3 research outputs found
Entanglement can increase asymptotic rates of zero-error classical communication over classical channels
It is known that the number of different classical messages which can be
communicated with a single use of a classical channel with zero probability of
decoding error can sometimes be increased by using entanglement shared between
sender and receiver. It has been an open question to determine whether
entanglement can ever increase the zero-error communication rates achievable in
the limit of many channel uses. In this paper we show, by explicit examples,
that entanglement can indeed increase asymptotic zero-error capacity, even to
the extent that it is equal to the normal capacity of the channel.
Interestingly, our examples are based on the exceptional simple root systems E7
and E8.Comment: 14 pages, 2 figur
Parity proofs of the Bell-Kochen-Specker theorem based on the 600-cell
The set of 60 real rays in four dimensions derived from the vertices of a
600-cell is shown to possess numerous subsets of rays and bases that provide
basis-critical parity proofs of the Bell-Kochen-Specker (BKS) theorem (a
basis-critical proof is one that fails if even a single basis is deleted from
it). The proofs vary considerably in size, with the smallest having 26 rays and
13 bases and the largest 60 rays and 41 bases. There are at least 90 basic
types of proofs, with each coming in a number of geometrically distinct
varieties. The replicas of all the proofs under the symmetries of the 600-cell
yield a total of almost a hundred million parity proofs of the BKS theorem. The
proofs are all very transparent and take no more than simple counting to
verify. A few of the proofs are exhibited, both in tabular form as well as in
the form of MMP hypergraphs that assist in their visualization. A survey of the
proofs is given, simple procedures for generating some of them are described
and their applications are discussed. It is shown that all four-dimensional
parity proofs of the BKS theorem can be turned into experimental disproofs of
noncontextuality.Comment: 19 pages, 11 tables, 3 figures. Email address of first author has
been corrected. Ref.[5] has been corrected, as has an error in Fig.3.
Formatting error in Sec.4 has been corrected and the placement of tables and
figures has been improved. A new paragraph has been added to Sec.4 and
another new paragraph to the end of the Appendi