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Register a new userRobust Self-Testing of Multiparticle Entanglement
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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. Due to 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-particle quantum entanglement. 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 the observed input-output statistics, we certify the genuine four-photon entanglement and further estimate their qualities with respect to realistic noise in a device-independent manner.
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It is well-known that observing nonlocal correlations allows us to draw conclusions about the quantum systems under consideration. In some cases this yields a characterisation which is essentially complete, a phenomenon known as self-testing. Self-testing becomes particularly interesting if we can make the statement robust, so that it can be applied to a real experimental setup. For the simplest self-testing scenarios the most robust bounds come from the method based on operator inequalities. In this work we elaborate on this idea and apply it to the family of tilted CHSH inequalities. These inequalities are maximally violated by partially entangled two-qubit states and our goal is to estimate the quality of the state based only on the observed violation. For these inequalities we have reached a candidate bound and while we have not been able to prove it analytically, we have gathered convincing numerical evidence that it holds. Our final contribution is a proof that in the usual formulation, the CHSH inequality only becomes a self-test when the violation exceeds a certain threshold. This shows that self-testing scenarios fall into two distinct classes depending on whether they exhibit such a threshold or not.
We generalize the procedure of entanglement swapping to obtain a scheme for manipulating entanglement in multiparticle systems. We describe how this scheme allows to establish multiparticle entanglement between particles belonging to distant users in a communication network through a prior distribution of singlets followed by only local measurements. We show that this scheme can be regarded as a method of generating entangled states of many particles and compare it with existing schemes using simple quantum computational networks. We highlight the practical advantages of using a series of entanglement swappings during the distribution of entangled particles between two parties. Applications of multiparticle entangled states in cryptographic conferencing and in reading messages from more than one source through a single measurement are also described.
Based on the ranks of reduced density matrices, we derive necessary conditions for the separability of multiparticle arbitrary-dimensional mixed states, which are equivalent to sufficient conditions for entanglement. In a similar way we obtain necessary conditions for the separability of a given mixed state with respect to partitions of all particles of the system into subsets. The special case of pure states is discussed separately.
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 $f_s/f_tapprox 0.988$ between the fidelity estimated from self-testing and that estimated from full tomography, proving high performance of self-testing methods.
We study the preparation and manipulation of states involving a small number of interacting particles. By controlling the splitting and fusing of potential wells, we show how to interconvert Mott-insulator-like and trapped BEC-like states. We also discuss the generation of Schrodinger cat states by splitting a microtrap and taking into practical consideration the asymmetry between the resulting wells. These schemes can be used to perform multiparticle interferometry with neutral atoms, where interference effects can be observed only when all the participating particles are measured.
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