Entanglement is a fundamental aspect of quantum physics, both conceptually and for its many applications. Classifying an arbitrary multipartite state as entangled or separable -- a task referred to as the separability problem -- poses a significant challenge, since a state can be entangled with respect to many different of its partitions. We develop a certification pipeline that feeds the statistics of random local measurements into a non-linear dimensionality reduction algorithm, to determine with respect to which partitions a given quantum state is entangled. After training a model on randomly generated quantum states, entangled in different partitions and of varying purity, we verify the accuracy of its predictions on simulated test data, and finally apply it to states prepared on IBM quantum computing hardware.
We consider the problem of demonstrating non-Bell-local correlations by performing local measurements in randomly chosen triads, i.e., three mutually unbiased bases, on a multipartite Greenberger-Horne-Zeilinger state. Our main interest lies on investigating the feasibility of using these correlations to certify multipartite entanglement in a device-independent setting. In contrast to previous works, our numerical results up to the eight-partite scenario suggest that if each triad is randomly but uniformly chosen according to the Haar measure, one always (except possibly for a set of measure z…
Techniques developed for device-independent characterizations allow one to certify certain physical properties of quantum systems without assuming any knowledge of their internal workings. Such a certification, however, often relies on the employment of device-independent witnesses catered for the particular property of interest. In this work, we consider a one-parameter family of multipartite, two-setting, two-outcome Bell inequalities and demonstrate the extent to which they are suited for the device-independent certification of genuine many-body entanglement (and hence the entanglement dept…
Genuine multipartite entanglement represents the strongest type of entanglement, which is an essential resource for quantum information processing. Standard methods to detect genuine multipartite entanglement, e.g., entanglement witnesses, state tomography, or quantum state verification, require full knowledge of the Hilbert space dimension and precise calibration of measurement devices, which are usually difficult to acquire in an experiment. The most radical way to overcome these problems is to detect entanglement solely based on the Bell-like correlations of measurement outcomes collected i…
Recently [Cavalcanti \textit{et al.} Nat Commun \textbf{6}, 7941 (2015)] proposed a method to certify the presence of entanglement in asymmetric networks, where some users do not have control over the measurements they are performing. Such asymmetry naturally emerges in realistic situtations, such as in cryptographic protocols over quantum networks. Here we implement such "semi-device independent" techniques to experimentally witness all types of entanglement on a three-qubit photonic W state. Furthermore we analise the amount of genuine randomness that can be certified in this scenario from a…
Multipartite entanglement, such as witnessed through the quantum Fisher information (QFI), is a crucial resource for quantum technologies, but its experimental certification is highly challenging. Here, we propose an experimentally friendly protocol to measure the QFI. It relies on recording the short-time dynamics of simple observables after a quench from a thermal state, works for spins, bosons, and fermions, and can be implemented in standard cold-atom experiments and other platforms with temporal control over the system Hamiltonian. To showcase the protocol, we simulate it for the one-dime…
Device independent certification schemes have gained a lot of interest lately, not only for their applications in quantum information tasks but also their implications towards foundations of quantum theory. The strongest form of device independent certification, known as self-testing, often requires for a Bell inequality to be maximally violated by specific quantum states and measurements. In this work, using the techniques developed recently in [S. Sarkar et al., npj Quantum Inf. 7, 151 (2021)], we provide the first self-testing scheme for the multipartite Greenberger-Horne-Zeilinger (GHZ) st…
Ensuring the correct functioning of quantum error correction (QEC) circuits is crucial to achieve fault tolerance in realistic quantum processors subjected to noise. The first checkpoint for a fully operational QEC circuit is to create genuine multipartite entanglement across all subsystems of physical qubits. We introduce a conditional witnessing technique to certify genuine multipartite entanglement (GME) that is efficient in the number of subsystems and, importantly, robust against experimental noise and imperfections. Specifically, we prove that the detection of entanglement in a linear nu…
Graph states -- one of the most representative families of multipartite entangled states, are important resources for multiparty quantum communication, quantum error correction, and quantum computation. Device-independent certification of highly entangled graph states plays a prominent role in the quantum information processing tasks. Here we have experimentally demonstrated device-independent certification for multipartite graph states, by adopting the robust self-testing scheme based on scalable Bell inequalities. Specifically, the prepared multi-qubit Greenberger-Horne-Zeilinger (GHZ) state…
Experimental certification of multipartite Bell correlations using only few-body symmetric correlations
East China Normal University（华东师范大学）；National University of Singapore（新加坡国立大学）；Universiteit Leiden（莱顿大学）；Sun Yat-sen University（中山大学）；Quantum Science Center of Guangdong–Hong Kong–Macao Greater Bay Area (Guangdong)（粤港澳大湾区量子科学中心（广东））
We extend a recent method to detect lower bounds to the quantum capacity of quantum communication channels by considering realistic scenarios with general input probe states and arbitrary detection procedures at the output. Realistic certification relies on a new bound for the coherent information of a quantum channel that can be applied with arbitrary bipartite mixed input states and generalized output measurements.
We present a protocol in which two or more parties can share multipartite entanglement over noisy quantum channels. The protocol is based on the entanglement purification presented by Shor and Preskill [Phys. Rev. Lett. 85, 441 (2000)] and the quantum teleportation via an isotropic state. We show that a nearly perfect purification implies a nearly perfect sharing of multipartite entanglement between two parties so that the protocol can assure a faithful sharing of multipartite entanglement with Shor and Preskill's proof on the entanglement purification.
A quantum internet aims at harnessing networked quantum technologies, namely by distributing bipartite entanglement between distant nodes. However, multipartite entanglement between the nodes may empower the quantum internet for additional or better applications for communications, sensing, and computation. In this work, we present an algorithm for generating multipartite entanglement between different nodes of a quantum network with noisy quantum repeaters and imperfect quantum memories, where the links are entangled pairs. Our algorithm is optimal for GHZ states with 3 qubits, maximising sim…
Limits on Broadcasting Genuine Multipartite Entanglement in Quantum Networks
S. N. Bose National Centre for Basic Sciences（S.N. 玻色基础科学国家中心）；Okinawa Institute of Science and Technology Graduate University（冲绳科学技术大学院大学）；Indian Institute of Technology Indore（印度理工学院印多尔分校）
The Clauser-Horne-Shimony-Holt inequality was originally proposed as a Bell inequality to detect nonlocality in bipartite systems. However, it can also be used to certify the nonlocality of multipartite quantum states. We apply this to study the nonlocality of multipartite Greenberger-Horne-Zeilinger, W and graph states under local decoherence processes. We derive lower bounds on the critical local-noise strength tolerated by GHZ states before becoming local. In addition, for the whole noisy dynamics, we derive lower bounds on the corresponding nonlocal content for the three classes of states.…
A quantum communication network can be constructed by distributing a multipartite entangled state to space-separated nodes. Entangled optical beams with highest flying speed and measurable brightness can be used as carriers to convey information in quantum communication networks. Losses and noises existing in real communication channels will reduce or even totally destroy entanglement. The phenomenon of disentanglement will result in the complete failure of quantum communication. Here, we present the experimental demonstrations on the disentanglement and the entanglement revival of tripartite …
Suppose that $m$ senders want to transmit classical information to $n$ receivers with zero probability of error using a noisy multipartite communication channel. The senders are allowed to exchange classical, but not quantum, messages among themselves, and the same holds for the receivers. If the channel is classical, a single use can transmit information if and only if multiple uses can. In sharp contrast, we exhibit, for each $m$ and $n$ with $m\ge 2$ or $n\ge 2$, a quantum channel of which a single use is not able to transmit information yet two uses can. This latter property requires and i…
The study of entanglement in multipartite quantum states plays a major role in quantum information theory and genuine multipartite entanglement signals one of its strongest forms for applications. However, its characterization for general (mixed) states is a highly nontrivial problem. We introduce a particularly simple subclass of multipartite states, which we term pair-entangled network (PEN) states, as those that can be created by distributing exclusively bipartite entanglement in a connected network. We show that genuine multipartite entanglement in a PEN state depends on both the level of …
We investigate the effect of noisy channels in a classical information transfer through a multipartite state which acts as a substrate for the distributed quantum dense coding protocol between several senders and two receivers. The situation is qualitatively different from the case with one or more senders and a single receiver. We obtain an upper bound on the multipartite capacity which is tightened in case of the covariant noisy channel. We also establish a relation between the genuine multipartite entanglement of the shared state and the capacity of distributed dense coding using that state…
The semi-device-independent framework allows one to draw conclusions about properties of an unknown quantum system under weak assumptions. Here we present a semi-device-independent scheme for the characterisation of multipartite entanglement based around a game played by several isolated parties whose devices are uncharacterised beyond an assumption about the dimension of their Hilbert spaces. Our scheme can certify that an $n$-partite high-dimensional quantum state features genuine multipartite entanglement. Moreover, the scheme can certify that a joint measurement on $n$ subsystems is entang…
The future of quantum communication relies on quantum networks composed by observers sharing multipartite quantum states. The certification of multipartite entanglement will be crucial to the usefulness of these networks. In many real situations it is natural to assume that some observers are more trusted than others in the sense that they have more knowledge of their measurement apparatuses. Here we propose a general method to certify all kinds of multipartite entanglement in this asymmetric scenario and experimentally demonstrate it in an optical experiment. Our results, which can be seen as…
We introduce the distribution of a secret multipartite entangled state in a real-world scenario as a quantum primitive. We show that in the presence of noisy quantum channels (and noisy control operations) any state chosen from the set of two-colorable graph states (CSS codewords) can be created with high fidelity while it remains unknown to all parties. This is accomplished by either blind multipartite entanglement purification, which we introduce in this paper, or by multipartite entanglement purification of enlarged states, which offers advantages over an alternative scheme based on standar…
Genuine multipartite entanglement (GME) offers more significant advantages in quantum information compared with entanglement. We propose a sufficient criterion for the detection of GME based on local sum uncertainty relations for chosen observables of subsystems. We apply the criterion to detect the GME properties of noisy $n$-partite W state when $n = 3, 4, 5$ and $6$, and find that the criterion can detect more noisy W states when $n$ ranges from 4 to 6. Moreover, the criterion is also used to detect the genuine entanglement of $3$-qutrit state. The result is stronger than that based on GME …
We propose an entanglement purification protocol for high-dimensional multipartite systems. In the protocol we can select a subensemble in a pure generalized Greenberger-Horne-Zeilinger (GHZ) state. This post-selection can be made by detecting the noise which contaminated the initial pure ensemble when the systems past through a noisy environment. For the detection of noise we investigate correlation properties of GHZ states and analyze their possible errors due to a noisy environment. We show that the presented protocol is more efficient than a simple generalization of the purification protoc…
We show how to efficiently send an M-partite entangled state along a spin chain of arbitrary size. Specifically, we show how an entangled M-partite W sate can be almost flawlessly transmitted from one end (Alice) to the other end (Bob) of a spin-1/2 chain described by a slightly modified XX model. We achieve an almost perfect transmission without employing external magnetic fields or modulating the coupling constants among the spins of the chain, the two standard approaches used to achieve a good transmission efficiency. Moreover, the protocol here proposed can be used to transform an M-partit…
Randomness Certification and Trade-offs in the Prepare-and-Broadcast Scenario
Federal University of Rio Grande do Norte（北里奥格兰德联邦大学）；International Institute of Physics, Federal University of Rio Grande do Norte（北里奥格兰德联邦大学国际物理研究所）；QuIIN - Quantum Industrial Innovation, EMBRAPII CIMATEC Competence Center in Quantum Technologies, SENAI CIMATEC（QuIIN-量子工业创新，EMBRAPII CIMATEC量子技术能力中心，SENAI CIMATEC）；Center for Macroscopic Quantum States bigQ, Department of Physics, Technical University of Denmark（丹麦技术大学物理学系宏观量子态bigQ中心）
The celebrated Einstein-Podolsky-Rosen quantum steering has a complex structure in the multipartite scenario. We show that a naively defined criterion for multipartite steering allows, like in Bell nonlocality, for a contradictory effect whereby local operations could create steering seemingly from scratch. Nevertheless, neither in steering nor in Bell nonlocality has this effect been experimentally confirmed. Operational consistency is reestablished by presenting a suitable redefinition: there is a subtle form of steering already present at the start, and it is only exposed -- as opposed to c…
We introduce the class of Genuinely Local Operation and Shared Randomness (LOSR) Multipartite Nonlocal correlations, that is, correlations between N parties that cannot be obtained from unlimited shared randomness supplemented by any composition of (N-1)-shared causal Generalized-Probabilistic-Theory (GPT) resources. We then show that noisy N-partite GHZ quantum states as well as the 3-partite W quantum state can produce such correlations. This proves, if the operational predictions of quantum theory are correct, that Nature's nonlocality must be boundlessly multipartite in any causal GPT. We …
We transform the way of finding entanglement criterion into two steps: to obtain necessary criterion of separability by maximizing an algebra function for a set of characteristic variables of the witness operator and the given number of partitions, then to obtain the sufficient criterion by minimizing an algebra function with respect to the characteristic variables for a given quantum state. Our method avoids the semi-definite program calculation in the witness operator entanglement detection. The necessary and sufficient criterion of separability for the three qubit X shaped state is given to…
Being able to implement effective entanglement distribution in noisy environments is a key step towards practical quantum communication, and long-term efforts have been made on the development of it. Recently, it has been found that the null-result weak measurement (NRWM) can be used to enhance probabilistically the entanglement of a single copy of amplitude-damped entangled state. This paper investigates remote distributions of bipartite and multipartite entangled states in the amplitudedamping environment by combining NRWMs and entanglement distillation protocols (EDPs). We show that the NRW…
A Multipartite entangled state has many different kinds of entanglement specified by the number of partitions. The most essential example of multipartite entanglement is the entanglement of multi-qubit Greenberger-Horne-Zeilinger (GHZ) state in white noise. We explicitly construct the entanglement witnesses for these states with stabilizer generators of the GHZ states. For a $N$ qubit GHZ state in white noise, we demonstrate the necessary and sufficient criterion of separability when it is divided into $k$ parties with $N\leq 2k-1$ for arbitrary $N$ and $k$. The criterion covers more than a ha…
