|
| related topics |
| {information, entropy, channel} |
| {state, states, entangled} |
| {alice, bob, state} |
| {entanglement, phys, rev} |
| {operator, operators, space} |
| {level, atom, field} |
| {temperature, thermal, energy} |
|
Bounds on localisable information via semidefinite programming
Barbara Synak, Karol Horodecki, Michal Horodecki
abstract: We investigate so-called localisable information of bipartite states and a
parallel notion of information deficit. Localisable information is defined as
the amount of information that can be concentrated by means of classical
communication and local operations where only maximally mixed states can be
added for free. The information deficit is defined as difference between total
information contents of the state and localisable information. We consider a
larger class of operations: the so called PPT operations, which in addition
preserve maximally mixed state (PPT-PMM operations). We formulate the related
optimization problem as sedmidefnite program with suitable constraints. We then
provide bound for fidelity of transition of a given state into product pure
state on Hilbert space of dimension d. This allows to obtain general upper
bound for localisable information (and also for information deficit). We
calculated the bounds exactly for Werner states and isotropic states in any
dimension. Surprisingly it turns out that related bounds for information
deficit are equal to relative entropy of entanglement (in the case of Werner
states - regularized one). We compare the upper bounds with lower bounds based
on simple protocol of localisation of information.
- oai_identifier:
- oai:arXiv.org:quant-ph/0405149
- categories:
- quant-ph
- comments:
- 14 pages, revtex
- arxiv_id:
- quant-ph/0405149
- journal_ref:
- J. Math. Phys. 46, 082107 (2005)
- created:
- 2004-05-25
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