dorsal/arxiv
View SchemaInequalities and separations among assisted capacities of quantum channels
| Authors | Charles H. Bennett, Igor Devetak, Peter W. Shor, John A. Smolin |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0406086 |
| URL | https://arxiv.org/abs/quant-ph/0406086 |
Abstract
We exhibit discrete memoryless quantum channels whose quantum capacity assisted by two-way classical communication, $Q_2$, exceeds their unassisted one-shot Holevo capacity $C_H$. These channels may be thought of as having a data input and output, along with a control input that partly influences, and a control output that partly reveals, which of a set of unitary evolutions the data undergoes en route from input to output. The channel is designed so that the data's evolution can be exactly inferred by a classically coordinated processing of 1) the control output, and 2) a reference system entangled with the control input, but not from either of these resources alone. Thus a two-way classical side channel allows the otherwise noisy evolution of the data to be corrected, greatly increasing the capacity. The same family of channels provides examples where the classical capacity assisted by classical feedback, $C_B$, and the quantum capacity assisted by classical feedback $Q_B$, both exceed $C_H$. A related channel, whose data input undergoes dephasing before interacting with the control input, has a classical capacity $C=C_H$ strictly less than its $C_2$, the classical capacity assisted by independent classical communication.
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"abstract": "We exhibit discrete memoryless quantum channels whose quantum capacity\nassisted by two-way classical communication, $Q_2$, exceeds their unassisted\none-shot Holevo capacity $C_H$. These channels may be thought of as having a\ndata input and output, along with a control input that partly influences, and a\ncontrol output that partly reveals, which of a set of unitary evolutions the\ndata undergoes en route from input to output. The channel is designed so that\nthe data\u0027s evolution can be exactly inferred by a classically coordinated\nprocessing of 1) the control output, and 2) a reference system entangled with\nthe control input, but not from either of these resources alone. Thus a two-way\nclassical side channel allows the otherwise noisy evolution of the data to be\ncorrected, greatly increasing the capacity. The same family of channels\nprovides examples where the classical capacity assisted by classical feedback,\n$C_B$, and the quantum capacity assisted by classical feedback $Q_B$, both\nexceed $C_H$. A related channel, whose data input undergoes dephasing before\ninteracting with the control input, has a classical capacity $C=C_H$ strictly\nless than its $C_2$, the classical capacity assisted by independent classical\ncommunication.",
"arxiv_id": "quant-ph/0406086",
"authors": [
"Charles H. Bennett",
"Igor Devetak",
"Peter W. Shor",
"John A. Smolin"
],
"categories": [
"quant-ph"
],
"title": "Inequalities and separations among assisted capacities of quantum channels",
"url": "https://arxiv.org/abs/quant-ph/0406086"
},
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