We consider the problem of quantum state certification, where one is given $n$ copies of an unknown $d$-dimensional quantum mixed state $ρ$, and one wants to test whether $ρ$ is equal to some known mixed state $σ$ or else is $ε$-far from $σ$. The goal is to use notably fewer copies than the $Ω(d^2)$ needed for full tomography on $ρ$ (i.e., density estimation). We give two robust state certification algorithms: one with respect to fidelity using $n = O(d/ε)$ copies, and one with respect to trace distance using $n = O(d/ε^2)$ copies. The latter algorithm also applies when $σ$ is unknown as well. These copy complexities are optimal up to constant factors.
We demonstrate to what extent many copies of maximally entangled two-qubit states enable for generating a greater amount of certified randomness than that can be certified from a single copy. Although it appears that greater the dimension of the system implies a higher amount of randomness, the non-triviality lies in the device-independent simultaneous certification of generated randomness from many copies of entangled states. This is because, most of the two-outcome Bell inequalities (viz., Clauser-Horne-Shimony-Holt, Elegant, or Chain Bell inequality) are optimized for a single copy of two-q…
We revisit the basic problem of quantum state certification: given copies of unknown mixed state $ρ\in\mathbb{C}^{d\times d}$ and the description of a mixed state $σ$, decide whether $σ= ρ$ or $\|σ- ρ\|_{\mathsf{tr}} \ge ε$. When $σ$ is maximally mixed, this is mixedness testing, and it is known that $Ω(d^{Θ(1)}/ε^2)$ copies are necessary, where the exact exponent depends on the type of measurements the learner can make [OW15, BCL20], and in many of these settings there is a matching upper bound [OW15, BOW19, BCL20]. Can one avoid this $d^{Θ(1)}$ dependence for certain kinds of mixed states $σ…
Self-testing protocols are methods to determine the presence of shared entangled states in a device independent scenario, where no assumptions on the measurements involved in the protocol are made. A particular type of self-testing protocol, called parallel self-testing, can certify the presence of copies of a state, however such protocols typically suffer from the problem of requiring a number of measurements that increases with respect to the number of copies one aims to certify. Here we propose a procedure to transform single-copy self-testing protocols into a procedure that certifies the t…
Authentication of quantum sources is a crucial task in building reliable and efficient protocols for quantum-information processing. Steady progress vis-à-vis verification of quantum devices in the scenario with fully characterized measurement devices has been observed in recent years. When it comes to the scenario with uncharacterized measurements, the so-called black-box scenario, practical verification methods are still rather scarce. Development of self-testing methods is an important step forward, but these results so far have been used for reliable verification only by considering the as…
We study efficient quantum certification algorithms for quantum state set and unitary quantum channel. We present an algorithm that uses $O(\varepsilon^{-4}\ln |\mathcal{P}|)$ copies of an unknown state to distinguish whether the unknown state is contained in or $\varepsilon$-far from a finite set $\mathcal{P}$ of known states with respect to the trace distance. This algorithm is more sample-efficient in some settings. Previous study showed that one can distinguish whether an unknown unitary $U$ is equal to or $\varepsilon$-far from a known or unknown unitary $V$ in fixed dimension with $O(\va…
We consider the problem of quantum state certification, where we are given the description of a mixed state $σ\in \mathbb{C}^{d \times d}$, $n$ copies of a mixed state $ρ\in \mathbb{C}^{d \times d}$, and $\varepsilon > 0$, and we are asked to determine whether $ρ= σ$ or whether $\| ρ- σ\|_1 > \varepsilon$. When $σ$ is the maximally mixed state $\frac{1}{d} I_d$, this is known as mixedness testing. We focus on algorithms which use incoherent measurements, i.e. which only measure one copy of $ρ$ at a time. Unlike those that use entangled, multi-copy measurements, these can be implemented without…
Certification of quantum devices received from unknown providers is a primary requirement before utilizing the devices for any information processing task. Here, we establish a protocol for certification of a particular set of $d$-outcome quantum measurements (with $d$ being arbitrary) in a setup comprising of a preparation followed by two measurements in sequence. We propose a set of temporal inequalities pertaining to different $d$ involving correlation functions corresponding to successive measurement outcomes, that are not satisfied by quantum devices. Using quantum violations of these ine…
The precise control of complex quantum systems promises numerous technological applications including digital quantum computing. The complexity of such devices renders the certification of their correct functioning a challenge. To address this challenge, numerous methods were developed in the last decade. In this tutorial, we explain prominent protocols for certifying the physical layer of quantum devices described by quantum states and processes. Such protocols are particularly important in the development of near-term devices. Specifically, we discuss methods of direct quantum state certific…
In this letter we consider the problem of certification of quantum measurements with an arbitrary number of outcomes. We propose a simple scheme for certifying any set of $d$-outcome projective measurements which do not share any common invariant proper subspace, termed here genuinely incompatible, and the maximally entangled state of two qudits. For our purpose, we focus on a simpler scenario, termed as one-sided device-independent scenario where the resource employed for certification is quantum steering. We also study robustness of our self-testing statements for a certain class of genuinel…
One of the requirements imposed on the realistic quantum computers is to provide computation results which can be repeated and reproduced. In the situation when one needs to repeat the quantum computation procedure several times, it is crucial that the copies of the quantum devices are similar in the sense of the produced results. In this work, we describe a simple procedure based on variational quantum eigensolver which can be utilized to compare quantum devices. The procedure is developed by combining Choi-Jamiołkowski isomorphism with the variational hybrid quantum-classical procedure for m…
Bosonic fault tolerant quantum computing requires preparations of Bosonic code states like cat states and GKP states with high fidelity and reliable quantum certification of these states. Although many proposals on preparing these states have been developed, few investigation has been done on how to reliably certify these experimental states. In this paper, we develop approaches to certify whether a continuous-variable state falls inside a certain Bosonic qubit code space by detecting a witness using Gaussian measurements. Our results can be applied to certification of various cat codes includ…
Certification of quantum properties with imperfect measurements
ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（光子科学研究所）；ICREA - Institució Catalana de Recerca i Estudis Avançats（加泰罗尼亚研究高级学院）；Physics Department E. Pancini - Università degli Studi di Napoli Federico II（那不勒斯费德里科二世大学）
Certification of quantum channels is based on quantum hypothesis testing and involves also preparation of an input state and choosing the final measurement. This work primarily focuses on the scenario when the false negative error cannot occur, even if it leads to the growth of the probability of false positive error. We establish a condition when it is possible to exclude false negative error after a finite number of queries to the quantum channel in parallel, and we provide an upper bound on the number of queries. On top of that, we found a class of channels which allow for excluding false n…
Quantum State Certification via Effective Parent Hamiltonians from Local Measurement Data
École de technologie supérieure, Université du Québec（魁北克大学高等技术学院）；Department of Electrical and Computer Engineering, McGill University（麦吉尔大学电气与计算机工程系）；QMill Oy（QMill公司）；Department of Mathematics, University of Toronto（多伦多大学数学系）；Escuela de Ingenieria y Ciencias, Tecnologico de Monterrey（蒙特雷理工学院工程与科学学院）
We compare the power of quantum and classical physics in terms of randomness certification from devices which are only partially characterised. We study randomness certification based on state discrimination and take noncontextuality as the notion of classicality. A contextual advantage was recently shown to exist for state discrimination. Here, we develop quantum and noncontextual semi-device independent protocols for random-number generation based on maximum-confidence discrimination, which generalises unambiguous and minimum-error state discrimination. We show that, for quantum eavesdropppe…
We study efficient quantum certification algorithms for unitary quantum process using no ancilla. Previous study showed that one can distinguish whether an unknown unitary $U$ is equal to or $\varepsilon$-far from a known or unknown unitary $V$ in fixed dimension with $O(\varepsilon^{-2})$ uses of the unitary, in which the Choi state is used and thus a high dimensional ancilla system is always needed. We give an algorithm that distinguishes the two cases with $O(\varepsilon^{-1})$ uses of the unitary, using fewer or no ancilla, outperforming previous relevant results.
Experimental certification of ensembles of high-dimensional quantum states with independent quantum devices
School of Physics, Hangzhou Normal University（杭州师范大学物理学院）；Quantum Computing Center, RIKEN（理化学研究所量子计算中心）；Physics Department, The University of Michigan（密歇根大学物理系）
In this report we study certification of quantum measurements, which can be viewed as the extension of quantum hypotheses testing. This extension involves also the study of the input state and the measurement procedure. Here, we will be interested in two-point (binary) certification scheme in which the null and alternative hypotheses are single element sets. Our goal is to minimize the probability of the type II error given some fixed statistical significance. In this report, we begin with studying the two-point certification of pure quantum states and unitary channels to later use them to pro…
The emergence of quantum theory at the beginning of 20$-th$ century has changed our view of the microscopic world and has led to applications such as quantum teleportation, quantum random number generation and quantum computation to name a few, that could never have been realised using classical systems. One such application that has attracted considerable attention lately is device-independent (DI) certification of composite quantum systems. The basic idea behind it is to treat a given device as a black box that given some input generates an output, and then to verify whether it works as expe…
Concomitant with the rapid development of quantum technologies, challenging demands arise concerning the certification and characterization of devices. The promises of the field can only be achieved if stringent levels of precision of components can be reached and their functioning guaranteed. This review provides a brief overview of the known characterization methods of certification, benchmarking, and tomographic recovery of quantum states and processes, as well as their applications in quantum computing, simulation, and communication.
We propose a family of noncontextuality inequalities and show that they can be used for certification of multiqubit quantum systems. Our scheme, unlike those based on non-locality, does not require spatial separation between the subsystems, yet it makes use of certain compatibility relations between measurements. Moreover, it is scalable in the sense that the number of expectation values that are to be measured to observe contextuality scales polynomially with the number of qubits that are being certified. In a particular case we also show our scheme to be robust errors and experimental imperf…
Device-independent certification of quantum devices is of crucial importance for the development of secure quantum information protocols. So far, the most studied scenario corresponds to a system consisting of different non-characterized devices that observers probe with classical inputs to obtain classical outputs. The certification of relevant quantum properties follows from the observation of correlations between these events that do not have a classical counterpart. In the fully device-independent scenario no assumptions are made on the devices and therefore their non-classicality follows …
Certifying that quantum devices behave as intended is crucial for quantum information science. Here, methods are developed for certification of both state preparation devices and measurement devices based on prepare-and-measure experiments with independent devices. The experimenter assumes the independence of the devices and knowledge of the Hilbert space dimension. Thus no precise characterisation of any part of the experiment is required. The certification is based on a randomised version of unambiguous state discrimination and targets the class of state ensembles corresponding to quantum $t…
The idea of self-testing is to render guarantees concerning the inner workings of a device based on the measurement statistics. It is one of the most formidable quantum certification and benchmarking schemes. Recently it was shown by Coladangelo et. al. (Nat Commun 8, 15485 (2017)) that all pure bipartite entangled states can be self tested in the device independent scenario by employing subspace methods introduced by Yang et. al. (Phys. Rev. A 87, 050102(R)). Here, we have adapted their method to show that any bipartite pure entangled state can be certified in the semi-device independent scen…
Quantum random number generators (QRNGs) promise perfectly unpredictable random numbers. However, the security certification of the random numbers in form of a stochastic model often introduces assumptions that are either hardly justified or indeed unnecessary. Two important examples are the restriction of an adversary to the classical regime as well as negligible correlations between consecutive measurement outcomes. Additionally, non-rigorous system characterization opens a security loophole. In this work we experimentally realize a QRNG that does not rely on the aforementioned assumptions a…
Communication games are one of the widely used tools that are designed to demonstrate quantum supremacy over classical resources. In that, two or more parties collaborate to perform an information processing task to achieve the highest success probability of winning the game. We propose a specific two-party communication game in the prepare-measure scenario that relies on an encoding-decoding task of specific information. We first demonstrate that quantum theory outperforms the classical preparation non-contextual theory, and the optimal quantum success probability of such a communication game…
Minimal informationally complete positive operator-valued measures (MIC-POVMs) are special kinds of measurement in quantum theory in which the statistics of their $d^2$-outcomes are enough to reconstruct any $d$-dimensional quantum state. For this reason, MIC-POVMs are referred to as standard measurements for quantum information. Here, we report an experiment with entangled photon pairs that certifies, for what we believe is the first time, a MIC-POVM for qubits following a device-independent protocol (i.e., modeling the state preparation and the measurement devices as black boxes, and using o…
Quantumness certification via non-demolition measurements
Dipartimento di Fisica, Università di Genova（热那亚大学物理系）；INFN - Sezione di Genova（意大利国家核物理研究所热那亚分部）；Istituto Nazionale di Ottica del Consiglio Nazionale delle Ricerche (CNR-INO)（意大利国家研究委员会光学研究所）；European Laboratory for Non-linear Spectroscopy, Universitá di Firenze（佛罗伦萨大学欧洲非线性光谱学实验室）
Lund University（隆德大学）；University of Jyväskylä（于韦斯屈莱大学）；Technical University of Denmark（丹麦技术大学）；Korea Advanced Institute of Science and Technology (KAIST)（韩国科学技术院）
No-cost Bell nonlocality certification from quantum tomography and its applications in quantum-magic-resource witnessing
University of Gdańsk（格但斯克大学）；International Centre for Theory of Quantum Technologies, University of Gdańsk（格但斯克大学量子技术理论国际中心）；Max Planck Institute for Quantum Optics（马克斯·普朗克量子光学研究所）；Faculty of Physics, Ludwig Maximilian University（慕尼黑大学物理学院）；Munich Center for Quantum Science and Technology（慕尼黑量子科学与技术中心）
While the standard formulation of quantum theory assumes a fixed background causal structure, one can relax this assumption within the so-called process matrix framework. Remarkably, some processes, termed causally nonseparable, are incompatible with a definite causal order. We explore a form of certification of causal nonseparability in a semi-device-independent scenario where the involved parties receive trusted quantum inputs, but whose operations are otherwise uncharacterised. Defining the notion of causally nonseparable distributed measurements, we show that certain causally nonseparable …
Although quantum communication systems are being deployed on a global scale, their realistic security certification is not yet available. Here we present a security evaluation and improvement protocol for complete quantum communication systems. The protocol subdivides a system by defining seven system implementation sub-layers based on a hierarchical order of information flow; then it categorises the known system implementation imperfections by hardness of protection and practical risk. Next, an initial analysis report lists all potential loopholes in its quantum-optical part. It is followed b…
