We estimate an unknown qubit from the long sequence of n random polarization measurements of precision Delta. Using the standard Ito-stochastic equations of the aposteriori state in the continuous measurement limit we calculate the advancement of fidelity. We show that the standard optimum value 2/3 is achieved asymptotically for n >> Delta^2 / 96 >> 1. We append a brief derivation of novel Ito-equations for the estimate state.
We experimentally address the significance of fidelity as a figure of merit in quantum state reconstruction of discrete (DV) and continuous variable (CV) quantum optical systems. In particular, we analyze the use of fidelity in quantum homodyne tomography of CV states and maximum-likelihood polarization tomography of DV ones, focussing attention on nonclassicality, entanglement and quantum discord as a function of fidelity to a target state. Our findings show that high values of fidelity, despite well quantifying geometrical proximity in the Hilbert space, may be obtained for states displaying…
Performance of quantum teleportation is typically measured by the average fidelity, an overlap between the input and output states. Along with the first moment, we introduce the second moment of fidelity in CV teleportation, i.e., the fidelity deviation as the figures of merit to assess the protocol's efficiency. We show that CV states, both Gaussian and non Gaussian, can be better characterized by considering both average fidelity and fidelity deviation, which is not possible with only average fidelity. Moreover, we shed light on the performance of the teleportation protocol in two different …
We present quantum fidelity benchmarks for continuous-variable (CV) quantum devices to outperform quantum channels which can transmit at most $k$-dimensional coherences for positive integers $k$. We determine an upper bound of an average fidelity over Gaussian distributed coherent states for quantum channels whose Schmidt class is $k$. This settles fundamental fidelity steps where the known classical limit and quantum limit correspond to the two endpoints of $k=1$ and $k= \infty $, respectively. It turns out that the average fidelity is useful to verify to what extent an experimental CV gate c…
We propose a measure of nonclassical correlation $N_{\mathcal F}^{\mathcal G}$ in terms of local Gaussian unitary operations based on square of the fidelity $\mathcal F$ for bipartite continuous-variable systems. This quantity is easier to calculate or estimate and is a remedy for the local ancilla problem associated with the geometric measurement-induced nonlocality. A simple computation formula of $N_{\mathcal F}^{\mathcal G}$ for any $(1+1)$-mode Gaussian states is presented and an estimation of $N_{\mathcal F}^{\mathcal G}$ for any $(n+m)$-mode Gaussian states is given. For any $(1+1)$-mod…
We introduce witnesses for the average channel fidelity between a known target gate and an arbitrary unknown channel, for continuous-variable (CV) systems. These are observables whose expectation value yields a tight lower bound to the average channel fidelity in question, thus constituting a practical tool for certification of experimental CV gates. Our framework applies to a broad class of target gates. Here, we focus on three specific types of targets: multi-mode Gaussian unitary channels, single-mode coherent state amplifiers, and the single-mode (non-Gaussian) cubic phase gate, which is a…
Universality cost of non-Gaussian enhancement in continuous-variable quantum teleportation: A fidelity--deviation trade-off
Institute for Convergence Research and Education in Advanced Technology, Yonsei University（延世大学先进技术与教育融合研究所）；Department of Statistics and Data Science, Yonsei University（延世大学统计与数据科学系）；Department of Physics, Jeju National University（济州国立大学物理系）；Department of Quantum Information, Yonsei University（延世大学量子信息系）
Risk-aware neural pulse compilation of continuously parameterized single-qubit gates with optimal-control benchmarking and NMR hardware validation
Koç University（科奇大学）；TÜBİTAK Research Institute for Fundamental Sciences (TBAE)（土耳其科学技术研究委员会基础科学研究院（TBAE））；Middle East Technical University（中东理工大学）；Shenzhen SpinQ Technology Co., Ltd.（深圳本源量子技术有限公司）
We present a method that combines continuous and pulsed microwave radiation patterns to achieve robust interactions among hyperfine trapped ions placed in a magnetic field gradient. More specifically, our scheme displays continuous microwave drivings with modulated phases, phase flips, and $π$ pulses. This leads to high-fidelity entangling gates which are resilient against magnetic field fluctuations, changes on the microwave amplitudes, and crosstalk effects. Our protocol runs with arbitrary values of microwave power, which includes the technologically relevant case of low microwave intensiti…
The Continuous-Variable (CV) quantum state of light allows for the teleportation of a Discrete-Variable (DV) photonic qubit. Such an operation is useful in the realm of hybrid quantum networks. However, it is known that the teleportation of a DV qubit via a Gaussian CV resource channel is severely limited under channel loss, with a teleportation fidelity beyond the classical limit unattainable for losses exceeding a small threshold of 0.5 dB. In this work, we present a new non-deterministic teleportation protocol that combines a Gaussian CV resource channel with a modified form of the Bell Sta…
Quantum teleportation is one of the crucial protocols in quantum information processing. It is important to accomplish an efficient teleportation under practical conditions, aiming at a higher fidelity desirably using fewer resources. The continuous-variable (CV) version of quantum teleportation was first proposed using a Gaussian state as a quantum resource, while other attempts were also made to improve performance by applying non-Gaussian operations. We investigate the CV teleportation to find its ultimate fidelity under energy constraint identifying an optimal quantum state. For this purpo…
Quantum teleportation (QT) is a fundamentally remarkable communication protocol that also finds many important applications for quantum informatics. Given a quantum entangled resource, it is crucial to know to what extent one can accomplish the QT. This is usually assessed in terms of output fidelity, which can also be regarded as an operational measure of entanglement. In the case of multipartite communication when each communicator possesses a part of $N$-partite entangled state, not all pairs of communicators can achieve a high fidelity due to monogamy property of quantum entanglement. We h…
The Eastin-Knill theorem is a central result of quantum error correction theory and states that a quantum code cannot correct errors exactly, possess continuous symmetries, and implement a universal set of gates transversely. As a way to circumvent this result, there are several approaches in which one gives up on either exact error correction or continuous symmetries. In this context, it is common to employ a complementary measure of fidelity as a way to quantify quantum state distinguishability and benchmark approximations in error correction. Despite having useful properties, evaluating fid…
Time-Frequency Continuous-Variable Quantum Teleportation with Single Photons
Telecom Paris, Institut Polytechnique de Paris（巴黎电信学院，巴黎理工学院）；Centre for Nanosciences and Nanotechnology, CNRS, Université Paris-Saclay（纳米科学与工程中心，法国国家科学研究中心，巴黎萨克雷大学）
