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related topics |
{state, states, entangled} |
{let, theorem, proof} |
{bell, inequality, local} |
{states, state, optimal} |
{classical, space, random} |
{measurement, state, measurements} |
{vol, operators, histories} |
{qubit, qubits, gate} |
{group, space, representation} |
{operator, operators, space} |
{temperature, thermal, energy} |
{algorithm, log, probability} |
{observables, space, algebra} |
{key, protocol, security} |
|
Compatibility of subsystem states
Paul Butterley, Anthony Sudbery, Jason Szulc
abstract: We examine the possible states of subsystems of a system of bits or qubits.
In the classical case (bits), this means the possible marginal distributions of
a probability distribution on a finite number of binary variables; we give
necessary and sufficient conditions for a set of probability distributions on
all proper subsets of the variables to be the marginals of a single
distribution on the full set. In the quantum case (qubits), we consider mixed
states of subsets of a set of qubits; in the case of three qubits, we find
quantum Bell inequalities -- necessary conditions for a set of two-qubit states
to be the reduced states of a single mixed state of three qubits. We conjecture
that these conditions are also sufficient.
- oai_identifier:
- oai:arXiv.org:quant-ph/0407227
- categories:
- quant-ph
- comments:
- 19 pages, LaTeX. In memoriam Asher Peres. Substantial revision: one
theorem removed, one author added
- arxiv_id:
- quant-ph/0407227
- journal_ref:
- Found. Phys. 36, 83-101 (2006)
- created:
- 2004-07-28
- updated:
- 2005-04-22
Full article ▸
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