Distillation of Greenberger-Horne-Zeilinger States by Combinatorial Methods

TY - JOUR

T1 - Distillation of Greenberger-Horne-Zeilinger States by Combinatorial Methods

AU - Vrana, Peter

AU - Christandl, Matthias

PY - 2019

Y1 - 2019

N2 - We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states distillable from pure multipartite states by local operations and classical communication (LOCC). Our proof is based on a modification of a combinatorial argument used in the fast matrix multiplication algorithm of Coppersmith and Winograd. Previous use of methods from algebraic complexity in quantum information theory concerned transformations with stochastic LOCC (SLOCC), resulting in an asymptotically vanishing success probability. In contrast, our new protocol works with an asymptotically vanishing error.

AB - We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states distillable from pure multipartite states by local operations and classical communication (LOCC). Our proof is based on a modification of a combinatorial argument used in the fast matrix multiplication algorithm of Coppersmith and Winograd. Previous use of methods from algebraic complexity in quantum information theory concerned transformations with stochastic LOCC (SLOCC), resulting in an asymptotically vanishing success probability. In contrast, our new protocol works with an asymptotically vanishing error.

KW - Quantum entanglement

KW - local operations and classical communication

KW - multipartite entanglement distillation

U2 - 10.1109/TIT.2019.2908646

DO - 10.1109/TIT.2019.2908646

M3 - Journal article

SN - 0018-9448

VL - 65

SP - 5945

EP - 5958

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

IS - 9

ER -