Stefano Pirandola, Seth Lloyd
By combining the Minkowski inequality and the quantum Chernoff bound, we derive easy-to-compute upper bounds for the error probability affecting the optimal discrimination of Gaussian states. In particular, these bounds are useful when the Gaussian states are unitarily inequivalent, i.e., they differ in their symplectic invariants.
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One advantage of quantum algorithms over classical computation is the possibility to spread out, process, analyse and extract information in multipartite configurations in coherent superpositions of classical states. This will be discussed in terms of quantum state identification problems based on a proper partitioning of mutually orthogonal sets of states. The question arises whether or not it is possible to encode equibalanced decision problems into quantum systems, so that a single invocation of a filter used for state discrimination suffices to obtain the result.
Efficiently Computable Strategies and Limits for Bosonic Channel Discrimination
本文研究了在能量约束下，通过量子通道判别协议实现误差指数的上限，利用Belavkin-Staszewski通道分歧的能耗约束链规则，推导出可高效计算的不对称误差指数界限，并展示了在能量约束下最优探测器为Fock-对角形式。
An easily computable measure of Gaussian quantum imaginarity
本文针对连续变量高斯态提出一种由位移向量和协方差矩阵直接表示、易于计算的高斯虚数性度量，并证明其可高效检测多模高斯虚数性，且能诱导多分多模高斯关联度量，揭示高斯虚数性是一种多分量子资源。
We address the limit of the Gaussian operations and classical communication in the problem of quantum state discrimination. We show that the optimal Gaussian strategy for the discrimination of the binary phase shift keyed (BPSK) coherent signal is a simple homodyne detection. We also propose practical near-optimal quantum receivers that beat the BPSK homodyne limit in all areas of the signal power. Our scheme is simple and does not require realtime electrical feedback.
We investigate the energy-constrained (EC) diamond norm distance between unitary channels acting on possibly infinite-dimensional quantum systems, and establish a number of results. Firstly, we prove that optimal EC discrimination between two unitary channels does not require the use of any entanglement. Extending a result by Acín, we also show that a finite number of parallel queries suffices to achieve zero error discrimination even in this EC setting. Secondly, we employ EC diamond norms to study a novel type of quantum speed limits, which apply to pairs of quantum dynamical semigroups. We …
All non-Gaussian states are advantageous for channel discrimination: Robustness of non-convex continuous variable quantum resources
本文针对任意资源理论定义广义鲁棒性并给出其操作解释，证明所有非高斯态（包括高斯态混合）在信道区分任务中均具优势，并给出福克态及高斯态凸包内非高斯态的鲁棒性公式。
In this paper, a computable multipartite multimode Gaussian quantum correlation measure ${\mathcal M}^{(k)}$ is proposed for any $k$-partite continuous-variable (CV) systems with $k\geq 2$. ${\mathcal M}^{(k)}$ depends only on the covariance matrix of CV states, is invariant under any permutation of subsystems, is a quantification without ancilla problem, nonincreasing under $k$-partite local Gaussian channels (particularly, invariant under $k$-partite local Gaussian unitary operations), vanishes on $k$-partite product states. For a $k$-partite Gaussian state $ρ$, ${\mathcal M}^{(k)}(ρ)=0$ if …
Near-optimal coherent state discrimination via continuously labelled non-Gaussian measurements
本文提出通过连续标记非高斯测量实现近最优相干态鉴别，超越高斯极限，无需光子检测，且在低能量下接近Hellstrom界。
Consider two bosonic modes which are prepared in one of two possible Gaussian states with the same local energy: either a tensor-product thermal state (with zero correlations) or a separable Gaussian state with maximal correlations (with both classical and quantum correlations, the latter being quantified by quantum discord). For the discrimination of these states, we compare the optimal joint coherent measurement with the best local measurement based on single-mode Gaussian detections. We show how the coherent measurement always strictly outperforms the local detection strategy for both singl…
We determine the optimal method of discriminating and comparing quantum states from a certain class of multimode Gaussian states and their mixtures when arbitrary global Gaussian operations and general Gaussian measurements are allowed. We consider the so-called constant-$\hat{p}$ displaced states which include mixtures of multimode coherent states arbitrarily displaced along a common axis. We first show that no global or local Gaussian transformations or generalized Gaussian measurements can lead to a better discrimination method than simple homodyne measurements applied to each mode separate…
All-Gaussian State Discrimination Beyond the Coherent Helstrom Bound
针对BPSK信号判别问题，提出仅用高斯光学（位移压缩态和零差探测）实现低于相干态任何测量错误率的方案，无需达到Helstrom界。
We propose a long-distance continuous-variable quantum key distribution (CVQKD) with four-state protocol using non-Gaussian state-discrimination detection. A photon subtraction operation, which is deployed at the transmitter, is used for splitting the signal required for generating the non-Gaussian operation to lengthen the maximum transmission distance of CVQKD. Whereby an improved state-discrimination detector, which can be deemed as an optimized quantum measurement that allows the discrimination of nonorthogonal coherent states beating the standard quantum limit, is applied at the receiver …
Parallelization of Adaptive Quantum Channel Discrimination in the Non-Asymptotic Regime
本文将自适应不优于并行量子信道判别的结论扩展至非渐近情形，通过显式构造并行策略并界定性能差异，证明了并行策略可在多项式时间内优化，从而为自适应策略性能提供了渐近紧致上界。
Local Gaussian bounds on the non-destructive discrimination of two-mode squeezed states
本研究探究利用局域高斯测量对双模压缩态的非破坏性区分，构造最优协议并扩展至含预共享纠缠的情形，将信息增益与扰动的权衡从有限维系统拓展至连续变量系统。
We provide rigorous, efficiently computable and tight bounds on the average error probability of multiple-copy discrimination between qubit mixed states by Local Operations assisted with Classical Communication (LOCC). In contrast to the pure-state case, these experimentally feasible protocols perform strictly worse than the general collective ones. Our numerical results indicate that the gap between LOCC and collective error rates persists in the asymptotic limit. In order for LOCC and collective protocols to achieve the same accuracy, the former requires up to twice the number of copies of t…
Optimal Discrimination of Gaussian States by Gaussian Measurements
本文研究了高斯测量在区分高斯态中的最优性，推导出基于协方差矩阵的条件以确定最优测量的存在，并展示了当条件不满足时区分度的差距。
Computable measures of non-Markovianity for Gaussian free fermion systems
本文针对高斯自由费米子开放系统，将 BLP、LFS 相关非马尔可夫性度量转化为可由两点关联函数计算的形式，并验证其对随机平均产生的非高斯态仍适用。
Computable fermionic non-Gaussianity from the covariance matrix
基于协方差矩阵的Williamson标准型，提出两类可计算的纯费米子态非高斯性度量（占据数熵和自然轨道参与熵），证明其单调性并约束非高斯门数量与经典模拟成本。
The non-linearity of a conditional photon-counting measurement can be used to `de-Gaussify' a Gaussian state of light. Here we present and experimentally demonstrate a technique for photon number resolution using only homodyne detection. We then apply this technique to inform a conditional measurement; unambiguously reconstructing the statistics of the non-Gaussian one and two photon subtracted squeezed vacuum states. Although our photon number measurement relies on ensemble averages and cannot be used to prepare non-Gaussian states of light, its high efficiency, photon number resolving capabi…
Genuine multimode entanglement in continuous variable systems can be quantified by exploring the geometry of the state-space, namely via the generalized geometric measure (GGM) which is defined as the shortest distance of a given multimode state from a nongenunely multimode entangled state. For multimode Gaussian states, we derive a closed form expression of GGM in terms of the symplectic invariants of the reduced states. Following that prescription, the characteristics of GGM for typical three- and four-mode Gaussian states are investigated. In the non-Gaussian paradigm, we compute GGM for ph…
Fermionic non-Gaussianity via computable measures and experimentally accessible bounds
该研究提出费米子非高斯性的几何度量，构建适用于强耦合的迭代形式体系，推导含两点和四点关联函数的见证量，经费米-哈伯德模型验证其性能更优，为研究强相互作用费米子量子模拟器非高斯性提供可扩展方法。
We experimentally demonstrate a new measurement scheme for the discrimination of two coherent states. The measurement scheme is based on a displacement operation followed by a photon number resolving detector, and we show that it outperforms the standard homodyne detector which we, in addition, proof to be optimal within all Gaussian operations including conditional dynamics. We also show that the non-Gaussian detector is superior to the homodyne detector in a continuous variable quantum key distribution scheme.
Adversarial quantum channel discrimination
本文提出了一种对抗性量子信道鉴别的新框架，引入最小输出信道分歧度，并展示了熵积累在量子密码学中的新应用。
The asymptotic state discrimination problem with simple hypotheses is considered for a cubic lattice of bosons. A complete solution is provided for the problems of the Chernoff and the Hoeffding bounds and Stein's lemma in the case when both hypotheses are gauge-invariant Gaussian states with translation-invariant quasi-free parts.
We address extended systems interacting with classical fluctuating environments and analyze the use of quantum probes to discriminate local noise, described by independent fluctuating fields, from common noise, corresponding to the interaction with a common one. In particular, we consider a bipartite system made of two non interacting harmonic oscillators and assess discrimination strategies based on homodyne detection, comparing their performances with the ultimate bounds on the error probabilities of quantum-limited measurements. We analyze in details the use of Gaussian probes, with emphasi…
Gaussian unsteerable channels and computable quantifications of Gaussian steering
针对连续变量高斯操控资源理论自由操作不完整的问题，本文刻画高斯不可操控信道结构，并提出仅依赖协方差矩阵、无需优化的两种可计算高斯操控量化。
What is the ultimate performance for discriminating two arbitrary quantum channels acting on a finite-dimensional Hilbert space? Here we address this basic question by deriving a general and fundamental lower bound. More precisely, we investigate the symmetric discrimination of two arbitrary qudit channels by means of the most general protocols based on adaptive (feedback-assisted) quantum operations. In this general scenario, we first show how port-based teleportation can be used to simplify these adaptive protocols into a much simpler non-adaptive form, designing a new type of teleportation …
Entanglement cost of bipartite quantum channel discrimination under positive partial transpose operations
本研究提出双分量量子通道鉴别的纠缠成本理论，通过k-可注入PPT测试器分析最优成功概率，并利用SDP方法计算纠缠成本。
Discriminating idempotent quantum channels
研究二元区分幂等量子通道，当两个通道共享共同全秩不变态时，图像包含条件决定渐进行为，所有误差指数可显式计算，且无适应优势，从而获得该通道族的强反向性质。
We investigate the performance of a Kennedy receiver, which is known as a beneficial tool in optical coherent communications, to the quantum state discrimination of the two superpositions of vacuum and single photon states corresponding to the $\hatσ_x$ eigenstates in the single-rail encoding of photonic qubits. We experimentally characterize the Kennedy receiver in vacuum-single photon two-dimensional space using quantum detector tomography and evaluate the achievable discrimination error probability from the reconstructed measurement operators. We furthermore derive the minimum error rate ob…
Chiral Discrimination on Gate-Based Quantum Computers
本研究提出了一种基于门的量子计算方法，用于手性鉴别，通过离散化STIRAP和STAP协议，实现了对1,2-丙二醇分子的实验验证。
The characterisation of Quantum Channel Discrimination (QCD) offers critical insight for future quantum technologies in quantum metrology, sensing and communications. The task of multi-channel discrimination creates a scenario in which the discrimination of multiple quantum channels can be equated to the idea of pattern recognition, highly relevant to the tasks of quantum reading, illumination and more. Whilst the optimal quantum strategy for many scenarios is an entangled idler-assisted protocol, the extension to a multi-hypothesis setting invites the exploration of discrimination strategies …
Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources, and thus nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise.…
Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measu…
We demonstrate an optical receiver that achieves the quantum Chernoff bound for discriminating coherent states from thermal states in the multi-copy scenario. In contrast, we find that repeated use of the receiver approaching the Helstrom bound for single-copy measurement is sub-optimal in this multi-copy case. Furthermore, for a large class of multi-copy discrimination tasks between a pure and a mixed state, we prove that any Helstrom-bound achieving single-copy receiver is suboptimal by a factor of at least two in error-probability exponent compared to the multi-copy quantum Chernoff bound. …
We derive a computable analytical formula for the quantum fidelity between two arbitrary multimode Gaussian states which is simply expressed in terms of their first- and second-order statistical moments. We also show how such a formula can be written in terms of symplectic invariants and used to derive closed forms for a variety of basic quantities and tools, such as the Bures metric, the quantum Fisher information and various fidelity-based bounds. Our result can be used to extend the study of continuous-variable protocols, such as quantum teleportation and cloning, beyond the current one-mod…
The ability to precisely discriminate multiple quantum channels is fundamental to achieving quantum enhancements in data-readout, target detection, pattern recognition, and more. Optimal discrimination protocols often rely on entanglement shared between an incident probe and a protected idler-mode. While these protocols can be highly advantageous over classical ones, the storage of idler-modes is extremely challenging in practice. In this work, we investigate idler-free block protocols based on the use of multipartite entangled probe states. In particular, we focus on a class of idler-free pro…
We suggest an improved version of Robertson-Schrödinger uncertainty relation for canonically conjugate variables by taking into account a pair of characteristics of states: non-Gaussianity and mixedness quantified by using fidelity and entropy, respectively. This relation is saturated by both Gaussian and Fock states, and provides strictly improved bound for any non-Gaussian states or mixed states. For the case of Gaussian states, it is reduced to the entropy-bounded uncertainty relation derived by Dodonov. Furthermore, we consider readily computable measures of both characteristics, and find …
Optimizing state-discrimination receivers for continuous-variable quantum key distribution over a wiretap channel
本文针对窃听信道下的连续变量量子密钥分发，设计了一种优化态鉴别接收机（KOR），在城域网距离上相比近似最优测量和外差协议提升安全密钥率，并验证了位移前馈方案的可行性。
We present explicit expressions for the central piece of a variational method developed by Shi et al. which extends variational wave functions that are efficiently computable on classical computers beyond mean-field to generalized Gaussian states [1]. In particular, we derive iterative analytical expressions for the evaluation of expectation values of products of fermionic creation and annihilation operators in a Grassmann variable-free representation. Using this result we find a closed expression for the energy functional and its gradient of a general fermionic quantum many-body Hamiltonian. …
Quantum Wasserstein distance for Gaussian states
本文提出了一种计算任意两个单模高斯态之间量子瓦森斯坦距离的一般公式，并展示了如何通过该公式恢复经典高斯分布和热态的瓦森斯坦距离。
We address the issue of quantifying the non-Gaussian character of a bosonic quantum state and introduce a non-Gaussianity measure based on the Hilbert-Schmidt distance between the state under examination and a reference Gaussian state. We analyze in details the properties of the proposed measure and exploit it to evaluate the non-Gaussianity of some relevant single- and multi-mode quantum states. The evolution of non-Gaussianity is also analyzed for quantum states undergoing the processes of Gaussification by loss and de-Gaussification by photon-subtraction. The suggested measure is easily com…
Entanglement cost of discriminating quantum states under locality constraints
本文研究局部约束下区分量子态的纠缠代价，引入谱PPT距离量化测量局域性并给出下界，同时建立上界，证明单个Bell态可辅助纯态最优区分任意其他态。
We consider how to quantify non-Gaussianity for the correlation of a bipartite quantum state by using various measures such as relative entropy and geometric distances. We first show that an intuitive approach, i.e., subtracting the correlation of a reference Gaussian state from that of a target non-Gaussian state, fails to yield a non-negative measure with monotonicity under local Gaussian channels. Our finding clearly manifests that quantum-state correlations generally have no Gaussian extremality. We therefore propose a different approach by introducing relevantly averaged states to address…
Singular Asymptotics of SPADE in Quantum Source Discrimination
研究弱且间距小的发射源在奇异区域中，使用空间模式解复用（SPADE）进行远场鉴别的有限光子行为，通过奇异学习理论分析对齐和未对齐情况下的贝叶斯自由能渐近性和Neyman-Pearson检验性能。
Noise-robust discrimination of incoherent point sources with spatial-mode demultiplexing
该研究提出仅用最低两阶厄米-高斯模式的空间模式解复用（SPADE）测量，在分辨非相干点源时抗噪声性能优于直接成像（DI），每像素背景信号光子比0.11时仍接近量子极限，为天文观测等场景提供实用探测方案。
The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory. It can not only efficiently be computed in the Hilbert space dimension, but for non-interacting bosonic systems, one can compute the negativity efficiently in the number of modes. However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian. To provide a remedy for this state of affairs, in this work we introd…
Pulsed homodyne quantum tomography usually requires a high detection efficiency limiting its applicability in quantum optics. Here, it is shown that the presence of low detection efficiency ($<50\%$) does not prevent the tomographic reconstruction of quantum states of light, specifically, of Gaussian type. This result is obtained by applying the so-called "minimax" adaptive reconstruction of the Wigner function to pulsed homodyne detection. In particular, we prove, by both numerical and real experiments, that an effective discrimination of different Gaussian quantum states can be achieved. Our…
The required set of operations for universal continuous-variable quantum computation can be divided into two primary categories: Gaussian and non-Gaussian operations. Furthermore, any Gaussian operation can be decomposed as a sequence of phase-space displacements and symplectic transformations. Although Gaussian operations are ubiquitous in quantum optics, their experimental realizations generally are approximations of the ideal Gaussian unitaries. In this work, we study different performance criteria to analyze how well these experimental approximations simulate the ideal Gaussian unitaries. …
We propose observable bounds for Gaussian illumination to maximize the signal-to-noise ratio, which minimizes the discrimination error between the presence and absence of a low-reflectivity target using Gaussian states. The observable bounds are achieved with mode-by-mode measurements. In the quantum regime using a two-mode squeezed vacuum state, our observable receiver outperforms the other feasible receivers whereas it cannot approach the quantum Chernoff bound. The corresponding observable cannot be implemented with heterodyne detections due to the additional vacuum noise. In the classical …
Barycentric bounds on the error exponents of quantum hypothesis exclusion
本文从信息论角度研究量子状态排除的最优误差概率及其误差指数，提出基于多变量对数欧几里得柴可夫斯基散度的单字母上界，改进了现有上界，并扩展至量子信道排除，推导出可计算的上界。
A computable branching random walk for the many-body Wigner quantum dynamics
本文提出了一种用于许多体Wigner方程的分支随机游走算法，并分析了其在相空间量子动力学中的数值应用。通过引入辅助函数，截断的Wigner方程被转化为积分形式及其伴随对应关系，这两种形式都可以改写为 renewal 型方程，并具有透明的概率解释。我们证明分支随机游走的第一个时刻恰好是伴随方程的解。更重要的是，我们详细说明了这种随机模型，结合重要性抽样和重采样，为一种数值可行的方案铺平了道路，在此方案中，Wigner量子动力学以时间推进的方式进行模拟，并通过粒子数增长速率的（精确）估计器来控制复杂性。典型的数值实验在高斯势垒散射和类氦系统上验证了我们的理论发现，并展示了该Wigner分支随机游走算法的准确性、效率和可计算性。
Time-frequency (TF) filtering of analog signals has played a crucial role in the development of radio-frequency communications, and is currently being recognized as an essential capability for communications, both classical and quantum, in the optical frequency domain. How best to design optical time-frequency (TF) filters to pass a targeted temporal mode (TM), and to reject background (noise) photons in the TF detection window? The solution for coherent TF filtering is known, the quantum pulse gate, whereas the conventional, more common method is implemented by a sequence of incoherent spectr…
We address the effects of realistic photodetection, with nonunit quantum efficiency and background noise (dark counts), on the performances of quantum communication schemes based on photon-number entangled states. We consider channels based on Gaussian twin-beam states and non-Gaussian two-mode coherent states and evaluate the channel capacity by optimizing the bit discrimination threshold. We found that TWB-based channels are more robust against noise than TMC-based ones and that this result is almost independent on the statistics of dark counts.
Gaussian boson sampling is a promising scheme for demonstrating a quantum computational advantage using photonic states that are accessible in a laboratory and, thus, offer scalable sources of quantum light. In this contribution, we study two-point photon-number correlation functions to gain insight into the interference of Gaussian states in optical networks. We investigate the characteristic features of statistical signatures which enable us to distinguish classical from quantum interference. In contrast to the typical implementation of boson sampling, we find additional contributions to the…
The maximum observable correlation between the two components of a bipartite quantum system is a property of the joint density operator, and is achieved by making particular measurements on the respective components. For pure states it corresponds to making measurements diagonal in a corresponding Schmidt basis. More generally, it is shown that the maximum correlation may be characterised in terms of a `correlation basis' for the joint density operator, which defines the corresponding (nondegenerate) optimal measurements. The maximum coincidence rate for spin measurements on two-qubit systems …
Comment on "Scalable Quantum Machine Learning: Trainability, Expressivity and Efficiency": Polynomial Evaluation of the Triplet-Block Readout
本文针对arXiv:2607.24014v1的三重态块读出经典成本主张，提出O(n⁴)确定性算法，推翻其指数成本结论，且不影响其他相关结果。
The science of quantum information has arisen over the last two decades centered on the manipulation of individual quanta of information, known as quantum bits or qubits. Quantum computers, quantum cryptography and quantum teleportation are among the most celebrated ideas that have emerged from this new field. It was realized later on that using continuous-variable quantum information carriers, instead of qubits, constitutes an extremely powerful alternative approach to quantum information processing. This review focuses on continuous-variable quantum information processes that rely on any com…
We develop a quantum learning scheme for binary discrimination of coherent states of light. This is a problem of technological relevance for the reading of information stored in a digital memory. In our setting, a coherent light source is used to illuminate a memory cell and retrieve its encoded bit by determining the quantum state of the reflected signal. We consider a situation where the amplitude of the states produced by the source is not fully known, but instead this information is encoded in a large training set comprising many copies of the same coherent state. We show that an optimal g…
Entanglement properties of Gaussian states of light as well as the security of continuous variable quantum key distribution with Gaussian states in free-space fading channels are studied. These qualities are shown to be sensitive to the statistical properties of the transmittance distribution in the cases when entanglement is strong or when channel excess noise is present. Fading, i.e. transmission fluctuations, caused by beam wandering due to atmospheric turbulence, is a frequent challenge in free-space communication. We introduce a method of fading discrimination and subsequent post-selectio…
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