Giulio Chiribella, Giacomo M. D'Ariano, Paolo Perinotti
We consider quantum-memory assisted protocols for discriminating quantum channels. We show that for optimal discrimination of memory channels, memory assisted protocols are needed. This leads to a new notion of distance for channels with memory. For optimal discrimination and estimation of sets of unitary channels memory-assisted protocols are not required.
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We quantify the usefulness of a bipartite quantum state in the ancilla-assisted channel discrimination of arbitrary quantum channels, formally defining a worst-case-scenario channel discrimination power for bipartite quantum states. We show that such a quantifier is deeply connected with the operator Schmidt decomposition of the state. We compute the channel discrimination power exactly for pure states, and provide upper and lower bounds for general mixed states. We show that highly entangled states can outperform any state that passes the realignment criterion for separability. Furthermore, w…
Adaptive quantum channel discrimination using methods of quantum metrology
本文提出基于量子计量方法的高效算法，用于实现最优自适应量子信道鉴别策略，揭示了信道鉴别与估计问题之间的结构相似性。
We prove that every entangled state is useful as a resource for the problem of minimum-error channel discrimination. More specifically, given a single copy of an arbitrary bipartite entangled state, it holds that there is an instance of a quantum channel discrimination task for which this state allows for a correct discrimination with strictly higher probability than every separable state.
We provide a simple example that illustrates the advantage of adaptive over non-adaptive strategies for quantum channel discrimination. In particular, we give a pair of entanglement-breaking channels that can be perfectly discriminated by means of an adaptive strategy that requires just two channel evaluations, but for which no non-adaptive strategy can give a perfect discrimination using any finite number of channel evaluations.
We show that every entangled state provides an advantage in bi- and multi-channel discrimination that singles out its degree of entanglement, quantified in terms of its Schmidt number and of the corresponding robustness measures.
Unambiguous discrimination of the change point for quantum channels
研究量子通道变更点的精确鉴别问题，提出无歧义鉴别中的上下界方法，分析单位ary通道序列的平均成功概率表达式。
We solve the problem of discriminating with minimum error probability two given Pauli channels. We show that, differently from the case of discrimination between unitary transformations, the use of entanglement with an ancillary system can strictly improve the discrimination, and any maximally entangled state allows to achieve the optimal discrimination. We also provide a simple necessary and sufficient condition in terms of the structure of the channels for which the ultimate minimum error probability can be achieved without entanglement assistance. When such a condition is satisfied, the opt…
Improving quantum channel discrimination with resourceful states
该研究证明在任何状态资源理论中，鲁棒性度量可精确量化量子信道判别问题中（含或不含辅助系统）使用资源态带来的最大平均成功概率提升，为资源在判别任务中的优势提供了完整刻画。
A collection of quantum channels is called incompatible if they cannot be obtained as marginals from a single channel. No-cloning theorem is the most prominent instance of incompatibility of quantum channels. We show that every collection of incompatible channels can be more useful than compatible ones as preprocessings in a state discrimination task with multiple ensembles of states. This is done by showing that the robustness of channel incompatibility which is a measure for incompatibility of channels exactly quantifies the maximum advantage in the state discrimination. We also show that in…
We study the power of measurements implementable with local quantum operations and classical communication (or LOCC measurements for short) in the setting of quantum channel discrimination. More precisely, we consider discrimination procedures that attempt to identify an unknown channel, chosen uniformly from two known alternatives, that take the following form: (i) the input to the unknown channel is prepared in a possibly entangled state with an ancillary system, (ii) the unknown channel is applied to the input system, and (iii) an LOCC measurement is performed on the output and ancillary sy…
Discrimination of bosonic dephasing quantum channels
本研究探讨了区分两个玻色子退相量子信道的问题，证明了无歧义区分不可行，并在有或无输入能量约束下优化了错误概率，且将结果推广至多次区分。
We introduce and study norms in the space of hermitian operators, obtained from base norms in positively generated subspaces. These norms are closely related to discrimination of so-called generalized quantum channels, including quantum states, channels and networks. We further introduce generalized quantum decision problems and show that the maximal average payoff of decision procedures is again given by these norms. We also study optimality of decision procedures, in particular, we obtain a necessary and sufficient condition under which an optimal 1-tester for discrimination of quantum chann…
Experimental study of multiple-shot unitary channels discrimination using the IBM Q computers
本研究在IBM量子处理器上实验验证多次射击酉信道辨识，发现过深或过度纠缠的电路不利，而最小化纠缠且深度适中的电路对噪声更鲁棒。
Discrimination of dephasing channels
本文研究有限维系统的退相位信道区分问题，解析求解了无能量约束下qubit、qutrit和ququart的最优输入态，并证明纠缠辅助策略在此场景下完全无效。
For minimum-error channel discrimination tasks that involve only unitary channels, we show that sequential strategies may outperform the parallel ones. Additionally, we show that general strategies that involve indefinite causal order are also advantageous for this task. However, for the task of discriminating a uniformly distributed set of unitary channels that forms a group, we show that parallel strategies are, indeed, optimal, even when compared to general strategies. We also show that strategies based on the quantum switch cannot outperform sequential strategies in the discrimination of u…
We consider the problem of optimally discriminating two Pauli channels in the minimax strategy, maximizing the smallest of the probabilities of correct identification of the channel. We find the optimal input state at the channel and show the conditions under which using entanglement strictly enhances distinguishability. We finally compare the minimax strategy with the Bayesian one.
A no-signalling channel transforming quantum systems in Alice's and Bob's laboratories is compatible with two different causal structures: (A < B) Alice's output causally precedes Bob's input and (B< A) Bob's output causally precedes Alice's input. I show that a quantum superposition of circuits operating within these two causal structures enables the perfect discrimination between no-signalling channels that can not be perfectly distinguished by any ordinary circuit.
In this work, we consider optimal state discrimination for a quantum system that interacts with an environment, i.e., states evolve under a quantum channel. We show the conditions on a quantum channel and an ensemble of states such that a measurement for optimal state discrimination is preserved. In particular, we show that when an ensemble of states with equal {\it a priori} probabilities is given, an optimal measurement can be preserved over any quantum channel by applying local operations and classical communication, that is, by manipulating the quantum states before and after the channel a…
We present an instance of a task of minimum-error discrimination of two qubit-qubit quantum channels for which a sequential strategy outperforms any parallel strategy. We then establish two new classes of strategies for channel discrimination that involve indefinite causal order and show that there exists a strict hierarchy among the performance of all four strategies. Our proof technique employs a general method of computer-assisted proofs. We also provide a systematic method for finding pairs of channels that showcase this phenomenon, demonstrating that the hierarchy between the strategies i…
Power of sequential protocols in hidden quantum channel discrimination
研究隐藏系统量子信道判别（HQCD）问题，发现序贯协议能实现完美判别并达到海森堡极限，而深度为1的并行和多回合协议无法解决该问题，证明序贯协议在实验现实场景中更具优势。
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。
Dilation, Discrimination and Uhlmann's Theorem of Link Products of Quantum Channels
该研究针对量子信道这一量子信息核心问题，建立量子信道链接积的Stinespring扩张定理，分析自链接对信道可区分度的提升作用，并验证对角信道可达到Uhlmann定理的最大值，为量子网络研究提供理论支撑。
Dynamics of many-qubit systems, that may correspond to computational processing with quantum systems, can be efficiently and generally approximated by a sequence of two- and single-qubit gates. In practical applications, however, a quantum gate prepared as a unitary transformation may appear as a noisy channel and consequently may inhibit quantum advantages. In this work, we apply the scheme of channel discrimination to detect if a quantum gate that is actually realized is unitary or noisy. We show that a two-qubit unitary transformation and its noisy counterpart can be optimally discriminated…
We find optimality conditions for testers in discrimination of quantum channels. These conditions are obtained using semidefinite programming and are similar to optimality conditions for POVMs obtained by Holevo for ensembles of quantum states. We get a simple condition for existence of an optimal tester with any given input state with maximal Schmidt rank, in particular with a maximally entangled input state and we show the pitfalls of using input states with not maximal Schmidt rank. In case when maximally entangled state is not the optimal input state an error estimate is obtained. The resu…
Purification enables an unbounded query separation in sequential quantum channel discrimination
本文证明在顺序量子信道鉴别中，利用纯化资源（即使环境参考系未知）能严格提升成功概率，优于裸访问和平行策略，并给出具体信道实例验证该优势。
Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained. In both scenarios, the testing between quantum states are relatively well-understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channe…
We determine a fundamental upper bound on the performance of any adaptive protocol for discrimination or estimation of a channel which has an unknown parameter encoded in the state of its environment. Since our approach relies on the principle of data processing, the bound applies to a variety of discrimination measures, including quantum relative entropy, hypothesis testing relative entropy, Rényi relative entropy, fidelity, and quantum Fisher information. We apply the upper bound to thermal (amplifier) channels with a known transmissivity (gain) but unknown excess noise. In these cases, we f…
Profitable entanglement for channel discrimination
本文研究了辅助纠缠在区分两个一般量子比特信道中的作用，通过构造性方法分别分析了极值和非极值信道，确定了纠缠提升成功概率的精确条件。
The accurate and reliable characterization of quantum dynamical processes underlies efforts to validate quantum technologies, where discrimination between competing models of observed behaviors inform efforts to fabricate and operate qubit devices. We present a novel protocol for quantum channel discrimination that leverages advances in direct characterization of quantum dynamics (DCQD) codes. We demonstrate that DCQD codes enable selective process tomography to improve discrimination between entangling and correlated quantum dynamics. Numerical simulations show selective process tomography re…
Robustness of quantum data hiding against entangled catalysts and memory
本文研究量子数据隐藏在催化剂和量子记忆辅助下的鲁棒性，证明可分隐藏态不受这些资源影响，而某些纠缠态可被量子记忆几乎完美区分。
Parallel quantum channel discrimination and numerical ranges in tensor product subspaces
本研究针对并行量子信道完美鉴别问题，提出结合半定规划与二分法的高效算法，并证明张量积子空间数值域最小角度的可加性，从而肯定解决了一个公开猜想。
Single-shot quantum channel discrimination is a fundamental task in quantum information theory. It is well known that entanglement with an ancillary system can help in this task, and furthermore that an ancilla with the same dimension as the input of the channels is always sufficient for optimal discrimination of two channels. A natural question to ask is whether the same holds true for the output dimension. That is, in cases when the output dimension of the channels is (possibly much) smaller than the input dimension, is an ancilla with dimension equal to the output dimension always sufficien…
The class of quantum states known as Werner states have several interesting properties, which often serve to illuminate unusual properties of quantum information. Closely related to these states are the Holevo-Werner channels whose Choi matrices are Werner states. Exploiting the fact that these channels are teleportation covariant, and therefore simulable by teleportation, we compute the ultimate precision in the adaptive estimation of their channel-defining parameter. Similarly, we bound the minimum error probability affecting the adaptive discrimination of any two of these channels. In this …
Efficient and operational quantifier of non-divisibility in terms of channel discrimination
本文提出利用信道区分概念，通过半定规划高效检测和量化量子信道的非可分性，为开放量子系统研究提供可操作方法。
We propose a scheme by using the feed-forward control (FFC) to realize a better effect of discrimination of two nonorthogonal states after passing a noise channel based on the minimum- error (ME) discrimination. We show that the application of our scheme can highly improve the effect of discrimination compared with the ME discrimination without the FFC for any pair of nonorthogonal states and any degree of amplitude damping (AD). Especially, the effect of our optimal discrimination can reach that of the two initial nonorthogonal pure states in the presence of the noise channel in a determinist…
A quantum analogue of the famous Blackwell Theorem in classical statistics has recently been proposed. Given two quantum channels A and B, a set of payoff functions have been proven to have values for B at least as high as they are for A if and only if there exists a quantum garbling channel E such that A=EB. When such a channel E exists, we can globally compare A and B in terms of their `noisiness'. We show that this method of channel noise comparison is equivalent to one obtained by considering the degradation of the distinguishability of states. Here, the channel A is said to be at least as…
Boosting State Discrimination in Quantum Brownian Motion Channel via Memory-Induced Coherence Preservation
研究在量子布朗运动通道中利用初始热噪声提升连续变量态辨别能力，通过结合压缩诱导相干性保持机制，降低态辨别错误概率，正交零差检测接近最优性能，为高温量子通信提供稳健架构。
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 show how to optimally discriminate between K distinct quantum states, of which N copies are available, using one-at-a-time interactions with each of the N copies. While this task (famously) requires joint measurements on all N copies, we show that it can be solved with one-at-a-time "coherent measurements" performed by an apparatus with log(K) qubits of quantum memory. We apply the same technique to optimal discrimination between K distinct N-particle matrix product states of bond dimension D, using a coherent measurement apparatus with log(K) + log(D) qubits of memory.
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。
We formulate minimum-error and unambiguous discrimination problems for quantum processes in the language of process positive operator valued measures (PPOVM). In this framework we present the known solution for minimum-error discrimination of unitary channels. We derive a "fidelity-like" lower bound on the failure probability of the unambiguous discrimination of arbitrary quantum processes. This bound is saturated (in a certain range of apriori probabilities) in the case of unambiguous discrimination of unitary channels. Surprisingly, the optimal solution for both tasks is based on the optimiz…
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 …
Entanglement in quantum channel discrimination: sometimes less is more
研究纠缠在量子信道区分中的作用，发现过度纠缠会显著降低区分能力，并引入最大纠缠最坏情况（MEWC）和最佳情况（MEBC）信道对的概念。
Many quantum mechanical experiments can be viewed as multi-round interactive protocols between known quantum circuits and an unknown quantum process. Fully quantum "coherent" access to the unknown process is known to provide an advantage in many discrimination tasks compared to when only incoherent access is permitted, but it is unclear if this advantage persists when the process is noisy. Here, we show that a quantum advantage can be maintained when distinguishing between two noisy single qubit rotation channels. Numerical and analytical calculations reveal a distinct transition between optim…
We address binary phase-shift-keyed communication channels based on Gaussian states and prove that squeezing improves state discrimination at fixed energy of the channel, also in the presence of phase diffusion. We then assess performances of homodyne detection against the ultimate quantum limits to discrimination, and show that homodyning achieves optimality in large noise regime. Finally, we consider noise in the preparation of the seed signal (before phase encoding) and show that also in this case squeezing may improve state discrimination in realistic conditions.
Characterising memory in quantum channel discrimination via constrained separability problems
本文通过受限分离性问题研究量子通道判别中记忆的作用，揭示了经典与量子记忆在自适应通道判别协议中的层次关系。
Enhancing Quantum State Discrimination with Indefinite Causal Order
针对未知有噪信道下的量子态辨识问题，提出基于不定因果序的量子开关及其高阶泛化超开关协议，显著提升了特定信道与系综的猜测概率。
In this work we study the problem of single-shot discrimination of von Neumann measurements, which we associate with measure-and-prepare channels. There are two possible approaches to this problem. The first one is simple and does not utilize entanglement. We focus only on the discrimination of classical probability distributions, which are outputs of the channels. We find necessary and sufficient criterion for perfect discrimination in this case. A more advanced approach requires the usage of entanglement. We quantify the distance between two measurements in terms of the diamond norm (called …
In this paper, we address the problem of discriminating two given quantum operations. Firstly, based on the Bloch representation of single qubit systems, we give the exact minimum error probability of discriminating two single qubit quantum operations by unentangled input states. In particular, for the Pauli channels discussed in [Phys. Rev. A {\bf 71}, 062340 (2005)], we use a more intuitional and visual method to deal with their discrimination problem. Secondly, we consider the condition for perfect discrimination of two quantum operations. Specially, we get that two generalized Pauli channe…
Limits for molecular spectroscopy from quantum channel discrimination
本研究将分子吸收光谱学的基本极限建模为量子信道判别问题，通过半定规划优化探针态，证明非经典探针在随机损耗下仍显著优于传统激光光谱，并为多频率光子分配提供额外优势。
It is well known that for the discrimination of classical and quantum channels in the finite, non-asymptotic regime, adaptive strategies can give an advantage over non-adaptive strategies. However, Hayashi [IEEE Trans. Inf. Theory 55(8), 3807 (2009)] showed that in the asymptotic regime, the exponential error rate for the discrimination of classical channels is not improved in the adaptive setting. We extend this result in several ways. First, we establish the strong Stein's lemma for classical-quantum channels by showing that asymptotically the exponential error rate for classical-quantum cha…
This paper introduces coherent quantum channel discrimination as a coherent version of conventional quantum channel discrimination. Coherent channel discrimination is phrased here as a quantum interactive proof system between a verifier and a prover, wherein the goal of the prover is to distinguish two channels called in superposition in order to distill a Bell state at the end. The key measure considered here is the success probability of distilling a Bell state, and I prove that this success probability does not increase under the action of a quantum superchannel, thus establishing this meas…
This expository article gives an overview of the theory of hypothesis testing of quantum states in finite dimensional Hilbert spaces. Optimal measurement strategy for testing binary quantum hypotheses, which result in minimum error probability, is discussed. Collective and individual adaptive measurement strategies in testing hypotheses in the multiple copy scenario, with various upper and lower bounds on error probability, are outlined. A brief account on quantum channel discrimination and the role of entangled states in achieving enhanced precision in the task of channel discrimination is gi…
Fast quantum state discrimination with nonlinear PTP channels
本文研究基于确定性正迹保持信道的非线性量子计算模型，在量子比特情形下利用耗散诱导分岔产生吸引不动点，构建内禀容错的非线性量子态鉴别器，实现鲁棒且可能指数加速的量子态区分。
Composite Classical and Quantum Channel Discrimination
研究非对称设定下二元复合信道判别问题，证明了量子信道并行与自适应策略的Stein指数界限，发现经典信道中自适应策略在非凸假设下具有优势，并推广了复合态判别结果。
We address the problem of discriminating with minimal error probability two given quantum operations. We show that the use of entangled input states generally improves the discrimination. For Pauli channels we provide a complete comparison of the optimal strategies where either entangled or unentangled input states are used.
Towards the ultimate limits of quantum channel discrimination and quantum communication
本研究推进了量子信道判别及其基本极限的理解，开发了量子散度新工具，建立无记忆信道判别的量子Stein引理，证明相干与顺序策略下指数强逆性质等价，并揭示信道容量与信道散度数学结构的深刻联系。
The optimal exponential error rate for adaptive discrimination of two channels is discussed. In this problem, adaptive choice of input signal is allowed. This problem is discussed in various settings. It is proved that adaptive choice does not improve the exponential error rate in these settings. These results are applied to quantum state discrimination.
Experimental quantum channel discrimination using metastable states of a trapped ion
本研究利用单个囚禁$^{40}\ ext{Ca}^{+}$离子的6维$\ ext{D}_{5/2}$亚稳态空间，实现了三种经典通信编码对应量子信道的非歧义单次区分，准确率超99%，突破了经典重复查询方式的局限。
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。
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