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arXiv:1612.08578

Complete and Deterministic Bell State Measurement Using Nonlocal Spin Products

Keiichi Edamatsu

Published Dec 27, 2016• 3 citations
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Abstract

A simple protocol for complete and deterministic Bell state measurement is proposed. It consists of measurements of nonlocal spin product operators with the help of shared entanglement as an ancillary resource. The protocol realizes not only nonlocal Bell state measurement between a pair of distant qubits but also a complete Bell filter that transmits either one of the Bell states indicated by the measurement outcome. These schemes will be useful in quantum technologies where nonlocal Bell state measurement is indispensable.

DOI
10.48550/arxiv.1612.08578

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Abstract Measuring a nonlocal observable on a space-like separated quantum system is a resource-hungry and experimentally challenging task. Several theoretical measurement schemes have already been proposed to increase its feasibility, using a shared maximally-entangled ancilla. We present a new approach to this problem, using the language of generalized quantum measurements, to show that it is actually possible to measure a nonlocal spin product observable without necessarily requiring a maximally-entangled ancilla. This approach opens the door to more economical arbitrary-strength nonlocal measurements, with applications ranging from nonlocal weak values to possible new tests of Bell inequalities. The relation between measurement strength and the amount of ancillary entanglement needed is made explicit, bringing a new perspective on the links that tie quantum nonlocality, entanglement and information transmission together.
We propose a protocol and physical implementation for partial Bell-state measurements of Fermionic qubits, allowing for deterministic quantum computing in solid-state systems without the need for two-qubit gates. Our scheme consists of two spin qubits in a double quantum dot where the two dots have different Zeeman splittings and resonant tunneling between the dots is only allowed when the spins are antiparallel. This converts spin parity into charge information by means of a projective measurement and can be implemented with established technologies. This measurement-based qubit scheme greatly simplifies the experimental realization of scalable quantum computers in electronic nanostructures.
With reference to a system of n spin‐1/2 particles which are distributed between two space‐like separated parties, we present two procedures to perform an instantaneous and local measurement of any nondegenerate observable having as its eigenstates the orthonormal basis of n‐partite entangled states introduced in [S. Bose, V. Vedral, and P. L. Knight, Phys. Rev. A 57, 822 (1998)], whose vectors reduce to the Bell states for n = 2 and to the GHZ states for n = 3. The first procedure implements a genuine nondemolition measurement by resorting to two n‐particle entangled states as an additional resource. The second one distinguishes between those eigenstates, though without preserving them (i.e., it is a demolition measurement), but it requires only a single couple of additional particles in a (maximally entangled) Bell state. Both methods are instantaneous, in the sense that the outcome of the measurement process is completely determined as soon as the local operations, whose duration can be made as short as one wishes, have been independently performed in the two distant regions where the particles are located.
Summary form only given. The idea of quantum teleportation is to utilize the nonlocal correlations between an Einstein-Podolsky-Rosen pair of particles to prepare a quantum system in some state, which is the exact replica of an arbitrary unknown state of a distant individual system. Three experiments in this direction were published recently. In this paper, we experimentally demonstrate a quantum teleportation scheme which satisfies all four of the above conditions. The input state is an arbitrary polarization state and the BSM can distinguish all four orthogonal Bell states so that the state has a 100% certainty to be teleported in principle. This is because the BSM is based on nonlinear interactions which are necessary and non-trivial physical processes for correlating the input state and the entangled EPR pair.
We propose a simple scheme for complete Bell-state measurement of photons using hyperentangled states---entangled in multiple degrees of freedom. In addition to hyperentanglement, our scheme requires only linear optics and single photon detectors, and is realizable with current technology. At the cost of additional classical communication, our Bell-state measurement can be implemented nonlocally. We discuss the possible application of these results to quantum dense coding and quantum teleportation.