dorsal/arxiv
View SchemaRandomizing quantum states: Constructions and applications
| Authors | Patrick Hayden, Debbie Leung, Peter W. Shor, Andreas Winter |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0307104 |
| URL | https://arxiv.org/abs/quant-ph/0307104 |
| DOI | 10.1007/s00220-004-1087-6 |
| Journal | Commun. Math. Phys. 250(2):371-391, 2004. |
Abstract
The construction of a perfectly secure private quantum channel in dimension d is known to require 2 log d shared random key bits between the sender and receiver. We show that if only near-perfect security is required, the size of the key can be reduced by a factor of two. More specifically, we show that there exists a set of roughly d log d unitary operators whose average effect on every input pure state is almost perfectly randomizing, as compared to the d^2 operators required to randomize perfectly. Aside from the private quantum channel, variations of this construction can be applied to many other tasks in quantum information processing. We show, for instance, that it can be used to construct LOCC data hiding schemes for bits and qubits that are much more efficient than any others known, allowing roughly log d qubits to be hidden in 2 log d qubits. The method can also be used to exhibit the existence of quantum states with locked classical correlations, an arbitrarily large amplification of the correlation being accomplished by sending a negligibly small classical key. Our construction also provides the basic building block for a method of remotely preparing arbitrary d-dimensional pure quantum states using approximately log d bits of communication and log d ebits of entanglement.
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"abstract": "The construction of a perfectly secure private quantum channel in dimension d\nis known to require 2 log d shared random key bits between the sender and\nreceiver. We show that if only near-perfect security is required, the size of\nthe key can be reduced by a factor of two. More specifically, we show that\nthere exists a set of roughly d log d unitary operators whose average effect on\nevery input pure state is almost perfectly randomizing, as compared to the d^2\noperators required to randomize perfectly. Aside from the private quantum\nchannel, variations of this construction can be applied to many other tasks in\nquantum information processing. We show, for instance, that it can be used to\nconstruct LOCC data hiding schemes for bits and qubits that are much more\nefficient than any others known, allowing roughly log d qubits to be hidden in\n2 log d qubits. The method can also be used to exhibit the existence of quantum\nstates with locked classical correlations, an arbitrarily large amplification\nof the correlation being accomplished by sending a negligibly small classical\nkey. Our construction also provides the basic building block for a method of\nremotely preparing arbitrary d-dimensional pure quantum states using\napproximately log d bits of communication and log d ebits of entanglement.",
"arxiv_id": "quant-ph/0307104",
"authors": [
"Patrick Hayden",
"Debbie Leung",
"Peter W. Shor",
"Andreas Winter"
],
"categories": [
"quant-ph"
],
"doi": "10.1007/s00220-004-1087-6",
"journal_ref": "Commun. Math. Phys. 250(2):371-391, 2004.",
"title": "Randomizing quantum states: Constructions and applications",
"url": "https://arxiv.org/abs/quant-ph/0307104"
},
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