dorsal/arxiv
View SchemaTowards the Classical Communication Complexity of Entanglement Distillation Protocols with Incomplete Information
| Authors | Andris Ambainis, Ke Yang |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0207090 |
| URL | https://arxiv.org/abs/quant-ph/0207090 |
Abstract
Quantum entanglement distillation protocols are LOCC protocols between Alice and Bob that convert imperfect EPR pairs, or, in general, partially entangled bipartite states into perfect or near-perfect EPR pairs. The classical communication complexity of these protocols is the minimal amount of classical communication needed for the conversion. In this paper, we focus on the communication complexity of protocols that operate with incomplete information, i.e., where the inputs are mixed states and/or prepared adversarially. We study 3 models of imperfect EPR pairs. In the measure-r model, r out of n EPR pairs are measured by an adversary; in the depolarization model, Bob's share of qubits underwent a depolarization channel; in the fidelity model, the only information Alice and Bob possess is the fidelity of the shared state. For the measure-r model and the depolarization model, we prove tight and almost-tight bounds on the outcome of LOCC protocols that don't use communication. For the fidelity model, we prove a lower bound on the communication complexity that matches the upper bound given by Ambainis, Smith, and Yang [ASY02].
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"abstract": "Quantum entanglement distillation protocols are LOCC protocols between Alice\nand Bob that convert imperfect EPR pairs, or, in general, partially entangled\nbipartite states into perfect or near-perfect EPR pairs. The classical\ncommunication complexity of these protocols is the minimal amount of classical\ncommunication needed for the conversion. In this paper, we focus on the\ncommunication complexity of protocols that operate with incomplete information,\ni.e., where the inputs are mixed states and/or prepared adversarially.\n We study 3 models of imperfect EPR pairs. In the measure-r model, r out of n\nEPR pairs are measured by an adversary; in the depolarization model, Bob\u0027s\nshare of qubits underwent a depolarization channel; in the fidelity model, the\nonly information Alice and Bob possess is the fidelity of the shared state.\n For the measure-r model and the depolarization model, we prove tight and\nalmost-tight bounds on the outcome of LOCC protocols that don\u0027t use\ncommunication. For the fidelity model, we prove a lower bound on the\ncommunication complexity that matches the upper bound given by Ambainis, Smith,\nand Yang [ASY02].",
"arxiv_id": "quant-ph/0207090",
"authors": [
"Andris Ambainis",
"Ke Yang"
],
"categories": [
"quant-ph"
],
"title": "Towards the Classical Communication Complexity of Entanglement Distillation Protocols with Incomplete Information",
"url": "https://arxiv.org/abs/quant-ph/0207090"
},
"schema_id": "dorsal/arxiv",
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