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Register a new userBound entangled states fit for robust experimental verification
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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.
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We derive an explicit analytic estimate for the entanglement of a large class of bipartite quantum states which extends into bound entanglement regions. This is done by using an efficiently computable concurrence lower bound, which is further employed to numerically construct a volume of $3 times 3$ bound entangled states.
Bound entanglement, being entangled yet not distillable, is essential to our understandings of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we shall construct such kind of nonlocal bound entangled states for all finite dimensions larger than two, making possible their experimental demonstrations on most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality.
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.
Self-testing refers to a method with which a classical user can certify the state and measurements of quantum systems in a device-independent way. Especially, the self-testing of entangled states is of great importance in quantum information process. A comprehensible example is that violating the CHSH inequality maximally necessarily implies the bipartite shares a singlet. One essential question in self-testing is that, when one observes a non-maximum violation, how close is the tested state to the target state (which maximally violates certain Bell inequality)? The answer to this question describes the robustness of the used self-testing criterion, which is highly important in a practical sense. Recently, J. Kaniewski predicts two analytic self-testing bounds for bipartite and tripartite systems. In this work, we experimentally investigate these two bounds with high quality two-qubit and three-qubit entanglement sources. The results show that these bounds are valid for various of entangled states we prepared, and thus, we implement robust self-testing processes which improve the previous results significantly.
We present a construction of new bound entangled states from given bound entangled states for arbitrary dimensional bipartite systems. One way to construct bound entangled states is to show that these states are PPT (positive partial transpose) and violate the range criterion at the same time. By applying certain operators to given bound entangled states or to one of the subsystems of the given bound entangled states, we obtain a set of new states which are both PPT and violate the range criterion. We show that the derived bound entangled states are not local unitary equivalent to the original bound entangled states by detail examples.
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