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Register a new userExperimental Verification of Anisotropic Invariance for Three-Qubit States
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We experimentally test the recently predicted anisotropic invariance properties of pure three-qubit states, via generation and measurement of polarisation-path entangled three-qubit states. These properties do not require aligned reference frames and can be determined from measurements on any two of the qubits. They have several applications, such as a universal ordering of pairwise quantum correlations, strong monogamy relations for Bell inequalities and quantum steering, and a complementarity relation for Bell nonlocality versus 3-tangle, some of which we also test. The results indicate that anisotropic invariance, together with the three qubit Bloch vector lengths, can provide a robust and complete set of invariants for such states under local unitary transformations.
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In this paper, we investigate the genuine three-way nonlocality which is recognized as the strongest form of tripartite correlations. We consider theoretically and experimentally a series of suitable Bell-type inequalities a violation of which is sufficient for the detection of three-way nonlocality. For the generalized GHZ (gGHZ) states, it is demonstrated that they do violate tripartite Bell-type inequalities for any degree of tripartite entanglement even if they do not violate Svetlichny inequality. It implies that three-way entangled gGHZ can always exhibit genuine three-way nonlocality under the requirement of time-order-dependent principle. Furthermore, we have determined the maximal amount of noise admissible for the gGHZ states to still remain genuine three-way nonlocal.
Preparing and certifying bound entangled states in the laboratory is an intrinsically hard task, due to both the fact that they typically form narrow regions in the state space, and that a certificate requires a tomographic reconstruction of the density matrix. Indeed, the previous experiments that have reported the preparation of a bound entangled state relied on such tomographic reconstruction techniques. However, the reliability of these results crucially depends on the extra assumption of an unbiased reconstruction. We propose an alternative method for certifying the bound entangled character of a quantum state that leads to a rigorous claim within a desired statistical significance, while bypassing a full reconstruction of the state. The method is comprised by a search for bound entangled states that are robust for experimental verification, and a hypothesis test tailored for the detection of bound entanglement that is naturally equipped with a measure of statistical significance. We apply our method to families of states of $3times 3$ and $4times 4$ systems, and find that the experimental certification of bound entangled states is well within reach.
We introduce a set of Bell inequalities for a three-qubit system. Each inequality within this set is violated by all generalized GHZ states. More entangled a generalized GHZ state is, more will be the violation. This establishes a relation between nonlocality and entanglement for this class of states. Certain inequalities within this set are violated by pure biseparable states. We also provide numerical evidence that at least one of these Bell inequalities is violated by a pure genuinely entangled state. These Bell inequalities can distinguish between separable, biseparable and genuinely entangled pure three-qubit states. We also generalize this set to n-qubit systems and may be suitable to characterize the entanglement of n-qubit pure states.
We report an experimental realization of adaptive Bayesian quantum state tomography for two-qubit states. Our implementation is based on the adaptive experimental design strategy proposed in [F.Huszar and N.M.T.Houlsby, Phys.Rev.A 85, 052120 (2012)] and provides an optimal measurement approach in terms of the information gain. We address the practical questions, which one faces in any experimental application: the influence of technical noise, and behavior of the tomographic algorithm for an easy to implement class of factorized measurements. In an experiment with polarization states of entangled photon pairs we observe a lower instrumental noise floor and superior reconstruction accuracy for nearly-pure states of the adaptive protocol compared to a non-adaptive. At the same time we show, that for the mixed states the restriction to factorized measurements results in no advantage for adaptive measurements, so general measurements have to be used.
The states of three-qubit systems split into two inequivalent types of genuine tripartite entanglement, namely the Greenberger-Horne-Zeilinger (GHZ) type and the $W$ type. A state belonging to one of these classes can be stochastically transformed only into a state within the same class by local operations and classical communications. We provide local quantum operations, consisting of the most general two-outcome measurement operators, for the deterministic transformations of three-qubit pure states in which the initial and the target states are in the same class. We explore these transformations, originally having standard GHZ and standard $W$ states, under the local measurement operations carried out by a single party and $p$ ($p=2,3$) parties (successively). We find a notable result that the standard GHZ state cannot be deterministically transformed to a GHZ-type state in which all its bipartite entanglements are nonzero, i.e., a transformation can be achieved with unit probability when the target state has at least one vanishing bipartite concurrence.
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