dorsal/arxiv
View SchemaQuantum and Classical Message Identification via Quantum Channels
| Authors | Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0401060 |
| URL | https://arxiv.org/abs/quant-ph/0401060 |
| Journal | Festschrift "A S Holevo 60" (O. Hirota, ed.), pp 171-188, Rinton Press, 2004. Reprinted in Quantum Inf. Comput., vol. 4(6&7), pp 563-578, 2004 |
Abstract
We discuss concepts of message identification in the sense of Ahlswede and Dueck via general quantum channels, extending investigations for classical channels, initial work for classical-quantum (cq) channels and "quantum fingerprinting". We show that the identification capacity of a discrete memoryless quantum channel for classical information can be larger than that for transmission; this is in contrast to all previously considered models, where it turns out to equal the common randomness capacity (equals transmission capacity in our case): in particular, for a noiseless qubit, we show the identification capacity to be 2, while transmission and common randomness capacity are 1. Then we turn to a natural concept of identification of quantum messages (i.e. a notion of "fingerprint" for quantum states). This is much closer to quantum information transmission than its classical counterpart (for one thing, the code length grows only exponentially, compared to double exponentially for classical identification). Indeed, we show how the problem exhibits a nice connection to visible quantum coding. Astonishingly, for the noiseless qubit channel this capacity turns out to be 2: in other words, one can compress two qubits into one and this is optimal. In general however, we conjecture quantum identification capacity to be different from classical identification capacity.
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"abstract": "We discuss concepts of message identification in the sense of Ahlswede and\nDueck via general quantum channels, extending investigations for classical\nchannels, initial work for classical-quantum (cq) channels and \"quantum\nfingerprinting\".\n We show that the identification capacity of a discrete memoryless quantum\nchannel for classical information can be larger than that for transmission;\nthis is in contrast to all previously considered models, where it turns out to\nequal the common randomness capacity (equals transmission capacity in our\ncase): in particular, for a noiseless qubit, we show the identification\ncapacity to be 2, while transmission and common randomness capacity are 1.\n Then we turn to a natural concept of identification of quantum messages (i.e.\na notion of \"fingerprint\" for quantum states). This is much closer to quantum\ninformation transmission than its classical counterpart (for one thing, the\ncode length grows only exponentially, compared to double exponentially for\nclassical identification). Indeed, we show how the problem exhibits a nice\nconnection to visible quantum coding. Astonishingly, for the noiseless qubit\nchannel this capacity turns out to be 2: in other words, one can compress two\nqubits into one and this is optimal. In general however, we conjecture quantum\nidentification capacity to be different from classical identification capacity.",
"arxiv_id": "quant-ph/0401060",
"authors": [
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"journal_ref": "Festschrift \"A S Holevo 60\" (O. Hirota, ed.), pp 171-188, Rinton\n Press, 2004. Reprinted in Quantum Inf. Comput., vol. 4(6\u00267), pp 563-578, 2004",
"title": "Quantum and Classical Message Identification via Quantum Channels",
"url": "https://arxiv.org/abs/quant-ph/0401060"
},
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