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| {particle, mechanics, theory} |
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Channel kets, entangled states, and the location of quantum information
Robert B. Griffiths
abstract: The well-known duality relating entangled states and noisy quantum channels
is expressed in terms of a channel ket, a pure state on a suitable tripartite
system, which functions as a pre-probability allowing the calculation of
statistical correlations between, for example, the entrance and exit of a
channel, once a framework has been chosen so as to allow a consistent set of
probabilities. In each framework the standard notions of ordinary (classical)
information theory apply, and it makes sense to ask whether information of a
particular sort about one system is or is not present in another system.
Quantum effects arise when a single pre-probability is used to compute
statistical correlations in different incompatible frameworks, and various
constraints on the presence and absence of different kinds of information are
expressed in a set of all-or-nothing theorems which generalize or give a
precise meaning to the concept of ``no-cloning.'' These theorems are used to
discuss: the location of information in quantum channels modeled using a
mixed-state environment; the $CQ$ (classical-quantum) channels introduced by
Holevo; and the location of information in the physical carriers of a quantum
code. It is proposed that both channel and entanglement problems be classified
in terms of pure states (functioning as pre-probabilities) on systems of $p\geq
2$ parts, with mixed bipartite entanglement and simple noisy channels belonging
to the category $p=3$, a five-qubit code to the category $p=6$, etc.; then by
the dimensions of the Hilbert spaces of the component parts, along with other
criteria yet to be determined.
- oai_identifier:
- oai:arXiv.org:quant-ph/0409106
- categories:
- quant-ph
- comments:
- Latex 32 pages, 4 figures in text using PSTricks. Version 3: Minor
typographical errors corrected
- doi:
- 10.1103/PhysRevA.71.042337
- arxiv_id:
- quant-ph/0409106
- journal_ref:
- Phys. Rev. A 71 (2005) 042337
- created:
- 2004-09-16
- updated:
- 2005-05-26
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