength …
We propose a high efficiency tomographic scheme to reconstruct an unknown quantum state of the qubits by using a series of quantum nondemolition (QND) measurements. The proposed QND measurements of the qubits are implemented by probing the the stationary transmissions of the dispersively-coupled resonator. It is shown that only one kind of QND measurements is sufficient to determine all the diagonal elements of the density matrix of the detected quantum state. The remaining non-diagonal elements of the density matrix can be determined by other spectral measurements by beforehand transferring t…
In quantum metrology schemes, one generally needs to prepare $m$ copies of $N$ entangled particles, such as entangled photon states, and then they are detected in a destructive process to estimate an unknown parameter. Here, we present a novel experimental scheme for estimating this parameter by using repeated indirect quantum nondemolition measurements in the setup called "photon box". This interaction-based scheme is able to achieve the phase sensitivity scaling as $1/N$ with a Fock state of $N$ photons. Moreover, we only need to prepare one initial $N$-photon state and it can be used repeti…
We use a reservoir engineering technique based on two-tone driving to generate and stabilize a quantum squeezed state of a micron-scale mechanical oscillator in a microwave optomechanical system. Using an independent backaction evading measurement to directly quantify the squeezing, we observe $4.7\pm0.9$ dB of squeezing below the zero-point level, surpassing the 3 dB limit of standard parametric squeezing techniques. Our measurements also reveal evidence for an additional mechanical parametric effect. The interplay between this effect and the optomechanical interaction enhances the amount of …
We report the experimental nondemolition measurement of coherence, predictability and concurrence on a system of two qubits. The quantum circuits proposed by De Melo et al. are implemented on IBM Q (superconducting circuit) and IonQ (trapped ion) quantum computers. Three criteria are used to compare the performance of the different machines on this task: measurement accuracy, nondemolition of the observable, and quantum state preparation. We find that the IonQ quantum computer provides constant state fidelity through the nondemolition process, outperforming IBM Q systems on which the fidelity …
Dispersive coupling based on the Rabi model with large detuning is widely used for quantum nondemolition (QND) qubit readout in quantum computation. However, the measurement speed and fidelity are usually significantly limited by the Purcell effects, i.e.: Purcell decay, critical photon numbers, and qubit-dependent Kerr nonlinearity. To avoid these effects, we propose how to realize an ideal QND readout of a gradiometric flux qubit with a tunable gap via its non-perturbative dispersive coupling (NPDC) to a frequency-tunable measurement resonator. We show that this NPDC-based readout mechanism …
Optically-interfaced spins in the solid state are a promising platform for quantum technologies. A crucial component of these systems is high-fidelity, projective measurement of the spin state. In previous work with laser-cooled atoms and ions, and solid-state defects, this has been accomplished using fluorescence on an optical cycling transition; however, cycling transitions are not ubiquitous. In this work, we demonstrate that modifying the electromagnetic environment using an optical cavity can induce a cycling transition in a solid-state atomic defect. By coupling a single Erbium ion defec…
According to quantum mechanics, if we keep observing a continuous variable we generally disturb its evolution. For a class of observables, however, it is possible to implement a so-called quantum nondemolition measurement: by confining the perturbation to the conjugate variable, the observable is estimated with arbitrary accuracy, or prepared in a well-known state. For instance, when the light bounces on a movable mirror, its intensity is not perturbed (the effect is just seen on the phase of the radiation), but the radiation pressure allows to trace back its fluctuations by observing the mirr…
While quantum mechanics exquisitely describes the behavior of microscopic systems, one ongoing challenge is to explore its applicability to systems of larger size and mass. Unfortunately, quantum states of increasingly macroscopic objects are more easily corrupted by unintentional measurements from the classical environment. Additionally, even the intentional measurements from the observer can further perturb the system. In optomechanics, coherent light fields serve as the intermediary between the fragile mechanical states and our inherently classical world by exerting radiation pressure force…
We propose a technique for quantum nondemolition (QND) measurement and heralded preparation of Fock states by dynamics of electromagnetically induced transparency (EIT). An atomic ensemble trapped in an optical cavity is driven by two external continuous-wave classical fields to form EIT in steady state. As soon as a weak coherent field is injected into the cavity, the EIT system departs from steady state, falls into transient state dynamics by the dispersive coupling between cavity injected photons and atoms. Because the imaginary part of time-dependent linear susceptibility Im[X(t)] of the a…
We develop a measurement operator formalism to handle quantum nondemolition (QND) measurement induced entanglement generation between two atomic gases. We first derive how the QND entangling scheme reduces to a positive operator-valued measure, and consider its limiting case when it can be used to construct a projection operator that collapses the state to a total spin projection state. We then analyze how a stroboscopic sequence of such projections made in the x and z basis evolves the initial wave function. Such a sequence of QND projections can enhance the entanglement between the atomic en…
The efficient and reliable characterization of quantum states plays a vital role in most, if not all, quantum information processing tasks. In this work, we present a universally optimal protocol for verifying entangled states by employing the so-called quantum nondemolition measurements, such that the verification efficiency is equivalent to that of the optimal global strategy. Instead of being probabilistic as the standard verification strategies, our protocol is constructed sequentially, which is thus more favorable for experimental realizations. In addition, the target states are preserved…
We show that continuous quantum nondemolition (QND) measurement of an atomic ensemble is able to improve the precision of frequency estimation even in the presence of independent dephasing acting on each atom. We numerically simulate the dynamics of an ensemble with up to N = 150 atoms initially prepared in a (classical) spin coherent state, and we show that, thanks to the spin squeezing dynamically generated by the measurement, the information obtainable from the continuous photocurrent scales superclassically with respect to the number of atoms N. We provide evidence that such superclassical…
We propose an approach to nondestructively detect $N$ qubits by measuring the transmissions of a dispersively-coupled cavity. By taking into account all the cavity-qubits quantum correlations (i.e., beyond the usual coarse-grained/mean-field approximations), it is revealed that for an unknown normalized $N$-qubit state $|ψ_N>=\sum_{k=0}^{2^N-1}β_k|k>_N$, each detected peak in the cavity transmitted spectra marks one of the basis states $|k>_N$ and the relative height of such a peak is related to the corresponding superposed-probability $|β_k|^2$. Our results are able to unambiguously account f…
The conventional method of qubit measurements in circuit QED is employing the dispersive regime of qubit-cavity coupling, which results in an approximated scheme of quantum nondemolition (QND) readout. This scheme becomes problematic in the case of strong coupling and/or strong measurement drive, owing to the so-called Purcell effect. A recent proposal by virtue of longitudinal coupling suggests a new scheme to realize fast, high-fidelity, and {\it ideal QND} readout of qubit state. The aim of the present work is twofold: (i) In parallel to what has been done in the past years for the dispersi…
We propose a multimeasurement estimation protocol for Quantum Nondemolition (QND) measurements in a Rabi clock interferometer. The method is well suited for current state-of-the-art optical lattice clocks with QND measurement capabilities. The protocol exploits the correlations between multiple non-destructive measurements of the initially prepared coherent spin state. A suitable Gaussian estimator for the clock laser detuning is presented, and an analytic expression for the sensitivity of the protocol is derived. We use this analytic expression to optimise the protocol using available experim…
The ability to nondestructively detect the presence of a single, traveling photon has been a long-standing goal in optics, with applications in quantum information and measurement. Realising such a detector is complicated by the fact that photon-photon interactions are typically very weak. At microwave frequencies, very strong effective photon-photon interactions in a waveguide have recently been demonstrated. Here we show how this type of interaction can be used to realize a quantum nondemolition measurement of a single propagating microwave photon. The scheme we propose uses a chain of solid…
We analyze a direct parity measurement of the state of three superconducting qubits in circuit quantum electrodynamics. The parity is inferred from a homodyne measurement of the reflected/transmitted microwave radiation and the measurement is direct in the sense that the parity is measured without the need for any quantum circuit operations or for ancilla qubits. Qubits are coupled to two resonant cavity modes, allowing the steady state of the emitted radiation to satisfy the necessary conditions to act as a pointer state for the parity. However, the transient dynamics violates these condition…
In the field of cavity optomechanics, proposals for quantum nondemolition (QND) measurements of phonon number provide a promising avenue by which one can study the quantum nature of nanoscale mechanical resonators. Here, we investigate these QND measurements for an optomechanical system whereby quadratic coupling arises due to shared symmetries between a single optical resonance and a mechanical mode. We establish a relaxed limit on the amount of linear coupling that can exist in this type of system while still allowing for a QND measurement of Fock states. This new condition enables optomecha…
In this paper, we propose a resources-optimal linear-optical scheme for quantum nondemolition detection of single-photon presence. By measuring the state of ancillary photons, the presence of a photon in signal mode is revealed with a success probability of 1/2 without any disturbance to its state. We also show how to tune the setup to perform quantum nondemolition measurement of the signal photon state, and we provide tradeoff between the extracted information and the signal state disturbance. Moreover, the optimality of resources and methods by which to increase the success probability are d…
