Towards the Communication Complexity of Entanglement Distillation Protocols
Year: 2002
Type: preprint
Abstract: Quantum entanglement distillation protocols are LOCC protocols that, over ``imperfect'' EPR pairs shared between Alice and Bob as input, output perfect or near-perfect EPR pairs. In this paper, we study the communication complexity of these protocols, that is, the minimal number of (classical) bits needed for Alice and Bob. To our knowledge, it is the first paper that studies entanglemend distillation protocols in the resource-bounded case. We consider 3 models for imperfect EPR pairs. In the measure-$r$ model, $r$ out of $n$ EPR pairs are measured by an adversary (and thus become ``corrupted''); in the depolarization model, the qubits of Bob underwent a depolarization channel; in the fidelity model, the only information Alice and Bob possess is the fidelity of the shared state. For the first 2 models, we prove tight and almost-tight bounds on the base case, i.e., how well Alice and Bob can do if they are not allowed to communicate. For the fidelity model, we prove a very tight lower bound (up to an additive constant) on the communication complexity. This lower bound implies the optimality of the Random Hash protocol in [ASY02].
Source: arXiv (Cornell University)
Authors: Andris Ambainis, Ke Yang
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2978787958