|
| related topics |
| {states, state, optimal} |
| {key, protocol, security} |
| {let, theorem, proof} |
| {information, entropy, channel} |
| {error, code, errors} |
| {algorithm, log, probability} |
| {alice, bob, state} |
| {qubit, qubits, gate} |
|
Invertible Quantum Operations and Perfect Encryption of Quantum States
Ashwin Nayak, Pranab Sen
abstract: In this note, we characterize the form of an invertible quantum operation,
i.e., a completely positive trace preserving linear transformation (a CPTP map)
whose inverse is also a CPTP map. The precise form of such maps becomes
important in contexts such as self-testing and encryption. We show that these
maps correspond to applying a unitary transformation to the state along with an
ancilla initialized to a fixed state, which may be mixed.
The characterization of invertible quantum operations implies that one-way
schemes for encrypting quantum states using a classical key may be slightly
more general than the ``private quantum channels'' studied by Ambainis, Mosca,
Tapp and de Wolf (FOCS 2000). Nonetheless, we show that their results, most
notably a lower bound of 2n bits of key to encrypt n quantum bits, extend in a
straightforward manner to the general case.
- oai_identifier:
- oai:arXiv.org:quant-ph/0605041
- categories:
- quant-ph
- comments:
- 9 pages. Version 3 has minor edits, a correction to Theorem 2.2, and
a proof sketch.Author affiliation updated.Version 4 has an additional
reference. To appear in QIC
- arxiv_id:
- quant-ph/0605041
- created:
- 2006-05-03
- updated:
- 2006-11-02
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