142 research outputs found
A variant of Peres-Mermin proof for testing noncontextual realist models
For any state in four-dimensional system, the quantum violation of an
inequality based on the Peres-Mermin proof for testing noncontextual realist
models has experimentally been corroborated. In the Peres-Mermin proof, an
array of nine holistic observables for two two-qubit system was used. We, in
this letter, present a new symmetric set of observables for the same system
which also provides a contradiction of quantum mechanics with noncontextual
realist models in a state-independent way. The whole argument can also be cast
in the form of a new inequality that can be empirically tested.Comment: 3 pages, To be published in Euro. Phys. Let
Observables have no value: a no-go theorem for position and momentum observables
A very simple illustration of the Bell-Kochen-Specker contradiction is
presented using continuous observables in infinite dimensional Hilbert space.
It is shown that the assumption of the \emph{existence} of putative values for
position and momentum observables for one single particle is incompatible with
quantum mechanics.Comment: 6 pages, 1 Latex figure small corrections, refference and comments
adde
Proposed experimental tests of the Bell-Kochen-Specker theorem
For a two-particle two-state system, sets of compatible propositions exist
for which quantum mechanics and noncontextual hidden-variable theories make
conflicting predictions for every individual system whatever its quantum state.
This permits a simple all-or-nothing state-independent experimental
verification of the Bell-Kochen-Specker theorem.Comment: LaTeX, 8 page
Kochen-Specker theorem for a single qubit using positive operator-valued measures
A proof of the Kochen-Specker theorem for a single two-level system is
presented. It employs five eight-element positive operator-valued measures and
a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure
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
Parity proofs of the Kochen-Specker theorem based on the 24 rays of Peres
A diagrammatic representation is given of the 24 rays of Peres that makes it
easy to pick out all the 512 parity proofs of the Kochen-Specker theorem
contained in them. The origin of this representation in the four-dimensional
geometry of the rays is pointed out.Comment: 14 pages, 6 figures and 3 tables. Three references have been added.
Minor typos have been correcte
Quantum codewords contradict local realism
Quantum codewords are highly entangled combinations of two-state systems. The
standard assumptions of local realism lead to logical contradictions similar to
those found by Bell, Kochen and Specker, Greenberger, Horne and Zeilinger, and
Mermin. The new contradictions have some noteworthy features that did not
appear in the older ones.Comment: 9 pages LaTeX, 1 figur
Kochen-Specker Vectors
We give a constructive and exhaustive definition of Kochen-Specker (KS)
vectors in a Hilbert space of any dimension as well as of all the remaining
vectors of the space. KS vectors are elements of any set of orthonormal states,
i.e., vectors in n-dim Hilbert space, H^n, n>3 to which it is impossible to
assign 1s and 0s in such a way that no two mutually orthogonal vectors from the
set are both assigned 1 and that not all mutually orthogonal vectors are
assigned 0. Our constructive definition of such KS vectors is based on
algorithms that generate MMP diagrams corresponding to blocks of orthogonal
vectors in R^n, on algorithms that single out those diagrams on which algebraic
0-1 states cannot be defined, and on algorithms that solve nonlinear equations
describing the orthogonalities of the vectors by means of statistically
polynomially complex interval analysis and self-teaching programs. The
algorithms are limited neither by the number of dimensions nor by the number of
vectors. To demonstrate the power of the algorithms, all 4-dim KS vector
systems containing up to 24 vectors were generated and described, all 3-dim
vector systems containing up to 30 vectors were scanned, and several general
properties of KS vectors were found.Comment: 19 pages, 6 figures, title changed, introduction thoroughly
rewritten, n-dim rotation of KS vectors defined, original Kochen-Specker 192
(117) vector system translated into MMP diagram notation with a new graphical
representation, results on Tkadlec's dual diagrams added, several other new
results added, journal version: to be published in J. Phys. A, 38 (2005). Web
page: http://m3k.grad.hr/pavici
Parity proofs of the Kochen-Specker theorem based on 60 complex rays in four dimensions
It is pointed out that the 60 complex rays in four dimensions associated with
a system of two qubits yield over 10^9 critical parity proofs of the
Kochen-Specker theorem. The geometrical properties of the rays are described,
an overview of the parity proofs contained in them is given, and examples of
some of the proofs are exhibited.Comment: 17 pages, 13 tables, 3 figures. Several new references have been
adde
Critical noncolorings of the 600-cell proving the Bell-Kochen-Specker theorem
Aravind and Lee-Elkin (1997) gave a proof of the Bell-Kochen-Specker theorem
by showing that it is impossible to color the 60 directions from the center of
a 600-cell to its vertices in a certain way. This paper refines that result by
showing that the 60 directions contain many subsets of 36 and 30 directions
that cannot be similarly colored, and so provide more economical demonstrations
of the theorem. Further, these subsets are shown to be critical in the sense
that deleting even a single direction from any of them causes the proof to
fail. The critical sets of size 36 and 30 are shown to belong to orbits of 200
and 240 members, respectively, under the symmetries of the polytope. A
comparison is made between these critical sets and other such sets in four
dimensions, and the significance of these results is discussed.Comment: 2 new references added, caption to Table 9 correcte
- ā¦