Certification Of Entanglement Research Articles

Experimental post-selection loophole-free time-bin and energy-time nonlocality with integrated photonics

Time-bin (TB) and energy-time (ET) entanglements are crucial resources for long-distance quantum information processing. However, their standard implementations suffer from the so-called post-selection loophole that allows for classical simulation and thus prevents quantum advantage. The post-selection loophole has been addressed in proof-of-principle experiments. An open problem though is to close it in real-life applications based on integrated technologies. This is especially important since, so far, all integrated sources of TB and ET entanglements suffer from the post-selection loophole. Here, we report post-selection loophole-free certification of TB or ET entanglement in integrated technologies, by implementing in a silicon nitride chip the “hug” scheme [Phys. Rev. Lett. 102, 040401 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.040401] and certifying genuine TB entanglement through the violation of a Bell inequality.

Recovering quantum entanglement after its certification.

Entanglement is a crucial quantum resource with broad applications in quantum information science. For harnessing entanglement in practice, it is a prerequisite to certify the entanglement of a given quantum state. However, the certification process itself destroys the entanglement, thereby precluding further exploitation of the entanglement. Resolving this conflict, here, we present a protocol that certifies the entanglement of a quantum state without complete destruction and then probabilistically recovers the original entanglement to provide useful entanglement for further quantum applications. We experimentally demonstrate this protocol in a photonic quantum system and highlight its usefulness for selecting high-quality entanglement from a realistic entanglement source. Moreover, our study reveals various trade-off relations among the physical quantities involved in the protocol. Our results show how entanglement certification can be made compatible with subsequent quantum applications and be beneficial to sort entanglement for better performance in quantum technologies.

Self-Testing with Dishonest Parties and Device-Independent Entanglement Certification in Quantum Communication Networks.

We consider the task of device-independent quantum state certification in a network where some of the nodes may collude and act dishonestly. We introduce the paradigm of self-testing with dishonest parties and provide a certification protocol for the Greenberger-Horne-Zeilinger state in this framework, together with robust statements about the fidelity of the shared state. We extend our results to the cluster scenario, where many subgroups of parties may collude. Our findings provide a new operational motivation for the strong definition of genuine multipartite nonlocality originally introduced by Svetlichny.

Measurement-device-independent nonlinear entanglement witnesses

Entanglement witnesses (EWs) are one of the most effective methods to detect entanglement. It is known that nonlinear EW provide better entanglement detection than their linear counterparts, in that the former detect a strictly larger subset of entangled states than the latter. Whether linear or nonlinear, the method is measurement-device dependent, so that imperfect measurements may cause false certification of entanglement in a shared state. Measurement-device-independent EW provide an escape from such measurement dependence of the entanglement detection for linear EW. Here we present measurement-device-independent nonlinear EW for non-positive partial transpose entangled states as well as for bound entangled states with positive partial transpose. Although the witness considered herein does not detect a larger set of entangled states than other nonlinear EW, it is more efficient in that it never leads to a false detection corresponding to wrong measurements. The constructed measurement-device-independent nonlinear EW certify the entanglement of the same sets of entangled states as their device-dependent parents do, and therefore are better than the linear EW, device-independent or otherwise.

Quantifying high-dimensional spatial entanglement with a single-photon-sensitive time-stamping camera.

High-dimensional entanglement is a promising resource for quantum technologies. Being able to certify it for any quantum state is essential. However, to date, experimental entanglement certification methods are imperfect and leave some loopholes open. Using a single-photon-sensitive time-stamping camera, we quantify high-dimensional spatial entanglement by collecting all output modes and without background subtraction, two critical steps on the route toward assumptions-free entanglement certification. We show position-momentum Einstein-Podolsky-Rosen (EPR) correlations and quantify the entanglement of formation of our source to be larger than 2.8 along both transverse spatial axes, indicating a dimension higher than 14. Our work overcomes important challenges in photonic entanglement quantification and paves the way toward the development of practical quantum information processing protocols based on high-dimensional entanglement.

Distribution of genuine high-dimensional entanglement over 10.2 km of noisy metropolitan atmosphere

In a recent quantum key distribution experiment, high-dimensional protocols were used to show an improved noise resistance over a 10.2 km free-space channel. One of the unresolved questions in this context is whether the communicating parties actually shared genuine high-dimensional entanglement. In this letter we introduce an improved discretisation and entanglement certification scheme for high-dimensional time-bin setups and apply it to the data obtained during the experiment. Our analysis answers the aforementioned question affirmatively and thus the experiment constitutes the first transmission of genuine high-dimensional entanglement in a single degree of freedom over a long-range free-space channel.

Device-independent and semi-device-independent entanglement certification in broadcast Bell scenarios

It has recently been shown that by broadcasting the subsystems of a bipartite quantum state, one can activate Bell nonlocality and significantly improve noise tolerance bounds for device-independent entanglement certification. In this work we strengthen these results and explore new aspects of this phenomenon. First, we prove new results related to the activation of Bell nonlocality. We construct Bell inequalities tailored to the broadcast scenario, and show how broadcasting can lead to even stronger notions of Bell nonlocality activation. In particular, we exploit these ideas to show that bipartite states admitting a local hidden-variable model for general measurements can lead to genuine tripartite nonlocal correlations. We then study device-independent entanglement certification in the broadcast scenario, and show through semidefinite programming techniques that device-independent entanglement certification is possible for the two-qubit Werner state in essentially the entire range of entanglement. Finally, we extend the concept of EPR steering to the broadcast scenario, and present novel examples of activation of the two-qubit isotropic state. Our results pave the way for broadcast-based device-independent and semi-device-independent protocols.

Entanglement meter: estimation of entanglement with single copy in interferometer

Efficient certification and quantification of high dimensional entanglement of composite systems are challenging both theoretically as well as experimentally. Here, we demonstrate how to measure the linear entropy, negativity and the Schmidt number of bipartite systems from the visibility of Mach–Zehnder interferometer using single copies of the quantum state. Our result shows that for any two qubit pure bipartite state, the interference visibility is a direct measure of entanglement. We also propose how to measure the mutual predictability experimentally from the intensity patterns of the interferometric set-up without having to resort to local measurements of mutually unbiased bases. Furthermore, we show that the entanglement witness operator can be measured in a interference setup and the phase shift is sensitive to the separable or entangled nature of the state. Our proposal bring out the power of Interferometric set-up in entanglement detection of pure and several mixed states which paves the way towards design of entanglement meter.

Manipulation and Certification of High-Dimensional Entanglement through a Scattering Medium

A wavefront shaping approach enables protection of high-dimensional entangled photons traversing a scattering medium, a situation that typically hinders the building of practical quantum microscopy and quantum key distribution.

Quick Quantum Steering: Overcoming Loss and Noise with Qudits

A primary requirement for a robust and unconditionally secure quantum network is the establishment of quantum nonlocal correlations over a realistic channel. While loophole-free tests of Bell nonlocality allow for entanglement certification in such a device-independent setting, they are extremely sensitive to loss and noise, which naturally arise in any practical communication scenario. Quantum steering relaxes the strict technological constraints of Bell nonlocality by reframing it in an asymmetric manner, with a trusted party only on one side. However, tests of quantum steering still require either extremely high-quality entanglement or very low loss. Here we introduce a test of quantum steering that harnesses the advantages of high-dimensional entanglement to be simultaneously noise robust and loss tolerant. Despite being constructed for qudits, our steering test is designed for single-detector measurements and is able to close the fair-sampling loophole in a time-efficient manner. We showcase the improvements over qubit-based systems by experimentally demonstrating quantum steering in up to 53 dimensions, free of the fair-sampling loophole, through simultaneous loss and noise conditions corresponding to 14.2-dB loss equivalent to 79 km of telecommunication fiber, and 36% of white noise. We go on to show how the use of high dimensions counterintuitively leads to a dramatic reduction in total measurement time, enabling a quantum steering violation almost 2 orders of magnitude faster obtained by simply doubling the Hilbert space dimension. Our work conclusively demonstrates the significant resource advantages that high-dimensional entanglement provides for quantum steering in terms of loss, noise, and measurement time, and opens the door toward practical quantum networks with the ultimate form of security.Received 26 April 2022Revised 29 September 2022Accepted 21 October 2022DOI:https://doi.org/10.1103/PhysRevX.12.041023Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEntanglement detectionEntanglement measuresNonlocalityQuantum communicationQuantum entanglementQuantum InformationAtomic, Molecular & Optical

Entanglement witnessing for lattice gauge theories

Entanglement is assuming a central role in modern quantum many-body physics. Yet, for lattice gauge theories its certification remains extremely challenging. A key difficulty stems from the local gauge constraints underlying the gauge theory, which separate the full Hilbert space into a direct sum of subspaces characterized by different superselection rules. In this work, we develop the theoretical framework of entanglement witnessing for lattice gauge theories that takes this subtlety into account. We illustrate the concept at the example of a U(1) lattice gauge theory in 2+1 dimensions, without and with dynamical fermionic matter. As this framework circumvents costly state tomography, it opens the door to resource-efficient certification of entanglement in theoretical studies as well as in laboratory quantum simulations of gauge theories.

Processing Entangled Photons in High Dimensions with a Programmable Light Converter

High-dimensional entanglement offers a variety of advantages for both fundamental and applied applications in quantum information science. A central building block for such applications is a programmable processor of entangled states, which is crucial for the certification, manipulation, and distribution of high-dimensional entanglement. The leading technology for processing photons is integrated multiport interferometers. However, such devices are incompatible with structured light and their scaling is challenging. Here, we unlock these limitations by demonstrating a reconfigurable processor of entangled photons in high dimensions that is based on multiplane light conversion (MPLC), a technology that has recently been developed for multiplexing hundreds of spatial modes for classical communication. We use our programmable MPLC platform to certify three-dimensional entanglement in two mutually unbiased bases, perform 400 arbitrary random transformations on entangled photons, and convert the mode basis of entangled photons for entanglement distribution.

Closing the Locality and Detection Loopholes in Multiparticle Entanglement Self-Testing.

First proposed by Mayers and Yao, self-testing provides a certification method to infer the underlying physics of quantum experiments in a black-box scenario. Numerous demonstrations have been reported to self-test various types of entangled states. However, all the multiparticle self-testing experiments reported so far suffer from both detection and locality loopholes. Here, we report the first experimental realization of multiparticle entanglement self-testing closing the locality loophole in a photonic system, and the detection loophole in a superconducting system, respectively. We certify three-party and four-party GHZ states with at least 0.84(1) and 0.86(3) fidelities in a device-independent way. These results can be viewed as a meaningful advance in multiparticle loophole-free self-testing, and also significant progress on the foundations of quantum entanglement certification.

Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement

For a multipartite quantum state, the maximal violation of all Bell inequalities constitutes a measure of its nonlocality (Loubenets 2012 J. Math. Phys. 53, 022201). In the present article, for the maximal violation of Bell inequalities by a pure bipartite state, possibly infinite-dimensional, we derive a new upper bound expressed in terms of the Schmidt coefficients of this state. This new upper bound allows us also to specify general analytical relations between the maximal violation of Bell inequalities by a bipartite quantum state, pure or mixed, and such entanglement measures for this state as ‘negativity’ and ‘concurrence’. To our knowledge, no any general analytical relations between measures for bipartite nonlocality and entanglement have been reported in the literature though, for a general bipartite state, specifically such relations are important for the entanglement certification and quantification scenarios. As an example, we apply our new results to finding upper bounds on nonlocality of bipartite coherent states intensively discussed last years in the literature in view of their experimental implementations.

Thermal biphotons

The observation of the Hanbury Brown and Twiss (HBT) effect with thermal light marked the birth of quantum optics. All the thermal sources considered to date did not feature quantum signatures of light, as they consisted of independent emitters that emit uncorrelated photons. Here, we propose and demonstrate an incoherent light source based on phase-randomized spatially entangled photons, which we coin thermal biphotons. We show that in contrast to thermal light, the width of the HBT peak for thermal biphotons is determined by their correlations, leading to violation of the Siegert relation and breakdown of the speckle-fluctuations interpretation. We further provide an alternative interpretation of the results by drawing a connection between the HBT effect and coherent backscattering of light. Finally, we discuss the role of spatial entanglement in the observed results, deriving a relation between the Schmidt number and the degree of violation of the Siegert relation under the double-Gaussian approximation of spontaneous parametric down conversion. Our work reflects new insights on the coherence properties of thermal light in the presence of entanglement, paving the way for entanglement certification using disorder averaged measurements.

“All-versus-nothing” proof of genuine tripartite steering and entanglement certification in the two-sided device-independent scenario

We consider the task of certification of genuine entanglement of tripartite states. For this purpose, we first present an "all-versus-nothing" proof of genuine tripartite Einstein-Podolsky-Rosen (EPR) steering by demonstrating the non-existence of a hybrid local hidden state (LHS) model in the tripartite network as a motivation to our main result. A full logical contradiction of the predictions of the hybrid LHS model with quantum mechanical outcome statistics for any three-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) states and pure W-class states is shown. Using logical contradiction, we can distinguish between the GGHZ and W-class state in a two-sided device-independent (2SDI) steering scenario. We next formulate a 2SDI steering inequality which is a generalization of the fine-grained steering inequality (FGI) derived in \cite{PKM14} for the tripartite scenario. We show that the maximum quantum violation of this tripartite FGI can be used to certify genuine entanglement of three-qubit pure states.

Simple and maximally robust processes with no classical common-cause or direct-cause explanation

Guided by the intuition of coherent superposition of causal relations, recent works presented quantum processes without classical common-cause and direct-cause explanation, that is, processes which cannot be written as probabilistic mixtures of quantum common-cause and quantum direct-cause relations (CCDC). In this work, we analyze the minimum requirements for a quantum process to fail to admit a CCDC explanation and present "simple" processes, which we prove to be the most robust ones against general noise. These simple processes can be realized by preparing a maximally entangled state and applying the identity quantum channel, thus not requiring an explicit coherent mixture of common-cause and direct-cause, exploiting the possibility of a process to have both relations simultaneously. We then prove that, although all bipartite direct-cause processes are bipartite separable operators, there exist bipartite separable processes which are not direct-cause. This shows that the problem of deciding weather a process is direct-cause processis notequivalent to entanglement certification and points out the limitations of entanglement methods to detect non-classical CCDC processes. We also present a semi-definite programming hierarchy that can detect and quantify the non-classical CCDC robustnesses of every non-classical CCDC process. Among other results, our numerical methods allow us to show that the simple processes presented here are likely to be also the maximally robust against white noise. Finally, we explore the equivalence between bipartite direct-cause processes and bipartite processes without quantum memory, to present a separable process which cannot be realized as a process without quantum memory.

Entangled ripples and twists of light: radial and azimuthal Laguerre–Gaussian mode entanglement

It is well known that photons can carry a spatial structure akin to a ‘twisted’ or ‘rippled’ wavefront. Such structured light fields have sparked significant interest in both classical and quantum physics, with applications ranging from dense communications to light–matter interaction. Harnessing the full advantage of transverse spatial photonic encoding using the Laguerre–Gaussian (LG) basis in the quantum domain requires control over both the azimuthal (twisted) and radial (rippled) components of photons. However, precise measurement of the radial photonic degree-of-freedom has proven to be experimentally challenging primarily due to its transverse amplitude structure. Here we demonstrate the generation and certification of full-field LG entanglement between photons pairs generated by spontaneous parametric down conversion in the telecom regime. By precisely tuning the optical system parameters for state generation and collection, and adopting recently developed techniques for precise spatial mode measurement, we are able to certify fidelities up to 85% and entanglement dimensionalities up to 26 in a 43-dimensional radial and azimuthal LG mode space. Furthermore, we study two-photon quantum correlations between nine LG mode groups, demonstrating a correlation structure related to mode group order and inter-modal cross-talk. In addition, we show how the noise-robustness of high-dimensional entanglement certification can be significantly increased by using measurements in multiple LG mutually unbiased bases. Our work demonstrates the potential offered by the full spatial structure of the two-photon field for enhancing technologies for quantum information processing and communication.

Optimal Entanglement Certification from Moments of the Partial Transpose.

For the certification and benchmarking of medium-size quantum devices, efficient methods to characterize entanglement are needed. In this context, it has been shown that locally randomized measurements on a multiparticle quantum system can be used to obtain valuable information on the so-called moments of the partially transposed quantum state. This allows one to infer some separability properties of a state, but how to use the given information in an optimal and systematic manner has yet to be determined. We propose two general entanglement detection methods based on the moments of the partially transposed density matrix. The first method is based on the Hankel matrices and provides a family of entanglement criteria, of which the lowest order reduces to the known p_{3}-positive-partial-transpose criterion proposed in A. Elben etal. [Phys. Rev. Lett. 125, 200501 (2020)PRLTAO0031-900710.1103/PhysRevLett.125.200501]. The second method is optimal and gives necessary and sufficient conditions for entanglement based on some moments of the partially transposed density matrix.

Optimal Entanglement Witnesses: A Scalable Data-Driven Approach.

Multipartite entanglement is a key resource allowing quantum devices to outperform their classical counterparts, and entanglement certification is fundamental to assess any quantum advantage. The only scalable certification scheme relies on entanglement witnessing, typically effective only for special entangled states. Here, we focus on finite sets of measurements on quantum states (hereafter called quantum data), and we propose an approach which, given a particular spatial partitioning of the system of interest, can effectively ascertain whether or not the dataset is compatible with a separable state. When compatibility is disproven, the approach produces the optimal entanglement witness for the quantum data at hand. Our approach is based on mapping separable states onto equilibrium classical field theories on a lattice and on mapping the compatibility problem onto an inverse statistical problem, whose solution is reached in polynomial time whenever the classical field theory does not describe a glassy system. Our results pave the way for systematic entanglement certification in quantum devices, optimized with respect to the accessible observables.