This paper solves the open problem of characterizing the performance of quantum illumination (QI) with discrete variable states. By devising a novel quantum measurement approach along with meticulous analysis, our investigation demonstrates that, in the limit as $M \rightarrow \infty$, the maximally entangled $M$ mode Bell state achieves optimal performance, matching the two-mode squeezed vacuum in a high-noise regime and exceeding it in low-noise. This result challenges the dominance of continuous variable states in photonic sensing applications and extends the novelty of QI to regimes where no quantum advantage was believed to exist. A closer analysis reveals that this advantage stems from retained entanglement in the transmitted Bell state, a paradigm-shifting discovery since interaction with the environment in optical systems is believed to break entanglement. The complete mathematical analysis of this work provides granular insights into the interaction between photonic systems and environmental noise, motivating further research into discrete variable quantum sensing.
Discriminating between quantum states is a fundamental problem in quantum information protocols. The optimum approach saturates the Helstrom bound, which quantifies the unavoidable error probability of mistaking one state for another. Computing the error probability directly requires complete knowledge and diagonalization of the density matrices describing these states. Both of these fundamental requirements become impractically difficult to obtain as the dimension of the states grow large. In this article, we analyze quantum illumination as a quantum channel discrimination protocol and circum…
In the nonsignaling framework, nonclassicality in correlation arising from two spatially separated input-output devices gets manifested, solely, through its \emph{nonlocal} behavior. Study of correlations based on this said feature is commonly known as local-nonlocal paradigm. While in two-party scenario correlations can be of only two types either local or nonlocal, the situation gets more involved for multi-party scenario, \emph{e.g.,} for tripartite scenario, correlations can be of three types: fully local, two-way local, and genuinely nonlocal. Nonsignaling correlations having quantum real…
A new paradigm for secure communication, based on quantum illumination, is proposed. Alice uses spontaneous parametric down-conversion to send Bob a set of signal modes over a pure-loss channel while retaining the set of idler modes with which they are maximally entangled. Bob imposes a single information bit on the modes he receives from Alice via binary phase-shift keying. He then adds classical Gaussian noise and sends the noisy modulated modes back to Alice over the same pure-loss channel. Even though the loss and noise destroy any entanglement between the modes that Alice receives from Bo…
Bell's theorem basically states that local hidden variable theory cannot predict the correlations produced by quantum mechanics. It is based on the assumption that Alice and Bob can choose measurements from a measurement set containing multiple elements. We establish a new paradigm that departs from Bell's paradigm by assuming that there are no choices for Alice and Bob and that the measurements Alice and Bob will make are fixed from the start. We include a process of quantum computation in our model. To the best of our knowledge, we are the first to connect quantum computation and nonlocality…
Bell nonlocality, the fact that local hidden variable models cannot reproduce the correlations obtained by measurements on entangled states, is a cornerstone in our modern understanding of quantum theory. Apart from its fundamental implications, nonlocality is also at the core of device-independent quantum information processing, which successful implementation is achieved without precise knowledge of the physical apparatus. Here we show that a stronger form of Bell nonlocality, for which even nonlocal hidden variable models cannot reproduce the quantum predictions, allows for the device-indep…
The existence of observables that are incompatible or not jointly measurable is a characteristic feature of quantum mechanics, which lies at the root of a number of nonclassical phenomena, such as uncertainty relations, wave--particle dual behavior, Bell-inequality violation, and contextuality. However, no intuitive criterion is available for determining the compatibility of even two (generalized) observables, despite the overarching importance of this problem and intensive efforts of many researchers. Here we introduce an information theoretic paradigm together with an intuitive geometric pic…
Apart from the Bell nonlocality, which deals with the correlations generated from the local input-output statistics, quantum theory exhibits another kind of nonlocality that involves the indistiguishability of the locally preparable set of multipartite states. While Bell-type nonlocality cannot be distilled from a given local correlation, it is already reported that the latter kind of nonlocality can be activated from a "local", i.e., locally distinguishable set of states. Although, recently it is shown that a stronger notion of such a nonlocality, which deals with elimination instead of discr…
Dynamically preparing robust Bell states by time-boundary engineering
School of Physics, Beijing Institute of Technology（北京理工大学物理学院）；School of Physics Science and Technology, Kunming University（昆明大学物理科学与技术学院）；National Laboratory of Solid State Microstructures, Department of Physics, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University（南京大学固体微结构物理国家重点实验室、物理系和先进微结构协同创新中心）
Usually the 'hidden variables' of Bell's theorem are supposed to describe the pair of Bell particles. Here a semantic shift is proposed, namely to attach the hidden variables to a stochastic medium or field in which the particles move. It appears that under certain conditions one of the premises of Bell's theorem, namely 'measurement independence', is not satisfied for such 'background-based' theories, even if these only involve local interactions. Such theories therefore do not fall under the restriction of Bell's no-go theorem. A simple version of such background-based models are Ising model…
We find a single parameter family of genuinely entangled three qubit pure states, called the maximally Bell inequality violating states (MBV), which exhibit maximum Bell inequality violation by the reduced bipartite system for a fixed amount of genuine tripartite entanglement quantified by the so called tangle measure. This in turn implies that there holds a complementary relation between the Bell inequality violation by the reduced bipartite systems and the tangle present in the three qubit states, not necessarily pure. The MBV states also exhibit maximum Bell inequality violation by the redu…
Loss and noise quickly destroy quantum entanglement. Nevertheless, recent work has shown that a quadrature-entangled light source can reap a substantial performance advantage over all classical-state sources of the same average transmitter power in scenarios whose loss and noise makes them entanglement breaking, standoff target-detection being an example. In this paper, we make a first step in extending this quantum illumination paradigm to the optical imaging domain, viz., to obtain better spatial resolution for standoff optical sensing. Our canonical imaging scenario---restricted, for simpli…
Device-independent quantum key distribution is a secure quantum cryptographic paradigm that allows two honest users to establish a secret key, while putting minimal trust in their devices. Most of the existing protocols have the following structure: first, a bipartite nonlocal quantum state is distributed between the honest users, who perform local measurements to establish nonlocal correlations. Then, they announce the implemented measurements and extract a secure key by post-processing their measurement outcomes. We show that no protocol of this form allows for establishing a secret key when…
The Bell inequality, and its substantial experimental violation, offers a seminal paradigm for showing that the world is not in fact locally realistic. Here, going beyond the scope of Bell's inequality on physical states, we show that quantum teleportation can be used to quantitatively characterize quantum correlations of physical processes. The validity of the proposed formalism is demonstrated by considering the problem of teleportation through a linear three-node quantum network. A hierarchy is derived between the Bell nonlocality, nonbilocality, steering and nonlocality-steering hybrid cor…
Bell non-locality represents the ultimate consequence of quantum entanglement, fundamentally undermining the classical tenet that spatially-separated degrees of freedom possess objective attributes independently of the act of their measurement. Despite its importance, probing Bell non-locality in many-body systems is considered to be a formidable challenge, with a computational cost scaling exponentially with system size. Here we propose and validate an efficient variational scheme, based on the solution of inverse classical Ising problems, which in polynomial time can probe whether an arbitra…
Sapienza Università di Roma（罗马第一大学）；International Institute of Physics（国际物理研究所）；Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）
The violation of a Bell inequality is the paradigmatic example of device-independent quantum information: the nonclassicality of the data is certified without the knowledge of the functioning of devices. In practice, however, all Bell experiments rely on the precise understanding of the underlying physical mechanisms. Given that, it is natural to ask: Can one witness nonclassical behaviour in a truly black-box scenario? Here we propose and implement, computationally and experimentally, a solution to this ab-initio task. It exploits a robust automated optimization approach based on the Stochast…
In this paper, we propose a novel quantum backscatter communications (QBC) protocol, inspired by the quantum illumination (QI) concept. In the QBC paradigm, the transmitter generates entangled photon pair. The signal photon is transmitted and the idler photon is kept at the receiver. The tag antenna communicates by performing the pulse amplitude modulation (PAM), binary phase shift keying (BPSK) or quadratic phase shift keying (QPSK) on the signal impinging at the antenna. Using the sum-frequency-generation receiver, our QBC protocol achieves a 6 dB error exponent gain for PAM and BPSK, and 3 …
The entanglement resource required for quantum information processing comes in a variety of forms, from Bell states to multipartite GHZ states or cluster states. Purifying these resources after their imperfect generation is an indispensable step towards using them in quantum architectures. While this challenge, both in the case of Bell pairs and more general multipartite entangled states, is mostly overcome in the presence of perfect local quantum hardware with unconstrained qubit register sizes, devising optimal purification strategies for finite-size realistic noisy hardware has remained elu…
We study the faces of the set of quantum correlations, i.e., the Bell and noncontextuality inequalities without any quantum violation. First, we investigate the question whether every proper (tight) Bell inequality for two parties, other than the trivial ones from positivity, normalization and no-signaling can be violated by quantum correlations, i.e., whether the classical Bell polytope or the smaller correlation polytope share any facets with their respective quantum sets. To do this, we develop a recently derived bound on the quantum value of linear games based on the norms of game matrices…
We use hyper-entanglement to experimentally realize deterministic entanglement swapping based on quantum Elegant Joint Measurements. These are joint projections of two qubits onto highly symmetric, iso-entangled, bases. We report measurement fidelities no smaller than $97.4\%$. We showcase the applications of these measurements by using the entanglement swapping procedure to demonstrate quantum correlations in the form of proof-of-principle violations of both bilocal Bell inequalities and more stringent correlation criteria corresponding to full network nonlocality. Our results are a foray int…
We have experimentally created a robust, ultrabright and phase-stable polarization-entangled state close to maximally entangled Bell-state with $ \% 98 $-fidelity using the type-II spontaneous parametric down-conversion (SPDC) process in periodically-poled KTiOPO$ _4 $ (PPKTP) collinear crystal inside a Sagnac interferometer (SI). Bell inequality measurement, Freedman's test, as the different versions of CHSH inequality, and also visibility test which all can be seen as the nonlocal realism tests, imply that our created entangled state shows a strong violation from the classical physics or any…
The Kochen-Specker theorem, Bell inequalities, and several other tests that were designed to rule out hidden-variable theories, assume the existence of observables having infinitely sharp eigenvalues. A paradigmatic example is spin-1/2. It is measured with a Stern-Gerlach array whose outputs are divided into two classes, spin-up and spin-down, in correspondence to the two spots observed on a detection screen. The spot's finite size is attributed to imperfections of the measuring device. This assumption turns the experimental output into a dichotomic, discrete one, thereby allowing the assignme…
Nonlocality lies at the core of quantum mechanics from both a fundamental and applicative point of view. It is typically revealed by a Bell test, that is by violation of a Bell inequality, whose success depends both on the state of the system and on parameters linked to experimental settings. This leads to find, given the state, optimized parameters for a successful test. Here we provide, for a quite general class of quantum states, the explicit expressions of these optimized parameters and point out that, for a continuous change of the state, the corresponding suitable experimental settings m…
Quantum networks are the center of many of the recent advances in quantum science, not only leading to the discovery of new properties in the foundations of quantum theory but also allowing for novel communication and cryptography protocols. It is known that networks beyond that in the paradigmatic Bell's theorem imply new and sometimes stronger forms of nonclassicality. Due to a number of practical difficulties, however, the experimental implementation of such networks remains far less explored. Going beyond what has been previously tested, here we verify the nonlocality of an experimental tr…
Increasingly sophisticated quantum computers motivate the exploration of their abilities in certifying genuine quantum phenomena. Here, we demonstrate the power of state-of-the-art IBM quantum computers in correlation experiments inspired by quantum networks. Our experiments feature up to 12 qubits and require the implementation of paradigmatic Bell-State Measurements for scalable entanglement-swapping. First, we demonstrate quantum correlations that defy classical models in up to nine-qubit systems while only assuming that the quantum computer operates on qubits. Harvesting these quantum adva…
Most quantum systems that are used for generating entanglement and for practical applications are not isolated from the environment, and are hence susceptible to noise. Entanglement in more than one degree of freedom between two systems, known as hyperentanglement, is known to have certain advantages, including robustness against noise over conventional entangled states. Quantum illumination, imaging and communication schemes that involve sending one photon from a pair of entangled photons and retaining the other photon usually involve exposing only the signal photon to environmental noise. Th…
Cyclic systems of dichotomous random variables have played a prominent role in contextuality research, describing such experimental paradigms as the Klyachko-Can-Binicoglu-Shumovky, Einstein-Podolsky-Rosen-Bell, and Leggett-Garg ones in physics, as well as conjoint binary choices in human decision making. Here, we understand contextuality within the framework of the Contextuality-by-Default (CbD) theory, based on the notion of probabilistic couplings satisfying certain constraints. CbD allows us to drop the commonly made assumption that systems of random variables are consistently connected. C…
According to the theory of cosmic inflation, the large scale structures observed in our Universe (galaxies, clusters of galaxies, Cosmic Background Microwave - CMB - anisotropy ...) are of quantum mechanical origin. They are nothing but vacuum fluctuations, stretched to cosmological scales by the cosmic expansion and amplified by gravitational instability. At the end of inflation, these perturbations are placed in a two-mode squeezed state with the strongest squeezing ever produced in Nature (much larger than anything that can be made in the laboratory on Earth). This article studies whether a…
Since Bell's theorem, it is known that the concept of local realism fails to explain quantum phenomena. Indeed, the violation of a Bell inequality has become a synonym of the incompatibility of quantum theory with our classical notion of cause and effect. As recently discovered, however, the instrumental scenario -- a tool of central importance in causal inference -- allows for signatures of nonclassicality that do not hinge on this paradigm. If, instead of relying on observational data only, we can also intervene in our experimental setup, quantum correlations can violate classical bounds on …
Given a Bell inequality, if its maximal quantum violation can be achieved only by a single set of measurements for each party or a single quantum state, up to local unitaries, one refers to such a phenomenon as self-testing. For instance, the maximal quantum violation of the Clauser-Horne-Shimony-Holt inequality certifies that the underlying state contains the two-qubit maximally entangled state and the measurements of one party contains a pair of anti-commuting qubit observables. As a consequence, the other party automatically verifies the set of states remotely steered, namely the "assemblag…
We study and extend the semidefinite programming (SDP) hierarchies introduced in [Phys. Rev. Lett. 115, 020501] for the characterization of the statistical correlations arising from finite dimensional quantum systems. First, we introduce the dimension-constrained noncommutative polynomial optimization (NPO) paradigm, where a number of polynomial inequalities are defined and optimization is conducted over all feasible operator representations of bounded dimensionality. Important problems in device independent and semi-device independent quantum information science can be formulated (or almost f…
