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Can Quantum Entanglement Detection Schemes Improve Search?
"... Abstract. Quantum computation, in particular Grover’s algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an N element database require at most O(N) time complexity. Grover’s algorithm is able to ..."
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Abstract. Quantum computation, in particular Grover’s algorithm, has aroused a great deal of interest since it allows for a quadratic speedup to be obtained in search procedures. Classical search procedures for an N element database require at most O(N) time complexity. Grover’s algorithm is able to find a solution with high probability in O( N) time through an amplitude amplification scheme. In this work we draw elements from both classical and quantum computation to develop an alternative search proposal based on quantum entanglement detection schemes. In 2002, Horodecki and Ekert proposed an efficient method for direct detection of quantum entanglement. Our proposition to quantum search combines quantum entanglement detection alongside entanglement inducing operators. Grover’s quantum search relies on measuring a quantum superposition after having applied a unitary evolution. We deviate from the standard method by focusing on finetuning a unitary operator in order to infer the solution with certainty. Our proposal sacrifices space for speed and depends on the mathematical properties of linear positive maps Λ which have not been operationally characterized. Whether such a Λ can be easily determined remains an open question.
An efficient test for product states
, 2010
"... We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state ψ 〉 whose maximum overlap with a product state is 1 − ɛ, the test passes with probability 1 − Θ(ɛ), regardless of n or the local dimensions of the ..."
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We give a test that can distinguish efficiently between product states of n quantum systems and states which are far from product. If applied to a state ψ 〉 whose maximum overlap with a product state is 1 − ɛ, the test passes with probability 1 − Θ(ɛ), regardless of n or the local dimensions of the individual systems. The test uses two copies of ψ〉. We prove correctness of this test as a special case of a more general result regarding stability of maximum output purity of the depolarising channel. One application of the test is to Quantum MerlinArthur games, where we show that a witness from two unentangled provers can simulate a witness from arbitrarily many unentangled provers, up to a constant loss of soundness. Our test can also be used to construct an efficient test for determining whether a unitary operator is a tensor product. 1
Teleportation of entanglement over 143 km
, 2014
"... As a direct consequence of the nocloning theorem [1], the deterministic amplification as in classical communication is impossible for quantum states. This calls for more advanced techniques in a future global quantum network [2, 3], e.g. for cloud quantum computing [4, 5, 6]. A unique solution is ..."
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As a direct consequence of the nocloning theorem [1], the deterministic amplification as in classical communication is impossible for quantum states. This calls for more advanced techniques in a future global quantum network [2, 3], e.g. for cloud quantum computing [4, 5, 6]. A unique solution is the teleportation of an entangled state, i.e. entanglement swapping [7], representing the central resource to relay entanglement between distant nodes. Together with entanglement purification [8, 9, 10, 11] and a quantum memory [12, 13] it constitutes a socalled quantum repeater [9, 14]. Since the afore mentioned building blocks have been individually demonstrated in laboratory setups only, the applicability of the required technology in realworld scenarios remained to be proven. Here we present a freespace entanglementswapping experiment between the Canary Islands of La Palma and Tenerife, verifying the presence of quantum entanglement between two previously independent photons separated by 143 km. We obtained an expectation value for the entanglementwitness operator, more than 6 standard deviations beyond the classical limit. By consecutive generation of the two required photon pairs and spacelike separation of the relevant measurement events, we also showed the feasibility of the swapping protocol in a longdistance scenario, where the independence of the nodes is highly demanded. Since our results already allow for efficient implementation of entanglement purification, we anticipate our assay to lay the ground for a fullyfledged quantum repeater over a realistic highloss and even turbulent quantum channel.
COMPUTABLE CONSTRAINTS ON ENTANGLEMENTSHARING OF MULTIPARTITE QUANTUM STATES
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Associate Advisor
, 2014
"... This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to determine the quantum limit of Belltype linear inequalities. In c ..."
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This work develops analytic methods to quantitatively demarcate quantum reality from its subset of classical phenomenon, as well as from the superset of general probabilistic theories. Regarding quantum nonlocality, we discuss how to determine the quantum limit of Belltype linear inequalities. In contrast to semidefinite programweights, by means of leveraging the Hermiticity of quantum states. Recognizing that classical correlations correspond to measurements made on separable states, we also introduce a practical method for obtaining sufficient separability criteria. We specifically vet the candidacy of driven and undriven superradiance as schema for entanglement generation. We conclude by reviewing current approaches to quantum contextuality, emphasizing the operational distinction between nonlocal and ar X iv:1