G. Mauro D'Ariano, Matteo G. A. Paris, Paolo Perinotti
We address the problem of the optimal quantum estimation of the coupling parameter of a bilinear interaction, such as the transmittivity of a beam splitter or the internal phase-shift of an interferometer. The optimal measurement scheme exhibits Heisenberg scaling of the measurement precision versus the total energy.
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The Cramér-Rao approach and global quantum estimation of bosonic states
本文研究玻色态量子估计中Cramér-Rao方法在非独立同分布全局估计下的适用性，揭示其适用与失效情形，并强调外推至全局估计时需谨慎。
We address the estimation of the loss parameter of a bosonic channel probed by Gaussian signals. We derive the ultimate quantum bound on precision and show that no improvement may be obtained by having access to the environment degrees of freedom. We found that, for small losses, the variance of the optimal estimator is proportional to the loss parameter itself, a result that represents a qualitative improvement over the shot noise limit. An observable based on the symmetric logarithmic derivative is derived, which attains the ultimate bound and may be implemented using Gaussian operations and…
Quantum phase estimation for nondestructive monitoring and Wigner tomography of bosonic fields
该研究将量子相位估计经色散光-物质相互作用改造为玻色场非破坏性监测工具，结合相空间位移实现维格纳断层扫描，在多种量子态重建中获高保真度，适用于超导量子架构的玻色态表征等场景。
General Approach to Error Detection of Bosonic Codes via Phase Estimation
提出一种借助单辅助量子比特的自适应相位估计通用方法，用于检测玻色子码误差，精度达海森堡极限，并适用于多种码型及Fock态生成。
We propose a quantum metrology protocol for measuring frequencies and weak forces based on a periodic modulating quantum Jahn-Teller system composed of a single spin interacting with two bosonic modes. We show that in the first order of the frequency drive the time-independent effective Hamiltonian describes spin-dependent interaction between the two bosonic modes. In the limit of high-frequency drive and low bosonic frequency the quantum Jahn-Teller system exhibits critical behaviour which can be used for high-precision quantum estimation. A major advantage of our scheme is the robustness of …
Lower Bounding the Secret Key Capacity of Bosonic Gaussian Channels via Optimal Gaussian Measurements
通过最优高斯测量确定玻色高斯信道秘密密钥容量的下界，优化了热损耗和热放大信道的协议并简化了性能评估。
We derive families of optimal and near-optimal probe states for quantum estimation of the coupling constants of a general two-mode number-conserving bosonic Hamiltonian describing one-body and two-body dynamics. We find that the optimal states for estimating the dephasing of the modes, the self-interaction strength, and the contact interaction strength are related to the NOON states, whereas the optimal states for estimation of the intermode single particle tunneling amplitude are superpositions of antipodal SU(2) coherent states. For estimation of the amplitude of pair tunneling and the ampli…
Optimal quantum sensing of the nonlinear bosonic interactions using Fock states
本文提出利用Fock态作为探针，实现三线性玻色子相互作用的最优量子传感，使估计误差随总量子数按N^{-1/3}缩放，为离子阱和超导电路中的非线性量子技术提供新途径。
Hardware-native quantum phase estimation with circuit QED
提出一种利用电路量子电动力学（cQED）的迭代量子相位估计协议，通过二进制阈值测试和同质测量实现海森堡极限精度，无需逆量子傅里叶变换，降低了硬件复杂度。
We address the classical capacity of a quantum bosonic memory channel with additive noise, subject to an input energy constraint. The memory is modeled by correlated noise emerging from a Gauss-Markov process. Under reasonable assumptions, we show that the optimal modulation results from a "quantum water-filling" solution above a certain input energy threshold, similar to the optimal modulation for parallel classical Gaussian channels. We also derive analytically the optimal multimode input state above this threshold, which enables us to compute the capacity of this memory channel in the limit…
We investigate cat codes that can correct multiple excitation losses and identify two types of logical errors: bit-flip errors due to excessive excitation loss and dephasing errors due to quantum back-action from the environment. We show that selected choices of logical subspace and coherent amplitude can efficiently reduce dephasing errors. The trade-off between the two major errors enables optimized performance of cat codes in terms of minimized decoherence. With high coupling efficiency, we show that one-way quantum repeaters with cat codes feature drastically boosted secure communication r…
In continuous-variable quantum computing with qubits encoded in the infinite-dimensional Hilbert space of bosonic modes, it is a difficult task to realize strong and on-demand interactions between the qubits. One option is to engineer a beamsplitter interaction for photons in two superconducting cavities by driving an intermediate superconducting circuit with two continuous-wave drives, as demonstrated in a recent experiment. Here, we show how quantum optimal control theory (OCT) can be used in a systematic way to improve the beamsplitter interaction between the two cavities. We find that repl…
We describe an apparatus designed to make non-demolition measurements on a Bose-Einstein condensate (BEC) trapped in a double-well optical cavity. This apparatus contains, as well as the bosonic gas and the trap, an optical cavity. We show how the interaction between the light and the atoms, under appropriate conditions, can allow for a weakly disturbing yet highly precise measurement of the population imbalance between the two wells and its variance. We show that the setting is well suited for the implementation of quantum-limited estimation strategies for the inference of the key parameters …
Reshaping coupled bosonic networks: A bipartite-graph framework for optimal quantum excitation transfer
本文提出二分图框架表征耦合玻色网络的量子激发转移，揭示转移效率对网络构型与参数的依赖，发现暗模效应会降低转移效率，为相关领域网络设计优化提供新视角。
We use an exact quantum phase model to study the dynamical generation of particle-entanglement in a bosonic Josephson junction composed by two coupled and interacting Bose-Einstein condensates. Using analytical arguments, we show that linear coupling can accelerate the creation of entanglement with respect to the well known one-axis twisting model where coupling is absent. Furthermore, with a numerical analysis of optimal control schemes, we identify the optimal parameters for the fast generation of metrologically useful entanglement on short time scales: the optimal evolution is generated for…
Upper bounds for private communication over quantum channels can be derived by adopting channel simulation, protocol stretching, and relative entropy of entanglement. All these ingredients have led to single-letter upper bounds to the secret key capacity which can be directly computed over suitable resource states. For bosonic Gaussian channels, the tightest upper bounds have been derived by employing teleportation simulation over asymptotic resource states, namely the asymptotic Choi matrices of these channels. In this work, we adopt a different approach. We show that teleporting over an anal…
I propose a quantum sensor based on driven-dissipative quantum system for the joint estimation of two conjugated variables characterizing the phase space displacement. The quantum probe consists of lattice system with two level atoms and bosonic modes which interact via dipolar coupling. Interplay between the coherent dynamics and dissipative processes of losses of bosonic excitations leads to a steady state which exhibits a non-analytical behaviour. I show that close to the dissipative phase transition the sensitivity of one of the conjugated parameters either the magnitude of the phase of th…
We introduce a general model for a lossy bosonic memory channel and calculate the classical and the quantum capacity, proving that coherent state encoding is optimal. The use of a proper set of collective field variables allows to unravel the memory, showing that the n-fold concatenation of the memory channel is unitarily equivalent to the direct product of n single-mode lossy bosonic channels.
In this article we consider a bosonic Josephson junction, a model system composed by two coupled nonlinear quantum oscillators which can be implemented in various physical contexts, initially prepared in a product of weakly populated coherent states. We quantify the maximum achievable entanglement between the modes of the junction and then use shortcuts to adiabaticity, a method developed to speed up adiabatic quantum dynamics, as well as numerical optimization, to find time-dependent controls (the nonlinearity and the coupling of the junction) which bring the system to a maximally entangled s…
Optimal estimates of trace distance between bosonic Gaussian states and applications to learning
本研究解决了玻色高斯态矩近似误差对应的迹距离误差量化问题，证明矩误差为ε时态迹距离误差也以ε为标度且为最优，建立了迹距离紧界，并改进了高斯态层析的样本复杂度界。
Direct estimation of arbitrary observables of an oscillator
本文提出OREO协议，通过将振子可观测量的期望值映射到辅助量子比特上，实现高效测量相空间四阶矩和非高斯性等级，为连续变量量子信息处理提供新的测量和控制方法。
On estimates of the Bures distance between bosonic Gaussian states
本文提出将ArXiv:2408.11400的方法扩展以获取量子高斯态间Bures距离的上界，该界更适配Bures距离，可提升相关状态估计与学习的效果。
Gaussian Optimality of Energy-Constrained One-Shot Communication through Single-Mode Bosonic Gaussian Channels
该研究证明了带任意压缩热噪声的单模玻色高斯信道的能量受限单次Holevo容量具有高斯最优性，其结果可扩展至各类单模高斯信道，无需假设信道使用间的加性。
Optimal testing of fermionic and bosonic Gaussian states
本文针对五类高斯量子态提出常数样本复杂度的性质测试器，证明紧的 $\Theta(1/\varepsilon^2)$ 样本复杂度，并通过谱间隙下界和匹配下界确立最优性，且扩展到容忍设置。
A generic quantum channel can be represented in terms of a unitary interaction between the information-carrying system and a noisy environment. Here, the minimal number of quantum Gaussian environmental modes required to provide a unitary dilation of a multi-mode bosonic Gaussian channel is analyzed both for mixed and pure environment corresponding to the Stinespring representation. In particular, for the case of pure environment we compute this quantity and present an explicit unitary dilation for arbitrary bosonic Gaussian channel. These results considerably simplify the characterization of …
Joint Communication and Sensing over the Lossy Bosonic Quantum Channel
研究有损玻色子量子信道上的联合通信与感知问题，使用最优量子仪器实现数据传输与环境参数估计，刻画通信与检测速率的最优权衡并量化量子优势。
Interplay between time and energy in bosonic noisy quantum metrology
本文将能量与时间同时视为资源，研究了玻色噪声量子计量学中两者的非平凡相互作用，推导了精度界限并给出了最优时间分配方案，发现在多数情况下无需自适应或辅助纠缠即可达最优，且快速制备并测量 Fock 态在温度估计中优于经典策略。
We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Schäfer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these opti…
Lifshitz-like Metastability and Optimal Dephasing in Dissipative Bosonic Lattices
本研究发现在具有非均匀耗散的耦合玻色模网络中，退相干通过产生长寿命集体模式引发类似Lifshitz-tail的缓慢弛豫，揭示了最优退相干率可动态解耦并保护特定激发，为控制量子系统弛豫提供了新策略。
Optimal Quantum Information Transmission Under a Continuous-Variable Erasure Channel
本研究推导了能量约束下玻色连续变量擦除信道的量子容量与纠缠辅助量子容量，构建了渐近最优的随机编码，并设计出玻色版Hayden-Preskill协议，揭示了其信息恢复依赖输入输出模式比的特性。
Teleportation-based squeezer for bosonic cluster states
研究利用光的玻色子模式进行单向量子计算中寻找最优压缩门的问题，新方法使用不平衡分束器的振幅传输系数及零差检测等，性能优于现有方法，为低噪声压缩门开辟道路。
Realization of versatile and effective quantum metrology using a single bosonic mode
本研究针对量子计量中纠缠态制备难、易退相干的问题，提出基于单个玻色模式两次态转移的通用参数估计协议，在cQED平台以低光子数实现接近海森堡标度的7.5(6)dB计量增益，可扩展至多平台实用量子传感。
Bosonic quantum error-correcting codes with finite stellar rank
研究在有限非高斯资源下玻色子量子纠错码，用恒星秩作资源度量。对固定码族研究其权衡，超越固定码字直接优化编码，揭示不同噪声下码结构及资源阈值，确定恒星秩对玻色子QEC的操作意义。
We investigate the capacity of bosonic quantum channels for the transmission of quantum information. Achievable rates are determined from measurable moments of the channel by showing that every channel can asymptotically simulate a Gaussian channel which is characterized by second moments of the initial channel. We calculate the quantum capacity for a class of Gaussian channels, including channels describing optical fibers with photon losses, by proving that Gaussian encodings are optimal. Along the way we provide a complete characterization of degradable Gaussian channels and those arising fr…
In this article we use time-dependent Josephson coupling to enhance unconventional photon blockade in a system of two coupled nonlinear bosonic modes which are initially loaded with weakly populated coherent states, so the evolution is restricted to the manifold of up to two field quanta. Using numerical optimal control, we find the optimal coupling which minimizes the two-photon occupation of one mode, which is actually transferred to the other, while maintains a non-zero one-photon occupation in the same mode. Moreover, we choose the continuous coupling to vanish after the transfer between t…
Bosonic qubits encoded in continuous-variable systems provide a promising alternative to two-level qubits for quantum computation and communication. So far, photon loss has been the dominant source of errors in bosonic qubits, but the significant reduction of photon loss in recent bosonic qubit experiments suggests that dephasing errors should also be considered. However, a detailed understanding of the combined photon loss and dephasing channel is lacking. Here, we show that, unlike its constituent parts, the combined loss-dephasing channel is non-degradable, pointing towards a richer structu…
Exact quantum sensing limits for bosonic dephasing channels
本文研究玻色子退相干信道的区分与估计问题，通过将量子问题转化为经典概率密度问题，首次为非高斯玻色子信道建立了精确最优性能并给出显式策略。
We aim to devise feasible, efficient verification schemes for bosonic channels. To this end, we construct an average-fidelity witness that yields a tight lower bound for average fidelity plus a general framework for verifying optimal quantum channels. For both multi-mode unitary Gaussian channels and single-mode amplification channels, we present experimentally feasible average-fidelity witnesses and reliable verification schemes, for which sample complexity scales polynomially with respect to all channel specification parameters. Our verification scheme provides an approach to benchmark the p…
We construct quantum coherence resource theories in symmetrized Fock space (QCRTF), thereby providing an information-theoretic framework that connects analyses of quantum coherence in discrete-variable (DV) and continuous variable (CV) bosonic systems. Unlike traditional quantum coherence resource theories, QCRTF can be made independent of the single-particle basis and allow to quantify coherence within and between particle number sectors. For example, QCRTF can be formulated in such a way that neither Bose-Einstein condensates nor Heisenberg-Weyl coherent states are considered as quantum many…
Energy-constrained LOCC-assisted quantum capacity of bosonic dephasing channel
本文研究了能量约束下玻色退相位信道的LOCC辅助量子容量，通过推导能量约束压扁纠缠的上界并证明最优输入态和压扁信道的性质，给出了该容量的紧密上下界估计。
Quantum Noise Limited Nonlinear Phase-Preserving Amplification of a Bosonic Mode
本文肯定地回答了量子力学允许非线性保相放大，刻画了玻色噪声限制非线性保相放大器类别，并指出其用于Yurke-Stoler猫态和Kerr小猫态的最优放大。
There is a recent surge of interest and insights regarding the interplay of quantum optimal control and variational quantum algorithms. We study the framework in the context of qudits which are, for instance, definable as controllable electromagnetic modes of a superconducting cavity system coupled to a transmon. By employing recent quantum optimal control approaches described in (Petersson and Garcia, 2021), we showcase control of single-qudit operations up to eight states, and two-qutrit operations, mapped respectively onto a single mode and two modes of the resonator. We discuss the results…
We study the quantum capacity of continuous variable dephasing channel, which is a notable example of non-Gaussian quantum channel. We prove that a single letter formula applies. We then consider input energy restriction and show that by increasing it, the capacity saturates to a finite value. The optimal input state is found to be diagonal in the Fock basis and with a distribution that is a discrete version of a Gaussian. Relations between its mean/variance and dephasing rate/input energy are put forward. We also show that quantum capacity decays exponentially for large values of dephasing ra…
Bosonic Diffusive Channel: Quantum Metrology via Finite Non-Gaussian Resource
本研究通过压缩猫态和罗盘态实现退相干率的高精度估计，利用非高斯资源提升量子计量性能。
Sp(2N, R) interferometry in multi-mode Gaussian bosonic systems for optimal metrology and quantum control
利用 Sp(2N,R) 对称性，研究多模玻色子系统中的量子计量与量子控制，提出 Sp(2N,R) 回波实现量子 Fisher 信息设定的相位估计灵敏度，并引入几何方法逆转具有 Sp(2N,R) 动力学对称性的多体动力学。
Optimal two-mode bosonic loss codes from finite group symmetry
本文通过有限群对称性研究双模玻色子损耗码，推导Knill-Laflamme条件并构造最优码，证明其达到最大损耗距离，提出无限码族猜想。
Optimal Continuous- to Discrete-Variable Bipartite Entanglement Conversion
本文提出两种最优方案，利用本地操作和经典通信将连续变量双粒子纠缠转换为离散变量纠缠，通过二进制测量在有限测量轮次内实现高效率纠缠生成。
We investigate the performance of quantum parameter estimation based on a qubit probe in a dissipative bosonic environment beyond the traditional paradigm of weak-coupling and rotating-wave approximations. By making use of an exactly numerical hierarchical equations of motion method, we analyze the influences of the non-Markovian memory effect induced by the environment and the form of probe-environment interaction on the estimation precision. It is found that (i) the non-Markovianity can effectively boost the estimation performance and (ii) the estimation precision can be improved by introduc…
We systematically study the influence of amplitude modulation on the steady-state bosonic squeezing and entanglement in a dissipative three-mode optomechanical system, where a vibrational mode of the membrane is coupled to the left and right cavity modes via the radiation pressure. Numerical simulation results show that the steady-state bosonic squeezing and entanglement can be significantly enhanced by periodically modulated external laser driving either or both ends of the cavity. Remarkably, the fact that as long as one periodically modulated external laser driving either end of the cavitie…
Error Mitigation in Bosonic Systems via Virtual Distillation
研究通过虚拟蒸馏减轻玻色子系统误差，利用被动线性光学干涉仪对角化循环移位算子，推导可实验的协议来估计相关可观测量的虚拟蒸馏期望值，应用于受光子损失和退相影响的状态。
Bosonic rotation codes, introduced here, are a broad class of bosonic error-correcting codes based on phase-space rotation symmetry. We present a universal quantum computing scheme applicable to a subset of this class--number-phase codes--which includes the well-known cat and binomial codes, among many others. The entangling gate in our scheme is code-agnostic and can be used to interface different rotation-symmetric encodings. In addition to a universal set of operations, we propose a teleportation-based error correction scheme that allows recoveries to be tracked entirely in software. Focusi…
Efficient Convex Optimization for Bosonic State Tomography
本文提出基于凸优化的高效方法，用于高维和多模式玻色子态层析，通过改进计算和优化技术提升效率和可扩展性。
Continuous-variable systems protected by bosonic quantum error-correcting codes have emerged as a promising platform for quantum information processing. To date, design of codewords has centered on optimizing the occupation of basis states in the error-relevant basis. Here, we propose utilizing the phase degree of freedom in basis state probability amplitudes to devise codes that feature destructive interference, and thus reduced overlap, between error codewords. To showcase, we first consider the correction of excitation loss using single-mode codes with Fock-space parity structure and show t…
We consider a collection of bosonic modes corresponding to the vertices of a graph $Γ.$ Quantum tunneling can occur only along the edges of $Γ$ and a local self-interaction term is present. Quantum entanglement of one vertex with respect the rest of the graph is analyzed in the ground-state of the system as a function of the tunneling amplitude $τ.$ The topology of $Γ$ plays a major role in determining the tunneling amplitude $τ^*$ which leads to the maximum ground-state entanglement. Whereas in most of the cases one finds the intuitively expected result $τ^*=\infty$ we show that it there exis…
Complementarity between bosonic and fermionic many-body interferences with partially distinguishable particles
研究探讨了在部分可区分粒子存在下，玻色子与费米子干涉的互补性，建立了多体干涉的数学关系，并揭示了其在量子计量中的操作影响。
We analyze the efficiency of quantum simulations of fermionic and bosonic models in trapped ions. In particular, we study the optimal time of entangling gates and the required number of total elementary gates. Furthermore, we exemplify these estimations in the light of quantum simulations of quantum field theories, condensed-matter physics, and quantum chemistry. Finally, we show that trapped-ion technologies are a suitable platform for implementing quantum simulations involving interacting fermionic and bosonic modes, paving the way for overcoming classical computers in the near future.
We consider the problem of estimating an unknown but constant carrier phase modulation $θ$ using a general -- possibly entangled -- $n$-mode optical probe through $n$ independent and identical uses of a lossy bosonic channel with additive thermal noise. We find an upper bound to the quantum Fisher information (QFI) of estimating $θ$ as a function of $n$, the mean and variance of the total number of photons $N_{\rm S}$ in the $n$-mode probe, the transmissivity $η$ and mean thermal photon number per mode ${\bar n}_{\rm B}$ of the bosonic channel. Since the inverse of QFI provides a lower bound t…
We study the joint estimation of multiple Rabi frequencies in a multilevel system. By analytically identifying the optimal probe state and the optimal measurement, we obtain the highest precision limit for the joint estimation of multiple Rabi frequencies. We show that the joint estimation does not always outperform the separate estimation. In different regimes the joint estimation can either outperform or underperform the separate estimation. We further show that if additional adaptive quantum controls are allowed then the advantage of the joint estimation over the separate estimation can be …
Architectural scaling tradeoffs in modular 3D bosonic quantum processors
该研究针对模块化三维玻色量子处理器，对比三类架构的缩放权衡，建立系统评估框架，为相关硬件设计提供器件级参数依据。
We study the limitations on coherence evolutions under the constraints of thermodynamic laws, and focus on the optimal thermal operations (TO) reaching the bounds. For qubit case, we find a thermal operation involving only a single-mode reservoir (STO) which maintains the maximum coherence allowed by general TO. For higher dimensions, we derive general bounds on coherence merging under TO, and find STO to reach the bounds. By applying the bound to a two-qubit system, we prove that erasing correlations while preserving the marginal states is not free in the resource theory of thermodynamics. Du…
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