M. Piani, J. Watrous
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.
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Strategies to optimally discriminate between quantum states are critical in quantum technologies. We present an experimental demonstration of minimum error discrimination between entangled states, encoded in the polarization of pairs of photons. Although the optimal measurement involves projecting onto entangled states, we use a result of Walgate et al. to design an optical implementation employing only local polarization measurements and feed-forward, which performs at the Helstrom bound. Our scheme can achieve perfect discrimination of orthogonal states and minimum error discrimination of no…
We consider the problem of discriminating among a set of unitaries by means of measurements performed on the state undergoing the transformation. We show that use of entangled probes improves the discrimination in the two following cases: i) for a set of unitaries that are the UIR of a group and, ii) for any pair of transformations provided that multiple uses of the channel are allowed.
"Quantum conversation" is a way in which two parties can communicate classical information with each other using entanglement as a shared resource. We present this scheme using a multipartite entangled state after describing its generation through appropriate circuit diagrams. We make use of a discrimination scheme which allows one to perform a measurement on the system without destroying its entanglement. We later prove that this scheme is secure in a noiseless and a lossless quantum channel.
Distinguishing physical processes is one of the fundamental problems in quantum physics. Although distinguishability of quantum preparations and quantum channels have been studied considerably, distinguishability of quantum measurements remains largely unexplored. We investigate the problem of single-shot discrimination of quantum measurements using two strategies, one based on single quantum systems and the other one based on entangled quantum systems. First, we formally define both scenarios. We then construct sets of measurements (including non-projective) in arbitrary finite dimensions tha…
The so-called quasi-Bell entangled coherent states in a thermal environment are studied. In the analysis, we assume thermal noise affects only one of the two modes of each state. First the matrix representation of the density operators of the quasi-Bell entangled coherent states in a thermal environment is derived. Secondly we investigate the entanglement property of one of the quasi-Bell entangled coherent states with thermal noise. At that time a lower bound of the entanglement of formation for the state is computed. Thirdly the minimax discrimination problem for two cases of the binary set …
We consider one copy of a quantum system prepared with equal prior probability in one of two non-orthogonal entangled states of multipartite distributed among separated parties. We demonstrate that these two states can be optimally distinguished in the sense of conclusive discrimination by local operations and classical communications(LOCC) alone. And this proves strictly the conjecture that Virmani et.al. [8] confirmed numerically and analytically. Generally, the optimal protocol requires local POVM operations which are explicitly constructed. The result manifests that the distinguishable inf…
We analyze entanglement swapping (ES) of partially entangled pure states with arbitrary Schmidt rank from the perspective of quantum state discrimination. It is shown that the standard deterministic ES protocol is related with an optimal minimum-error strategy. In this case the amount of entanglement of the states resulting from swapping is, in general, lower than the maximum achievable for the quantum channels involved. In this regard, we show that the ES protocol can be probabilistically improved resorting to optimal maximum-confidence (MC) discrimination strategy. Additionally, we show that…
How can one discriminate different inequivalent classes of multiparticle entanglement experimentally? We present an approach for the discrimination of an experimentally prepared state from the equivalence class of another state. We consider two possible measures for the discrimination strength of an observable. The first measure is based on the difference of expectation values, the second on the relative entropy of the probability distributions of the measurement outcomes. The interpretation of these measures and their usefulness for experiments with limited resources are discussed. In the cas…
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…
Measurement-based quantum computation (MQC) is a leading paradigm for building a quantum computer. Cluster states being used in this context act as one-way quantum computers. Here, we consider Z-states as a type of highly entangled states like cluster states, which can be used for one-way or measurement based quantum computation. We define Z-state basis as a set of orthonormal states which are as equally entangled as the cluster states. We design new quantum circuits to non-destructively discriminate these highly entangled Z-states. The proposed quantum circuits can be generalized for N-qubit …
We show that there exist sets of three mutually orthogonal $d$-dimensional maximally entangled states which cannot be perfectly distinguished using one-way local operations and classical communication (LOCC) for arbitrarily large values of $d$. This contrasts with several well-known families of maximally entangled states, for which any three states can be perfectly distinguished. We then show that two-way LOCC is sufficient to distinguish these examples. We also show that any three mutually orthogonal $d$-dimensional maximally entangled states can be perfectly distinguished using measurements …
We show that entanglement guarantees difficulty in the discrimination of orthogonal multipartite states locally. The number of pure states that can be discriminated by local operations and classical communication is bounded by the total dimension over the average entanglement. A similar, general condition is also shown for pure and mixed states. These results offer a rare operational interpretation for three abstractly defined distance like measures of multipartite entanglement.
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.
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…
In the quantum system, perfect copying is impossible without prior knowledge. But, perfect copying is possible, if it is known that unknown states to be copied is contained by the set of orthogonal states, which is called the copied set. However, if our operation is limited to local operations and classical communications, this problem is not trivial. Recently, F. Anselmi, A. Chefles and M.B. Plenio constructed theory of local copying when the copied set consists of maximally entangled states. They also classified the copied set when it consists of two orthogonal states (New. J. Phys. 6, 164 (…
We study discrimination of m quantum measurements in the scenario when the unknown measurement with n outcomes can be used only once. We show that ancilla-assisted discrimination procedures provide a nontrivial advantage over simple (ancilla-free) schemes for perfect distinguishability and we prove that inevitably m <= n. We derive necessary and sufficient conditions of perfect distinguishability of general binary measurements. We show that the optimization of the discrimination of projective qubit measurements and their mixtures with white noise is equivalent to the discrimination of specific…
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 explore the question of using an entangled state as a universal resource for implementing quantum measurements by local operations and classical communication (LOCC). We show that for most systems consisting of three or more subsystems, there is no entangled state from the same space that can enable all measurements by LOCC. This is in direct contrast to the bipartite case, where a maximally entangled state is an universal resource. Our results are obtained showing an equivalence between the problem of local state transformation and that of entanglement-assisted local unambiguous state disc…
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。
It is shown that while entanglement remains a significant factor in discriminating a set of mutually orthogonal entangled states perfectly by local operations and classical communication (LOCC), entanglement content is not. In particular, for a class of entangled multi-qubit states, the maximum number of perfectly LOCC distinguishable orthogonal states is shown to be independent of the average entanglement of the states, and the spatial configuration with respect to which LOCC operations may be carried out. It is also pointed out that the make-up of an ensemble, that is, whether it consists on…
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…
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。
Global restrictions under local state discrimination
该研究探讨局域态区分对双体量子态全局性质的限制，发现CHSH违背与局域区分成功率的权衡关系，并将其扩展到定界最大纠缠态保真度等全局量，为量子密码学中限制纠缠对手等场景提供工具。
The propagation of macroscopic entangled states over large distances in the presence of loss is of fundamental interest and may have practical applications as well. Here we describe two different techniques in which state discrimination can be used to violate Bell's inequality with macroscopic phase-entangled coherent states. We find that Bell's inequality can be violated by these macroscopic states over a distance of approximately 400 km in commercially-available optical fibers.
In this work, we study the local distinguishability of maximally entangled states (MESs). In particular, we are concerned with whether any fixed number of MESs can be locally distinguishable for sufficiently large dimensions. Fan and Tian \emph{et al.} have already obtained two satisfactory results for the generalized Bell states (GBSs) and the qudit lattice states when applied to prime or prime power dimensions. We construct a general twist-teleportation scheme for any orthonormal basis with MESs that is inspired by the method used in [Phys. Rev. A \textbf{70}, 022304 (2004)]. Using this tele…
Local discrimination of orbital angular momentum in entangled states
本文提出利用方解石晶体及受控空间位移对局域判别参量下转换量子辐射的轨道角动量，并指出其在长距离量子通信中的应用潜力。
We demonstrate how to discriminate two non-orthogonal, entangled quantum state which are slightly different from each other by using pseudo-Hermitian system. The positive definite metric operator which makes the pseudo-Hermitian systems fully consistent quantum theory is used for such a state discrimination. We further show that non-orthogonal states can evolve through a suitably constructed pseudo-Hermitian Hamiltonian to orthogonal states. Such evolution ceases at exceptional points of the pseudo-Hermitian system.
Entanglement of minimal dimension and a class of local state discrimination problems
本文构造了无法通过LOCC完美鉴别的小规模双派正交纯态集，证明最小维度纠缠态可提升鉴别能力，且此类态集在任意两量子比特希尔伯特空间中均存在。
A bipartite state which is secretly chosen from a finite set of known entangled pure states cannot be immediately useful in standard quantum information processing tasks. To effectively make use of the entanglement contained in this unknown state, we introduce a new way to locally manipulate the original quantum system: either identify the state successfully or distill some pure entanglement. Remarkably, if many copies are available, we show that any finite set of entangled pure states, whatever orthogonal or not, can be locally distinguished in this way, which further implies that pure entang…
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.
Recently, the nonlocal optimal probabilistic cloning (NLOPC) of two non-orthogonal qubit states has been proposed [Phys. Rev. A 86, 052332 (2012)] by means of an experimental setup based on a pair of twin photons in a maximally entangled state. Here we study the performance of the NLOPC protocol when implemented via a partially entangled state. We show that the errors introduced by the use of partial entanglement can be undone by applying a quantum state discrimination process. Since quantum state discrimination is a probabilistic process the correction succeeds with a certain probability but …
We study the problem of locally distinguishing pure quantum states using shared entanglement as a resource. For a given set of locally indistinguishable states, we define a resource state to be useful if it can enhance local distinguishability and optimal if it can distinguish the states as well as global measurements and is also minimal with respect to a partial ordering defined by entanglement and dimension. We present examples of useful resources and show that an entangled state need not be useful for distinguishing a given set of states. We obtain optimal resources with explicit local prot…
Efficient discrimination schemes for unextendible product bases with strong quantum nonlocality
本文提出三种高效区分具有强量子非局域性的不可扩展产物基的方案，利用最大化纠缠态减少资源消耗。
Dilution of Entanglement: Unveiling Quantum State Discrimination Advantages
本文研究三量子比特GHZ SLOCC类中纠缠模式对态区分的影响，提出利用非最大纠缠态实现正交乘积态完美区分的方法，并揭示纠缠分类与非局域性的深层联系。
Single shot distinguishability of noisy quantum channels
研究单次鉴别噪声量子通道，分析单系统与纠缠探针在不同噪声下的最优性能及作用
Walgate and Scott have determined the maximum number of generic pure quantum states that can be unambiguously discriminated by an LOCC measurement [Journal of Physics A: Mathematical and Theoretical, 41:375305, 08 2008]. In this work, we determine this number in a more general setting in which the local parties have access to pre-shared entanglement in the form of a resource state. We find that, for an arbitrary pure resource state, this number is equal to the Krull dimension of (the closure of) the set of pure states obtainable from the resource state by SLOCC. Surprisingly, a generic resourc…
Entangled states can help in quantum state discrimination by local operations and classical communication (LOCC). For example, a Bell state is necessary (and sufficient) to perfectly discriminate a set of either three or four Bell states by LOCC. In this paper, we consider the task of LOCC discrimination of the states of noisy Bell ensembles, where a given ensemble consists of the states obtained by mixing the Bell states with an arbitrary two-qubit state with nonzero probabilities. It is proved that a Bell state is required for optimal discrimination by LOCC, even though the ensembles do not …
The problem of quantum state discrimination, which is a foundational aspect of quantum information theory, and its relation to the theory of majorization are discussed. The purpose of this study is to review different approaches to the problem and analyze different cases of quantum-state discrimination, most importantly the discrimination of bipartite entangled quantum states under local operations and classical communication. Two partial results on using entanglement as a resource for quantum-state discrimination and discrimination with remaining entanglement is given. The important points ar…
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…
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…
Usefulness of $d\otimes d$ dimensional pure entangled states for antidiscrimination of quantum measurements when $d$ is even
针对量子信道反歧视问题，研究表明当d为偶数时，所有$\boldsymbol{C}^d\boxtimes\boldsymbol{C}^d$纯纠缠态均可用于反歧视特定三个投影测量，且该类纠缠态在反歧视中比乘积探针更有用。
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…
We consider the problem of local operations and classical communication (LOCC) discrimination between two bipartite pure states of fermionic systems. We show that, contrary to the case of quantum systems, for fermionic systems it is generally not possible to achieve the ideal state discrimination performances through LOCC measurements. On the other hand, we show that an ancillary system made of two fermionic modes in a maximally entangled state is a sufficient additional resource to attain the ideal performances via LOCC measurements. The stability of the ideal results is studied when the prob…
We consider a general version of the phenomenon of more nonlocality with less entanglement, within the framework of the unambiguous (i.e., conclusive) quantum state discrimination problem under local quantum operations and classical communication. We show that although the phenomenon was obtained before for two qutrits, it can also be observed for two qubits, while still being at the single-copy level. We establish that the phenomenon is intrinsically connected to the concept of unextendible entangled bases, in the two-qubit case. In the process, we demonstrate a hierarchy of nonlocality among…
The question whether all entangled states can be used as a nonclassical resource has remained open so far. Here we provide a conclusive answer to this problem for the case of systems shared by two parties. We show that any entangled state $σ$ can enhance the teleportation power of some other state. This holds even if the state $σ$ is bound entangled.
It has been recently shown (Bartlett et al. 2003) that information encoded into relative degrees of freedom enables communication without a common reference frame using entangled bipartite states. In this case the relative information stored in the two-qubit system is shared between the polarization degrees of freedom and the degree of entanglement. In the present article a specific state discrimination problem is envisioned where the degree of entanglement carries the only relative parameter, so that certain maximally entangled states are perfectly distinguishable, while discrimination of pro…
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…
Post-measurement states are (very) useful for measurement discrimination
本文提出通过利用测量后量子态来提升量子测量鉴别的性能，证明其在某些情况下可显著提高鉴别能力。
Nondestructive discrimination of Bell states between distant parties
本文提出利用预共享纠缠资源对远距离各方持有的贝尔态进行无损区分的方案，证明无辅助资源时成功概率上限为1/4，并在IonQ量子计算机上验证其可超越经典界限。
We develop a concept of metasurface-assisted ghost imaging for non-local discrimination between a set of polarization objects. The specially designed metasurfaces are incorporated in the imaging system to perform parallel state transformations in general elliptical bases of quantum-entangled or classically-correlated photons. Then, only four or fewer correlation measurements between multiple metasurface outputs and a simple polarization-insensitive bucket detector after the object can allow for the identification of fully or partially transparent polarization elements and their arbitrary orien…
Employing the general BXOR operation and local state discrimination, the mixed state of the form ρ^{(k)}_{d}=\frac{1}{d^{2}}\sum_{m,n=0}^{d-1}(|ϕ_{mn}><ϕ_{mn}|)^{\otim es k} is proved to be quasi-pure, where $\{|ϕ_{mn}>\}$ is the canonical set of mutually orthogonal maximally entangled states in $d\times d$. Therefore irreversibility does not occur in the process of distillation for this family of states. Also, the distillable entanglement is calculated explicitly.
In quantum state discrimination, the observers are given a quantum system and aim to verify its state from the two or more possible target states. In the local quantum state marking as an extension of quantum state discrimination, there are N composite quantum systems and N possible orthogonal target quantum states. Distant Alice and Bob are asked to correctly mark the states of the given quantum systems via local operations and classical communication. Here we investigate the local state marking with N 4 ${\otimes}$ 4 systems, N=4, 5, 6, and 7. Therein, Alice and Bob allow for three local ope…
It is well known that one can extract all the information of an unknown quantum channel by means of quantum process tomography, such as standard quantum-process tomography and ancilla-assisted quantum process tomography (AAQPT). Furthermore, it has been shown that entanglement is not necessary for AAQPT, there exist separable states which are also useful for it. Surprisingly, in this work we find that not all entangled states are useful for AAQPT, there also exist some entangled states which are useless. The realignment operation used in entanglement detection can be related to the question wh…
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…
Quantum hypothesis testing has been greatly advanced for the binary discrimination of two states, or two channels. In this setting, we already know that quantum entanglement can be used to enhance the discrimination of two bosonic channels. Here, we remove the restriction of binary hypotheses and show that entangled photons can remarkably boost the discrimination of multiple bosonic channels. More precisely, we formulate a general problem of channel-position finding where the goal is to determine the position of a target channel among many background channels. We prove that, using entangled ph…
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.
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。
The dynamics of a general two qubits system in noninetrial frame is investigated analytically, where it is assumed that both of its subsystems are differently accelerated. Two classes of initial travelling states are considered:self transposed and a generic pure states. The entanglement contained in all possible generated entangled channels between the qubits and their Anti-qubits is quantified. The usefulness of the travelling channels as quantum channels to perform quantum teleportation is investigated. For the self transposed classes, we show that the generalized Werner state is the most ro…
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…
Inequivalent Quantum Resources from Multipartite State Discrimination
本文研究多体正交态对的局域判别资源消耗，发现不同态对需不等量量子资源，并揭示纠缠消耗的层级结构，表明LOCC判别代价依赖态本身。
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