A general quantum measurement on an unknown quantum state enables us to estimate what the state originally was. Simultaneously, the measurement has a destructive effect on a measured quantum state which is reflected by the decrease of the output fidelity. We show for any $d$-level system that quantum non-demolition (QND) measurement controlled by a suitably prepared ancilla is a measurement in which the decrease of the output fidelity is minimal. The ratio between the estimation fidelity and the output fidelity can be continuously controlled by the preparation of the ancilla. Different measurement strategies on the ancilla are also discussed. Finally, we propose a feasible scheme of such a measurement for atomic and optical 2-level systems based on basic controlled-NOT gate.
We propose the scheme implementing partial deterministic non-demolition Bell measurement. When it is used in quantum teleportation the information about an unknown input state is optimally distributed among three outgoing qubits. The optimality means that the output fidelities saturate the asymmetric cloning inequality. The flow of information among the qubits is controlled by the preparation of a pair of ancillary qubits used in the Bell measurement. It is also demonstrated that the measurement is optimal two-qubit operation in the sense of the trade-off between the state disturbance and the …
In Quantum Non Demolition measurements, the sequence of observations is distributed as a mixture of multinomial random variables. Parameters of the dynamics are naturally encoded into this family of distributions. We show the local asymptotic mixed normality of the underlying statistical model and the consistency of the maximum likelihood estimator. Furthermore, we prove the asymptotic optimality of this estimator as it saturates the usual Cramér Rao bound.
Quantum non-demolition (QND) measurements improve sensitivity by evading measurement back-action. The technique was first proposed to detect mechanical oscillations in gravity wave detectors,and demonstrated in the measurement of optical fields, leading to the development of rigorous criteria to distinguish QND from similar non-classical measurements. Recent QND measurements of macroscopic material systems such as atomic ensembles, and mechanical oscillators, show some QND features, but not full QND character. Here we demonstrate certified QND measurement of the collective spin of an atomic en…
An extensive debate on quantum non-demolition (QND) measurement, reviewed in Grangier et al. [Nature, {\bf 396}, 537 (1998)], finds that true QND measurements must have both non-classical state-preparation capability and non-classical information-damage tradeoff. Existing figures of merit for these non-classicality criteria require direct measurement of the signal variable and are thus difficult to apply to optically-probed material systems. Here we describe a method to demonstrate both criteria without need for to direct signal measurements. Using a covariance matrix formalism and a general n…
We present a quantum electrical circuit with Josephson junctions formed of two anharmonic oscillators coupled with an interaction $gγ_{1}^{2}γ_{2}^{2}$ where $γ_{1}$ and $γ_{2}$ are position-like coordinates. This type of coupling allows the quantum non-demolition measurement of the energy of one oscillator by monitoring the frequency of the second oscillator. Despite the fundamental tradeoff between the coupling strength $g$ and maximum photon storage capacity of the oscillators, it is possible to achieve high fidelity detection of up to 10 photons over time scale of the order of microseconds…
While relatively easy to engineer, static transverse coupling between a qubit and a cavity mode satisfies the criteria for a quantum non-demolition (QND) measurement only if the coupling between the qubit and cavity is much less than their mutual detuning. This can put significant limits on the speed of the measurement, requiring trade-offs in the circuit design between coupling, detuning, and decoherence introduced by the cavity mode. Here, we study a circuit in which the qubit-cavity and the cavity-feedline coupling can be turned on and off, which helps to isolate the qubit. We do not rely o…
We propose to take advantage of the weak coupling of ground-state helium-3 nuclear spin to its environment to produce long-lived macroscopic quantum states, nuclear spin squeezed states, in a gas cell at room temperature. To perform a quantum non-demolition measurement of a transverse component of the polarized collective nuclear spin, we maintain a population in helium-3 metastable state with a discharge. The collective spin associated to $F=1/2$ metastable level hybridizes with the ground state one by metastability exchange collisions. To access nuclear spin fluctuations, one continuously me…
We simply construct a quantum universal variable-length source code in which, independent of information source, both of the average error and the probability that the coding rate is greater than the entropy rate $H(rho_p)$, tend to 0. If $H(rho_p)$ is estimated, we can compress the coding rate to the admissible rate $H(rho_p)$ with a probability close to 1. However, when we perform a naive measurement for the estimation of $H(rho_p)$, the input state is demolished. By smearing the measurement, we successfully treat the trade-off between the estimation of $H(rho_p)$ and the non-demolition of t…
We investigate the trade-off between information gain and disturbance for a class of weak von Neumann measurements on spin-$\frac{1}{2}$ particles, and derive the unusual measurement pointer state that saturates this trade-off. We then consider the fundamental question of sharing the non-locality of a single particle of an entangled pair among multiple observers, and demonstrate that by exploiting the information gain disturbance trade-off, one can obtain an arbitrarily long sequence of consecutive and independent violations of the CHSH-Bell inequality.
The exact price of local realism in CHSH experiments: a measurement-dependence-detection trade-off surface, a moiré phase-locking mechanism that saturates it, and an unmeasured fringe in the fourfold coincidence sum
We propose and experimentally demonstrate an optimal non-unity gain Gaussian scheme for partial measurement of an unknown coherent state that causes minimal disturbance of the state. The information gain and the state disturbance are quantified by the noise added to the measurement outcomes and to the output state, respectively. We derive the optimal trade-off relation between the two noises and we show that the trade-off is saturated by non-unity gain teleportation. Optimal partial measurement is demonstrated experimentally using a linear optics scheme with feed-forward.
The quantum Cramér-Rao bound (QCRB) sets a fundamental limit for the measurement of classical signals with detectors operating in the quantum regime. Using linear-response theory and the Heisenberg uncertainty relation, we derive a general condition for achieving such a fundamental limit. When applied to classical displacement measurements with a test mass, this condition leads to an explicit connection between the QCRB and the Standard Quantum Limit which arises from a tradeoff between the measurement imprecision and quantum backaction; the QCRB can be viewed as an outcome of a quantum non-de…
We address the trade-off between information gain and state disturbance in measurement performed on qudit systems and devise a class of optimal measurement schemes that saturate the ultimate bound imposed by quantum mechanics to estimation and transmission fidelities. The schemes are minimal, i.e. they involve a single additional probe qudit, and optimal, i.e. they provide the maximum amount of information compatible with a given level of disturbance. The performances of optimal single-user schemes in extracting information by sequential measurements in a N -user transmission line are also inv…
Minimal Trade-off and Optimal Measurement for Multiparameter Quantum Estimation
The Chinese University of Hong Kong（香港中文大学）；The Hong Kong Institute of Quantum Information Science and Technology（香港量子信息科学与技术研究所）；State Key Laboratory of Quantum Information Technologies and Materials（量子信息技术与材料国家重点实验室）；Shenzhen University（深圳大学）
Tight tradeoff relation and optimal measurement for multiparameter quantum estimation
The Chinese University of Hong Kong（香港中文大学）；The Hong Kong Institute of Quantum Information Science and Technology, The Chinese University of Hong Kong（香港中文大学香港量子信息科学与技术研究所）；State Key Laboratory of Quantum Information Technologies and Materials, The Chinese University of Hong Kong（香港中文大学量子信息技术与材料国家重点实验室）；Shenzhen University（深圳大学）
A unified view on the phenomenon of monogamy exhibited by Bell inequalities and non-contextuality inequalities arising from the no-signaling and no-disturbance principles is presented using the graph-theoretic method introduced in \textit{Phys. Rev. Lett. 109, 050404 (2012)}. We propose a novel type of trade-off, namely Bell inequalities that do not exhibit monogamy features of their own can be activated to be monogamous by the addition of a local contextuality term. This is illustrated by means of the well-known $\mathcal{I}_{3322}$ inequality, and reveals a resource trade-off between biparti…
Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we show that topological error correcting codes, which protect against computational errors, are also extremely robust against losses. We present analytical results showing the maximum tolerable loss rate is 50 %, which is determined by the square-lattice bond percolation threshold. This saturates the bound set by the no-cloning theorem. Our numerical results support this, and show a graceful trade-off between computational and loss errors.
Ultimate tradeoff relation of quantum precision limits in multiparameter linear measurement
Hangzhou Dianzi University（杭州电子科技大学）；Zhejiang Key Laboratory of Quantum State Control and Optical Field Manipulation, Hangzhou Dianzi University（杭州电子科技大学量子态调控与光场操纵浙江省重点实验室）
Thermodynamics of Ahn--Doherty--Landahl Continuous Quantum Error Correction
University of Southern California（南加州大学）；National University of Singapore（新加坡国立大学）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；PUC-Rio（天主教里约热内卢 Pontifical 大学）
In quantum physics, measurement error and disturbance were first naively thought to be simply constrained by the Heisenberg uncertainty relation. Later, more rigorous analysis showed that the error and disturbance satisfy more subtle inequalities. Several versions of universally valid error-disturbance relations (EDR) have already been obtained and experimentally verified in the regimes where naive applications of the Heisenberg uncertainty relation failed. However, these EDRs were formulated for discrete measurements. In this paper, we consider continuous measurement processes and obtain new …
Mitigation of Measurement-Induced State Transitions via a Fast-Load and Fast-Clear Readout
Academia Sinica（中央研究院）；National Central University（中央大学）；National Cheng Kung University（国立成功大学）；National Taiwan University（国立台湾大学）；National Changhua University of Education（国立彰化师范大学）；Center for Quantum Science and Engineering, National Taiwan University（国立台湾大学量子科学与工程中心）；Physics Division, National Center for Theoretical Sciences（国家理论科学中心物理组）
Native Non-Clifford Gates in Quantum LDPC Codes: Conditions, Synthesis, and Scaling Limits
School of Electrical Engineering and Telecommunications, UNSW Sydney（新南威尔士大学电气工程和电信学院）；Centre for Quantum Software and Information, University of Technology Sydney（悉尼科技大学量子软件与信息中心）
