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arXiv:quant-ph/0112022 · Journal of Physics A Mathematical and General

Entanglement swapping between multi-qudit systems

Jan Bouda, Vladimír Bužek

Published May 9, 2001• 38 citations
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Abstract

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.

DOI
10.1088/0305-4470/34/20/304

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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.
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We propose a measurement scheme of generalized Bell states in which, although entanglement is destroyed, the nonlocality feature can be preserved and swapped. Here we consider two quantum systems: one consisting of two-party three-level maximal entangled pairs; the other being three-party two-level maximal entangled pairs. It is found that these local immeasurable states can be prepared without any classical communication and local operation. Moreover, nonmaximal entangled states cannot preserve nonlocality.
We present a general scheme for multiparty-controlled teleportation of an arbitrary m -qudit ( d -dimensional quantum system) state by using non-maximally entangled states as the quantum channel. The sender performs m generalized Bell-state measurements on her 2 m particles, the controllers take some single-particle measurements with the measuring basis X d and the receiver only needs to introduce one auxiliary two-level particle to extract quantum information probabilistically with the fidelity unit if he cooperates with all the controllers. All the parties can use some decoy photons to set up their quantum channel securely, which will forbid a dishonest party to eavesdrop freely. This scheme is optimal as the probability that the receiver obtains the originally unknown m -qudit state equals the entanglement of the quantum channel.
Exploring universal entanglement structure in many-body systems is both fundamental and challenging, particularly when the system undergoes non-unitary operations. In this work, we uncover a universal mechanism for realizing maximal entanglement swapping in fermionic Gaussian states subjected to projective Bell measurements. We consider two initially decoupled, half-filled copies of a free-fermion system in arbitrary dimensions and perform post-selective Bell measurements on half of the corresponding sites across the two copies. Remarkably, the post-measurement state factorizes into a product of Bell pairs, establishing maximal interlayer entanglement entirely independent of the initial Gaussian state. We derive this post-measurement state exactly for general particle-number-conserving fermionic Gaussian states, establishing both the validity and universality of the mechanism, with numerical simulations serving as consistency checks. This phenomenon arises from a robust interplay between fermionic statistics and Gaussianity, revealing a distinct fermionic route to measurement-induced maximal entanglement.