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arXiv:2009.02555

Entanglement swapping of d-dimension bipartite and multi-particle entangled states

Zhaoxu Ji, Peiru Fan, Huanguo Zhang

Published Sep 5, 2020• 1 citation
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Abstract

We consider entanglement swapping schemes for several d-level entangled states, including d-dimension maximally entangled states, GHZ-class states, and cat-like states, where each scheme is realized by generalized Bell measurements. We also consider the entanglement swapping chains proposed by Hardy et al. [Phys. Rev. A. 62(5) 052315] for maximally entangled states. Applications of the proposed entanglement swapping schemes in quantum cryptography are described.

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We consider entanglement swapping schemes for several d-level entangled states, including d-dimension maximally entangled states, GHZ-class states, and cat-like states, where each scheme is realized by generalized Bell measurements. We also consider the entanglement swapping chains proposed by Hardy et al. [Phys. Rev. A. 62(5) 052315] for maximally entangled states. Applications of the proposed entanglement swapping schemes in quantum cryptography are described.
We consider entanglement-swapping schemes with general (rather than maximally) entangled bipartite states of arbitary dimension shared pairwise between three or more parties in a chain. The intermediate parties perform generalized Bell measurements with the result that the two end parties end up sharing an entangled state which can be converted into maximally entangled states. We obtain an expression for the average amount of maximal entanglement concentrated in such a scheme and show that in a certain reasonably broad class of cases this scheme is provably optimal and that, in these cases, the amount of entanglement concentrated between the two ends is equal to that which could be concentrated from the weakest link in the chain.
We introduce a class of multi-particle Greenberger-Horne-Zeilinger (GHZ) states, and study entanglement swapping between two qubit systems for Bell states and for the class of GHZ states, respectively. We generalize the bi-system entanglement swapping of Bell states and multi-particle GHZ states to any number of qubit systems. We further study the entanglement swapping schemes between any number of Bell states and between any number of the introduced GHZ states in a detailed way, and propose the schemes that can generate two identical GHZ states. We illustrate the applications of such schemes in quantum information processing by proposing quantum protocols for quantum key distribution, quantum secret sharing and quantum private comparison.
We generalize the entanglement swapping scheme originally proposed for two pairs of qubits to an arbitrary number q of systems composed from an arbitrary number m j of qudits. Each of the systems is supposed to be prepared in a maximally entangled state of m j qudits, while different systems are not correlated at all. We show that when a set of ∑ q j = 1 a j particles (from each of the q systems a j particles are measured) is subjected to a generalized Bell-type measurement, the resulting set of ∑ q j = 1 ( m j - a j ) particles will collapse into a maximally entangled state.