|
related topics |
{states, state, optimal} |
{let, theorem, proof} |
{entanglement, phys, rev} |
{algorithm, log, probability} |
{state, states, entangled} |
{alice, bob, state} |
{bell, inequality, local} |
{time, systems, information} |
{equation, function, exp} |
{key, protocol, security} |
{state, algorithm, problem} |
{vol, operators, histories} |
|
The Existence of Quantum Entanglement Catalysts
Xiaoming Sun, Runyao Duan, Mingsheng Ying
abstract: Without additional resources, it is often impossible to transform one
entangled quantum state into another with local quantum operations and
classical communication. Jonathan and Plenio [Phys. Rev. Lett. 83, 3566(1999)]
presented an interesting example showing that the presence of another state,
called a catalyst, enables such a transformation without changing the catalyst.
They also pointed out that in general it is very hard to find an analytical
condition under which a catalyst exists. In this paper we study the existence
of catalysts for two incomparable quantum states. For the simplest case of
$2\times 2$ catalysts for transformations from one $4\times 4$ state to
another, a necessary and sufficient condition for existence is found. For the
general case, we give an efficient polynomial time algorithm to decide whether
a $k\times k$ catalyst exists for two $n\times n$ incomparable states, where
$k$ is treated as a constant.
- oai_identifier:
- oai:arXiv.org:quant-ph/0311133
- categories:
- quant-ph
- comments:
- 12 pages. Presentation part improved. Main results unchanged.
Essentially the journal version
- arxiv_id:
- quant-ph/0311133
- journal_ref:
- IEEE. Trans. Inform. Theory, Vol. 51, No. 1, January 2005
- created:
- 2003-11-19
- updated:
- 2005-01-18
Full article ▸
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