Kieran Hunter
We have investigated the problem of discriminating between nonorthogonal quantum states with least probability of error. We have determined that the best strategy for some sets of states is to make no measurement at all, and simply to always assign the most commonly occurring state. Conditions which describe such sets of states have been derived.
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It is well known that a minimum error quantum measurement for arbitrary binary optical coherent states can be realized by a receiver that comprises interfering with a coherent reference light, photon counting, and feedback control. We show that, for ternary optical coherent states, a minimum error measurement cannot always be realized by such a receiver. The problem of finding an upper bound on the maximum success probability of such a receiver can be formulated as a convex programming. We derive its dual problem and numerically find the upper bound. At least for ternary phase-shift keyed cohe…
Recently, the problem of discriminating multipartite unitary operations by local operations and classical communication (LOCC) has attracted significant attention. The latest work in the literature on this problem showed that two multipartite unitary operations can always be perfectly distinguished by LOCC when a finite number of runs are allowable. However, in these schemes, local entanglement (an entangled state holden by one party) was required, which seems to imply that local entanglement is necessary for perfect discrimination between unitary operations by LOCC. In this article, we show t…
We address the problem of unambiguous discrimination and identification among quantum observables. We set a general framework and investigate in details the case of qubit observables. In particular, we show that perfect discrimination with two shots is possible only for sharp qubit observables (e.g. Stern-Gerlach apparatuses) associated with mutually orthogonal directions. We also show that for sharp qubit observables associated to nonorthogonal directions unambiguous discrimination with an inconclusive result is always possible.
Factorizability of optimal quantum sequence discrimination under maximum-confidence measurements
该研究证明在最大置信度测量下，最优量子序列鉴别可分解为对每个单独状态的鉴别，并给出了最优量子态鉴别的必要条件。
Steering is the entanglement-based quantum effect that embodies the "spooky action at a distance" disliked by Einstein and scrutinized by Einstein, Podolsky, and Rosen. Here we provide a necessary and sufficient characterization of steering, based on a quantum information processing task: the discrimination of branches in a quantum evolution, which we dub subchannel discrimination. We prove that, for any bipartite steerable state, there are instances of the quantum subchannel discrimination problem for which this state allows a correct discrimination with strictly higher probability than in ab…
We consider the optimal discrimination of nonorthogonal qubit states with post-measurement information and provide an analytic structure of the optimal measurements. We also show that there is always a null optimal measurement when post-measurement information is given. Further, in discriminating four states using post-measurement information, we analytically provide the optimal probability of correct guessing and show that the uniqueness of optimal measurement is equivalent to the non-existence of non-null optimal measurement with post-measurement information.
We study an optimum measurement for quantum state discrimination, which maximizes the probability of correct results when the probability of inconclusive results is fixed at a given value. The measurement describes minimum-error discrimination if this value is zero, while under certain conditions it corresponds to optimized maximum-confidence discrimination, or to optimum unambiguous discrimination, respectively, when the fixed value reaches a definite minimum. Using operator conditions that determine the optimum measurement, we derive analytical solutions for the discrimination of two mixed q…
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…
We consider the problem of unambiguous (error-free) discrimination of N linearly independent pure quantum states with prior probabilities, where the goal is to find a measurement that maximizes the average probability of success. We derive an upper bound on the optimal average probability of success using a result on optimal local conversion between two bipartite pure states. We prove that an optimal measurement in general saturates our bound. In the exceptional cases we show that the bound is tight, but not always optimal.
One of the central problems in the study of quantum resource theories is to provide a given resource with an operational meaning, characterizing physical tasks in which the resource can give an explicit advantage over all resourceless states. We show that this can always be accomplished for all convex resource theories. We establish in particular that any resource state enables an advantage in a channel discrimination task, allowing for a strictly greater success probability than any state without the given resource. Furthermore, we find that the generalized robustness measure serves as an exa…
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…
Quantum coherence and entanglement orignate from the superposition principle. We derive a rigorous relation between the ${l_1}$-norm of coherence and concurrence, in that we show that the former is always greater than the latter. This result highlights the hierarchical relationship between coherence and concurrence, and proves coherence to be a fundamental and ubiquitous resource. We derive an analogous form of monogamy inequality which is based on the partial coherence of the reduced two-qubit and reduced single qubit of the particular class of three-qubit state. Moreover, we provide coherenc…
An unknown unitary gates, which is secretly chosen from several known ones, can always be distinguished perfectly. In this paper, we implement such a task on IBM's quantum processor. More precisely, we experimentally demonstrate the discrimination of two qubit unitary gates, the identity gate and the $\frac{2}{3}π$-phase shift gate, using two discrimination schemes -- the parallel scheme and the sequential scheme. We program these two schemes on the \emph{ibmqx4}, a $5$-qubit superconducting quantum processor via IBM cloud, with the help of the $QSI$ modules [S. Liu et al.,~arXiv:1710.09500, 2…
Trade-off between Information Gain and Disturbance in Local Discrimination of Entangled Quantum States
本文建立了局域态判别中信息增益与扰动的权衡关系，指出纠缠度越高局域判别越难，并提出基于稳定子形式的自适应非破坏性策略以降低预共享纠缠代价，同时应用于鲁棒的纠缠认证协议。
We introduce the concept of boundariness capturing the most efficient way of expressing a given element of a convex set as a probability mixture of its boundary elements. In other words, this number measures (without the need of any explicit topology) how far the given element is from the boundary. It is shown that one of the elements from the boundary can be always chosen to be an extremal element. We focus on evaluation of this quantity for quantum sets of states, channels and observables. We show that boundariness is intimately related to (semi)norms that provide an operational interpretati…
Local simultaneous state discrimination
本研究提出量子态区分新变体局部同时态区分（LSSD），刻画其性质并证明三方经典LSSD最优策略求解为NP难。
Quantum correlations and entanglement are fundamental resources for quantum information and quantum communication processes. Developments in these fields normally assume these resources stable and not susceptible of distortion. That is not always the case, Heisenberg interactions between qubits can produce distortion on entangled pairs generated for engineering purposes (e. g. for quantum computation or quantum cryptography). Experimental work shows how to produce entangled spin qubits in quantum dots and electron gases, so its identification and control are crucial for later applications. The…
Absorption-free (also known as ``interaction-free'') measurement aims to detect the presence of an opaque object using a test particle without that particle being absorbed by the object. Here we consider semi-transparent objects which have an amplitude $α$ of transmitting a particle while leaving the state of the object unchanged and an amplitude $β$ of absorbing the particle. The task is to devise a protocol that can decide which of two known transmission amplitudes is present while ensuring that no particle interacts with the object. We show that the probabilities of being able to achieve th…
Local approximation for perfect discrimination of quantum states
本文推导了渐近 LOCC 区分正交纯态误差概率的下界，证明了完美区分的必要条件，并据此证明部分极小 UPB 无法被完美区分，揭示了无纠缠强非局域性。
We demonstrate that quantum incompatibility can always be detected by means of a state discrimination task with partial intermediate information. This is done by showing that only incompatible measurements allow for an efficient use of premeasurement information in order to improve the probability of guessing the correct state. Thus, the gap between the guessing probabilities with pre- and postmeasurement information is a witness of the incompatibility of a given collection of measurements. We prove that all linear incompatibility witnesses can be implemented as some state discrimination proto…
Polynomial Separation between One-Way and Two-Way LOCC in Discrimination of Maximally Entangled States
该研究证明在最大纠缠态判别中，通过单次反馈的双向LOCC可将可区分候选态数量从常数提升至多项式级，实现单向与双向LOCC的分离，并给出九份拷贝的充分性结论。
We provide a feasible necessary and sufficient condition for when an unknown quantum operation (quantum device) secretely selected from a set of known quantum operations can be identified perfectly within a finite number of queries, and thus complete the characterization of the perfect distinguishability of quantum operations. We further design an optimal protocol which can achieve the perfect discrimination between two quantum operations by a minimal number of queries. Interestingly, employing the techniques from the theory of $q$-numerical range we find that an optimal perfect discrimination…
Optimal Discrimination of Mixed Symmetric Multi-mode Coherent States
本文研究区分对称多模相位随机化相干态的最优测量方法，发现可通过先计数总光子数再在子空间进行平方根测量来实现，并在部分情况下给出了线性光学电路实现方案。
Suppose that a system is known to be in one of two quantum states, $|ψ_1 > $ or $|ψ_2 >$. If these states are not orthogonal, then in conventional quantum mechanics it is impossible with one measurement to determine with certainty which state the system is in. However, because a non-Hermitian PT-symmetric Hamiltonian determines the inner product that is appropriate for the Hilbert space of physical states, it is always possible to choose this inner product so that the two states $|ψ_1 > $ and $|ψ_2 > $ are orthogonal. Thus, quantum state discrimination can, in principle, be achieved with a sin…
Information recycling in coherent state discrimination
针对连续变量量子通信中的相干态识别问题，提出信息回收（IR）策略，通过顺序最小错误识别（MED）回收无歧义识别（UD）的失败态，实现兼顾确定性与无错误子集的最优识别，为长距离CV-QKD接收器设计提供新思路。
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination problems in general probabilistic theories using a Bayesian strategy. After re-formulation of the theories with mathematical rigor, we first prove that an optimal observable to discriminate any (finite) number of states always exists in the most general setting. Next, we revisit our recently proposed geometric approach for the problem and show that, for two-s…
Minimal-error quantum state discrimination versus robustness of entanglement:More indistinguishability with less entanglement
本文研究了量子态鉴别与纠缠鲁棒性之间的关系，发现更少纠缠可带来更多不可区分性，并通过数值实验验证了相关边界条件。
Resource Theory of Imaginarity: New Distributed Scenarios
本文研究了分布式场景下虚部的提纯与转换，给出一般量子比特态和任意维度纯态的精确解，提出无需辅助系统的量子信道判别场景，并通过实验验证了虚部在信道判别与LOCC判别任务中的操作优势。
Discrimination of quantum states under locality constraints in the many-copy setting
研究多拷贝场景下受限局部测量的正交量子态假设检验，证明了LOCC操作下错误概率的指数衰减，给出了LOCC与PPT操作等效的充分条件，并揭示了SEP与PPT操作间的无限渐近分离。
We investigate the unambiguous comparison of quantum states in a scenario that is more general than the one that was originally suggested by Barnett et al. First, we find the optimal solution for the comparison of two states taken from a set of two pure states with arbitrary a priori probabilities. We show that the optimal coherent measurement is always superior to the optimal incoherent measurement. Second, we develop a strategy for the comparison of two states from a set of N pure states, and find an optimal solution for some parameter range when N=3. In both cases we use the reduction metho…
We address the issue of the discrimination between two-qubit amplitude damping channels by exploring several strategies. For the single-shot, we show that the excited state does not always give the optimal input, and that side entanglement assistance has limited benefit. On the contrary, feedback assistance from the environment is more beneficial. For the two-shot, we prove the in-utility of entangled inputs. Then focusing on individual (local) measurements, we find the optimal adaptive strategy.
We investigate the ability of a quantum measurement device to discriminate two states or, generically, two hypothesis. In full generality, the measurement can be performed a number $n$ of times, and arbitrary pre-processing of the states and post-processing of the obtained data is allowed. Even if the two hypothesis correspond to orthogonal states, perfect discrimination is not always possible. There is thus an intrinsic error associated to the measurement device, which we aim to quantify, that limits its discrimination power. We minimize various error probabilities (averaged or constrained) o…
Every quantum helps: Operational advantage of quantum resources beyond convexity
该研究解决了非凸量子资源的有用性问题，通过为广义鲁棒性度量提供两种操作解释，证明在一般资源理论中任何量子资源态在信道判别任务中均具有定性和定量的优势。
The present work is devoted to the development of a method for high-precision tomography of ion qubit registers under conditions of limited distinguishability of the states of a logical value 0 and a logical value 1. In the considered ion qubits, the identification of the quantum state is achieved by measuring the fluorescence of the ion by repeated excitation of the cyclic transition, which includes only the lower energy state that sets a logical value 0 and becomes bright, but does not include the upper metastable state that remains dark and sets logical value 1. It is important to note that…
In this paper, we consider the orthogonal product set (OPS) with strong quantum nonlocality. Based on the decomposition of plane geometry, we present a sufficient condition for the triviality of orthogonality-preserving POVM on fixed subsystem and partially answer an open question given by Yuan et al. Phys. Rev. A \textbf{102}, 042228 (2020)}. The connection between the nonlocality and the plane structure of OPS is established. We successfully construct a strongly nonlocal OPS in $\mathcal{C}^{d_{A}}\otimes \mathcal{C}^{d_{B}}\otimes \mathcal{C}^{d_{C}}$ $(d_{A,B,C}\geq 4)$, which contains few…
We investigated the super quantum discord based on weak measurements. The super quantum discord is an extension of the standard quantum discord defined by projective measurements and also describes the quantumness of correlations. We provide some equivalent conditions for zero super quantum discord by using quantum discord, classical correlation and mutual information. In particular, we find that the super quantum discord is zero only for product states, which have zero mutual information. This result suggests that non-zero correlations can always be detected using the quantum correlation with…
Attainability of quantum state discrimination bounds with collective measurements on finite copies
本文研究了有限副本联合测量下量子态判别界的可达性，推导了简单 qubit 例子中任意副本的 Helstrom 界解析式，并证明在许多情形下对所有 M 副本进行联合测量是饱和该界的必要条件。
Minimum error state discrimination between two mixed states ρand σcan be aided by the receipt of "classical side information" specifying which states from some convex decompositions of ρand σapply in each run. We quantify this phenomena by the average trace distance, and give lower and upper bounds on this quantity as functions of ρand σ. The lower bound is simply the trace distance between ρand σ, trivially seen to be tight. The upper bound is \sqrt{1 - tr(ρσ)}, and we conjecture that this is also tight. We reformulate this conjecture in terms of the existence of a pair of "unbiased decomposi…
For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resource measurement offers advantage for some quantum state discrimination task. Moreover, we give an operational interpretation of robustness, which quantifies the minimal amount of noise that must be added to a measurement to make it free. Specifically, …
Unconditionally superposition-robust entangled state in all multiparty quantum systems
本研究发现任意多体希尔伯特空间中存在无条件叠加鲁棒纠缠态，完善了多体系统叠加不可分性研究，揭示了多体与两体量子系统的差异，并展示了其在局域无歧义态鉴别中的应用。
We consider the multiple hypothesis testing problem for symmetric quantum state discrimination between r given states σ_1,...,σ_r. By splitting up the overall test into multiple binary tests in various ways we obtain a number of upper bounds on the optimal error probability in terms of the binary error probabilities. These upper bounds allow us to deduce various bounds on the asymptotic error rate, for which it has been hypothesised that it is given by the multi-hypothesis quantum Chernoff bound (or Chernoff divergence) C(σ_1,...,σ_r), as recently introduced by Nussbaum and Szkoła in analogy w…
In wireless systems there is always a trade-off between reducing the transmit power and mitigating the resultant signal-degradation imposed by the transmit-power reduction with the aid of sophisticated receiver algorithms, when considering the total energy consumption. Quantum-assisted wireless communications exploits the extra computing power offered by quantum mechanics based architectures. This paper summarizes some recent results in quantum computing and the corresponding application areas in wireless communications.
In classical and single-particle settings, non-trivial band topology always gives rise to robust boundary modes. For quantum many-body systems, however, multiple topological fermions are not always able to coexist, since Pauli exclusion prevents additional fermions from occupying the limited number of available topological modes. In this work, we show, through IBM quantum computers, how one can robustly stabilize more fermions than the number of topological modes through specially designed 2-fermion interactions. Our demonstration hinges on the realization of BDI- and D-class topological Hamil…
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