Given a unitary evolution $U$ on a multi-partite quantum system and an ensemble of initial states, how well can $U$ be simulated by local operations and classical communication (LOCC) on that ensemble? We answer this question by establishing a general, efficiently computable upper bound on the maximal LOCC simulation fidelity -- what we call an 'LOCC inequality'. We then apply our findings to the fundamental setting where $U$ implements a quantum Newtonian Hamiltonian over a gravitationally interacting system. Violation of our LOCC inequality can rule out the LOCCness of the underlying evolution, thereby establishing the non-classicality of the gravitational dynamics, which can no longer be explained by a local classical field. As a prominent application of this scheme we study systems of quantum harmonic oscillators initialised in coherent states following a normal distribution and interacting via Newtonian gravity, and discuss a possible physical implementation with torsion pendula. One of our main technical contributions is the analytical calculation of the above LOCC inequality for this family of systems. As opposed to existing tests based on the detection of gravitationally mediated entanglement, our proposal works with coherent states alone, and thus it does not require the generation of largely delocalised states of motion nor the detection of entanglement, which is never created at any point in the process.
We present a small network for the testing of the entanglement of two ballistic electron waveguide qubits. The network produces different output conditional on the presence or absence of entanglement. The structure of the network allows for the determination of successful entanglement operations through the measurement of the output of a single qubit. We also present a simple model of a dynamic coulomb-like interaction and use it to describe some characteristics of a proposed scheme for the entanglement of qubits in ballistic electron waveguides.
This is a comment on articles Phys. Rev. Lett. 119, 240401 (2017) [arXiv:1707.06050] and Phys. Rev. Lett. 119, 240402 (2017) [arXiv:1707.06036]. We argue that gravity-induced entanglement by Newtonian forces is agnostic to the quantum or classical nature of the gravitational true degrees of freedom.
We show that gravity and matter fields are generically entangled, as a consequence of the local Poincaré symmetry. First, we present a general argument, applicable to any particular theory of quantum gravity with matter, by performing the analysis in the abstract nonperturbative canonical framework, demonstrating the nonseparability of the scalar constraint, thus promoting the entangled states as the physical ones. Also, within the covariant framework, we show explicitly that the Hartle-Hawking state in the Regge model of quantum gravity is necessarily entangled. Our result is potentially rele…
Given a black-box representing an unknown Boolean function $f$ of $n$ variables, in this paper we propose a fast quantum algorithm to test whether or not a certain variable in the function $f$ is a junta variable. The proposed algorithm creates entanglement between the variable under test and an auxiliary qubit, where the entanglement is measured using concurrence measure to decide if the variable is junta. The paper shows applications to the proposed algorithm in learning and categorization of Boolean functions.
Characterization of quantum devices received from unknown providers is a significant primary task for any quantum information processing protocol. Self-testing protocols are designed for this purpose of certifying quantum components from the observed statistics under a set of minimal assumptions. Here we propose a self-testing protocol for certifying binary Pauli measurements employing the violation of a Leggett-Garg inequality. The scenario based on temporal correlations does not require entanglement, a costly and fragile resource. Moreover, unlike previously proposed self-testing protocols i…
We propose to detect quantum entanglement by a condition of local measurments. We find that this condition can detect efficiently the pure entangled states for both discrete and continuous variable systems. It does not depend on interference of decoherence from noise and detection loss in some systems, which allows a loophole-free test in real experiments. In particular, it is a necessary condition for the violation of some generalized Bell inequalities.
We consider the problem of deciding if a given three-party entangled pure state can be converted, with a non-zero success probability, into a given two-party pure state through local quantum operations and classical communication. We show that this question is equivalent to the well-known computational problem of deciding if a multivariate polynomial is identically zero. Efficient randomized algorithms developed to study the latter can thus be applied to the question of tripartite to bipartite entanglement transformations.
We present self-testing protocols to certify the presence of tensor products of Pauli measurements on maximally entangled states of local dimension $2^n$ for $n\in\mathbb{N}$. This provides self-tests of sets of informationally complete measurements in arbitrarily high dimension. We then show that this can be used for the device-independent certification of the entanglement of all bipartite entangled states by exploiting a connection to measurement device-independent entanglement witnesses and quantum networks. This work extends a more compact parallel work on the same subject and provides all…
We propose a scheme to realize entanglement swapping via superradiance, entangling two distant cavities without a direct interaction. The successful Bell-state-measurement outcomes are performed naturally by the electromagnetic reservoir, and we show how, using a quantum trajectory method, the non-local properties of the state obtained after the swapping procedure can be verified by the steering inequality. Furthermore, we discuss how the unsuccessful measurement outcomes can be used in an experiment of delayed-choice entanglement swapping. An extension of testing the quantum steering inequali…
We argue that Hartle-Hawking states in the Regge quantum gravity model generically contain non-trivial entanglement between gravity and matter fields. Generic impossibility to talk about "matter in a point of space" is in line with the idea of an emergent spacetime, and as such could be taken as a possible candidate for a criterion for a plausible theory of quantum gravity. Finally, this new entanglement could be seen as an additional "effective interaction", which could possibly bring corrections to the weak equivalence principle.
We investigate the phenomenon of gravity-induced entanglement in optomechanical systems. Assuming photon number conservation and the Newtonian potential expanded up to the quadratic order of the oscillator positions, we exactly solve the dynamics of the optomehcanical systems. Then, we find that the phase difference due to the Newtonian gravity leads to the large entanglement of photons in separated cavities. We clarify the generating mechanism of large gravity-induced entanglements in optomechanical systems in an exact manner. We also determine the characteristic time to generate the maximal …
We analyze the dynamics of a gravity-induced entanglement for N massive particles. Considering the linear configuration of these particles, we investigate the entanglement between a specific pair of particles under the influence of the gravitational interaction between the massive particles. As the particle number increases, the specific particle pair decoheres more easily due to the gravitational interaction with other particles. The time scale of the gravity-induced decoherence is analytically determined. We also discuss the entanglement dynamics of initially entangled particles, which exemp…
Quantum self-testing is a device-independent way to certify quantum states and measurements using only the input-output statistics, with minimal assumptions about the quantum devices. Because of the high demand on tolerable noise, however, experimental self-testing was limited to two-photon systems. Here, we demonstrate the first robust self-testing for multi-photon genuinely entangled quantum states. We prepare two examples of four-photon graph states, the Greenberger-Horne-Zeilinger (GHZ) states with a fidelity of 0.957(2) and the linear cluster states with a fidelity of 0.945(2). Based on t…
Collapse-based models for gravity do not violate the entanglement-based witness of non-classicality
QICI Quantum Information and Computation Initiative, School of Computing and Data Science, The University of Hong Kong（香港大学计算与数据科学学院量子信息与计算倡议）；Clarendon Laboratory, University of Oxford（牛津大学克拉伦登实验室）
We assess the quality of a source of allegedly pure two-qubit states using both standard tomography and methods inspired by device-independent self-testing. Even when the detection and locality loopholes are open, the latter methods can dispense with modelling of the system and the measurements. However, due to finite sample fluctuations, the estimated probability distribution usually does not satisfy the no-signaling conditions exactly. We implement data analysis that is robust against these fluctuations. We demonstrate a high ratio $f_s/f_t\approx 0.988$ between the fidelity estimated from s…
We conjecture that the total quantum entanglement of matter and vacuum in the universe tends to increase with time, like entropy, and that an effective force is associated with this tendency. We also suggest that gravity and dark energy are types of quantum entanglement forces, similar to Verlinde's entropic force, and give holographic dark energy with an equation of state comparable to current observational data. This connection between quantum entanglement and gravity could give some new insights into the origins of gravity, dark energy, and the arrow of time.
Twenty-five years after the invention of quantum teleportation, the concept of entanglement gained enormous popularity. This is especially nice to those who remember that entanglement was not even taught at universities until the 1990's. Today, entanglement is often presented as a resource, the resource of quantum information science and technology. However, entanglement is exploited twice in quantum teleportation. First, entanglement is the `quantum teleportation channel', i.e. entanglement between distant systems. Second, entanglement appears in the eigenvectors of the joint measurement that…
We discuss the physical interpretation of the gravity mediated entanglement effect. We show how to read it in terms of quantum reference systems. We pinpoint the single gravitational degree of freedom mediating the entanglement. We clarify why the distinction between longitudinal and transverse degrees of freedom is irrelevant for the interpretation of the results. We discuss the relation between the LOCC theorem and the interpretation of the effect, its different relevance for, respectively, the quantum gravity and quantum information communities, and the reason for the excitement raised by t…
The gravity-scalar field system in spherical symmetry provides a natural setting for exploring gravitational collapse and its aftermath in quantum gravity. In a canonical approach, we give constructions of the Hamiltonian operator, and of semiclassical states peaked on constraint free data. Such states provide explicit examples of physical states. We also show that matter-gravity entanglement is an inherent feature of physical states, whether or not there is a black hole.
Black hole entropy is one of the few windows toward the quantum aspects of gravitation and its study over the years have highlighted the holographic nature of gravity. At the non-perturbative level in quantum gravity, promising explanations are being explored in terms of the entanglement entropy between regions of space. In the context of loop quantum gravity, this translates into the analysis of the correlations between regions of the spin network states defining the quantum state of geometry of space. In this paper, we explore a class of states, motivated by results in condensed matter physi…
We show that the rich structure of multipartite entanglement can be tested following a device-independent approach. Specifically we present Bell inequalities for distinguishing between different types of multipartite entanglement, without placing any assumptions on the measurement devices used in the protocol, in contrast with usual entanglement witnesses. We first address the case of three qubits and present Bell inequalities that can be violated by W states but not by GHZ states, and vice versa. Next, we devise 'sub-correlation Bell inequalities' for any number of parties, which can provably…
We present two methods of calculating the spatial entanglement of an interacting electron system within the framework of density-functional theory. These methods are tested on the model system of Hooke's atom for which the spatial entanglement can be calculated exactly. We analyse how the strength of the confining potential affects the spatial entanglement and how accurately the methods that we introduced reproduce the exact trends. We also compare the results with the outcomes of standard first-order perturbation methods. The accuracies of energies and densities when using these methods are a…
An experimental scheme is proposed to test Bell's inequality by using superconducting nanocircuits. In this scheme, quantum entanglement of a pair of charge qubits separated in a sufficient long distance may be created by cavity quantum electrodynamic techniques; the population of qubits is experimentally measurable by dc currents through the probe junctions, and one measured outcome may be recorded for every experiment. Therefore, both locality and detection efficiency loopholes should be closed in the same experiment. We also propose a useful method to measure the amount of entanglement base…
We revisit the criterion of multi-particle entanglement based on the overlaps of a given quantum state $ρ$ with maximally entangled states. For a system of $m$ particles, each with $N$ distinct states, we prove that $ρ$ is $m$-particle negative partial transpose (NPT) entangled, if there exists a maximally entangled state $|{\rm MES}>$, such that $<{\rm MES}|ρ|{\rm MES}>>{1}/{N}$. While this sufficiency condition is weaker than the Peres-Horodecki criterion in all cases, it applies to multi-particle systems, and becomes especially useful when the number of particles ($m$) is large. We also con…
Evolution of tripartite entanglement in three-qubit Quantum Gravity-Induced Entanglement of Masses (QGEM) with quantum decoherence
Instituto de Física Teórica, UAM-CSIC（理论物理研究所，UAM-CSIC）；Van Swinderen Institute for Particle Physics and Gravity, University of Groningen（格罗宁根大学范斯温德恩粒子物理与引力研究所）；Departamento de Física Teórica and CIAFF, Universidad Autónoma de Madrid（马德里自治大学理论物理系及CIAFF）
We present a method to test quantum behavior of quantum information processing devices, such as quantum memories, teleportation devices, channels and quantum key distribution protocols. The test of quantum behavior can be phrased as the verification of effective entanglement. Necessary separability criteria are formulated in terms of a matrix of expectation values in conjunction with the partial transposition map. Our method is designed to reduce the resources for entanglement verification. A particular protocol based on coherent states and homodyne detection is used to illustrate the method. …
It has been proposed that quantum features of the gravitational field can be exposed experimentally by employing gravity as a mediator of entanglement. We show that in order to witness this type of entanglement experimentally, strong limits on acceleration noise, which has been neglected in previous work, must be overcome. In the case of two particles of similar mass, Casimir-Polder forces lead to a fundamental limit of tenths of femtometers per second squared per root Hertz. Limits are between three and six orders of magnitude less strict for two particles of unequal mass, depending on collis…
The violation of Bell's inequality requires a well-designed experiment to validate the result. In experiments using energy-time and time-bin entanglement, initially proposed by Franson in 1989, there is an intrinsic loophole due to the high postselection. To obtain a violation in this type of experiment, a chained Bell inequality must be used. However, the local realism bound requires a high visibility in excess of 94.63 percent in the time-bin entangled state. In this work, we show how such a high visibility can be reached in order to violate a chained Bell inequality with 6, 8 and 10 terms.
We consider the coupling of quantum fields to classical gravity in the formalism of ensembles on configuration space, a model that allows a consistent formulation of interacting classical and quantum systems. Explicit calculations show that there are solutions for which two quantum fields are in an entangled state, even though their interaction occurs solely via a common classical gravitational field, and that such entangled solutions can evolve from initially unentangled ones. These results support the observation of a previous paper that an observed generation of entanglement would not provi…
We investigate the generation rate of quantum gravity induced entanglement of masses(QGEM) in setup with multiple quantum massive particles, among of which only the gravity interaction due to the Newton potential is taken into account. When the distance between any two adjacent Stern-Gerlach (SG) devices is fixed, we consider all the possible configurations of the setup with the same number of particles. In particular, we systemically analyze the case of particle number n=4 and find that the prism setup with a massive particle at the center is the most efficient setup for the entanglement gene…
Self-testing, which refers to device independent characterization of the state and the measurement, enables the security of quantum information processing task certified independently of the operation performed inside the devices. Quantum states lie in the core of self-testing as key resources. However, for the different entangled states, usually different measurement settings should be taken in self-testing recipes. This may lead to the redundancy of measurement resources. In this work, we use fixed two-binary measurements and answer the question that what states can be self-tested with the s…
Previous results indicate that while chaos can lead to substantial entropy production, thereby maximizing dynamical entanglement, this still falls short of maximality. Random Matrix Theory (RMT) modeling of composite quantum systems, investigated recently, entails an universal distribution of the eigenvalues of the reduced density matrices. We demonstrate that these distributions are realized in quantized chaotic systems by using a model of two coupled and kicked tops. We derive an explicit statistical universal bound on entanglement, that is also valid for the case of unequal dimensionality o…
We study the derivation of the effective equation of motion for a pointlike particle in the framework of quantum gravity. Just like the geodesic motion of a classical particle is a consequence of classical field theory coupled to general relativity, we introduce the similar notion of an effective equation of motion, but starting from an abstract quantum gravity description. In the presence of entanglement between gravity and matter, quantum effects give rise to modifications of the geodesic trajectory, primarily as a consequence of the nonzero overlap between various coherent states of the gra…
We present a stronger version of the Doherty-Parrilo-Spedalieri (DPS) hierarchy of approximations for the set of separable states. Unlike DPS, our hierarchy converges exactly at a finite number of rounds for any fixed input dimension. This yields an algorithm for separability testing which is singly exponential in dimension and polylogarithmic in accuracy. Our analysis makes use of tools from algebraic geometry, but our algorithm is elementary and differs from DPS only by one simple additional collection of constraints.
