Distributed Entanglement

1999/07/24 by Valerie Coffman, Joydip Kundu, William K. Wootters · 1 voice · 270 citations
Computer Science · Physics and Astronomy · #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph

paper · pdf · doi:10.1103/physreva.61.052306

published as Phys.Rev.A61:052306,2000 · 13 pages LaTeX; references added, derivation of Eq. (11) simplified

arxiv created 1999/07/24 · openalex publication_date 2000/04/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider three qubits A, B, and C which may be entangled with each other. We show that there is a trade-off between A's entanglement with B and its entanglement with C. This relation is expressed in terms of a measure of entanglement called the "tangle," which is related to the entanglement of formation. Specifically, we show that the tangle between A and B, plus the tangle between A and C, cannot be greater than the tangle between A and the pair BC. This inequality is as strong as it could be, in the sense that for any values of the tangles satisfying the corresponding equality, one can find a quantum state consistent with those values. Further exploration of this result leads to a definition of the "three-way tangle" of the system, which is invariant under permutations of the qubits.

Citations

• Quantum teleportation using three-particle entanglement
• Mixed-State Entanglement and Distillation: Is there a “Bound” Entanglement in Nature?
• Entanglement of Formation of an Arbitrary State of Two Qubits
• Entanglement of a Pair of Quantum Bits
• Quantifying Entanglement

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Discussions

• If particles A and B are maximally entangled, then neither can be entangled to any particle C. This is called monogamy of entanglement. Distributed Entanglement: https://arxiv.org/abs/quant-ph/9907047 [stackexchange, 1 points]