129 research outputs found
Entanglement and Superdense Coding with Linear Optics
We discuss a scheme for a full superdense coding of entangled photon states
employing only linear-optics elements. By using the mixed basis consisting of
four states that are unambiguously distinguishable by a standard and polarizing
beam splitters we can deterministically transfer four messages by manipulating
just one of the two entangled photons. The sender achieves the determinism of
the transfer either by giving up the control over 50% of sent messages
(although known to her) or by discarding 33% of incoming photons.Comment: 8 pages, 1 figur
New Class of 4-Dim Kochen-Specker Sets
We find a new highly symmetrical and very numerous class (millions of
non-isomorphic sets) of 4-dim Kochen-Specker (KS) vector sets. Due to the
nature of their geometrical symmetries, they cannot be obtained from previously
known ones. We generate the sets from a single set of 60 orthogonal spin
vectors and 75 of their tetrads (which we obtained from the 600-cell) by means
of our newly developed "stripping technique." We also consider "critical KS
subsets" and analyze their geometry. The algorithms and programs for the
generation of our KS sets are presented.Comment: 7 pages, 3 figures; to appear in J. Math. Phys. Vol.52, No. 2 (2011
Nondestructive interaction-free atom-photon controlled-NOT gate
We present a probabilistic (ideally 50%) nondestructive interaction-free
atom-photon controlled-NOT gate, where nondestructive means that all four
outgoing target photon modes of the gate are available and feed-forwardable.
Individual atoms are controlled by a stimulated Raman adiabatic passage
transition and photons by a ring resonator with two outgoing ports. Realistic
estimates we obtain for ions confined in a Paul trap around which the resonator
is mounted show that a strong atom-photon coupling can be achieved. It is also
shown how the resonator can be used for controlling superposition of atom
states.Comment: 20 pages, 5 figures, Web page: http://m3k.grad.hr/pavici
Retraction of "Near-Deterministic Discrimination of All Bell States with Linear Optics," Phys. Rev. Lett. 107, 080403 (2011) and Erratum Phys. Rev. Lett. 107, 219901 (2011)
The original versions (1 and 2) of this paper paper contain a fatal error.
All my attempts to patch the error have failed. As a service to the community I
explain the error in some detail.Comment: The original paper (v. 1 and 2) was retracted from Phys. Rev. Lett.
107, 080403 (2011) and its Erratum Phys. Rev. Lett. 107. 219901 (2011
Kochen-Specker Sets and Generalized Orthoarguesian Equations
Every set (finite or infinite) of quantum vectors (states) satisfies
generalized orthoarguesian equations (OA). We consider two 3-dim
Kochen-Specker (KS) sets of vectors and show how each of them should be
represented by means of a Hasse diagram---a lattice, an algebra of subspaces of
a Hilbert space--that contains rays and planes determined by the vectors so as
to satisfy OA. That also shows why they cannot be represented by a special
kind of Hasse diagram called a Greechie diagram, as has been erroneously done
in the literature. One of the KS sets (Peres') is an example of a lattice in
which 6OA pass and 7OA fails, and that closes an open question of whether the
7oa class of lattices properly contains the 6oa class. This result is important
because it provides additional evidence that our previously given proof of noa
=< (n+1)oa can be extended to proper inclusion noa < (n+1)oa and that nOA form
an infinite sequence of successively stronger equations.Comment: 16 pages and 5 figure
Hilbert Lattice Equations
There are five known classes of lattice equations that hold in every infinite
dimensional Hilbert space underlying quantum systems: generalised
orthoarguesian, Mayet's E_A, Godowski, Mayet-Godowski, and Mayet's E equations.
We obtain a result which opens a possibility that the first two classes
coincide. We devise new algorithms to generate Mayet-Godowski equations that
allow us to prove that the fourth class properly includes the third. An open
problem related to the last class is answered. Finally, we show some new
results on the Godowski lattices characterising the third class of equations.Comment: 24 pages, 3 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
Water Reservoir Within the Karst Field Overburden: Gusic Polje, Croatia
The Gusic reservoir is a compensation basin constructed in the karst field. The reservoir lies on a Quaternary overburden free of ponors (sinkholes) and suffosions. After the reservoir filling the water losses were up to <6.4 m3/s. The bottom impermeability has been ensured with a 0.4 m thick clay base blanket. During reservoir exploitation, suffosions and ponors developed through which 2 m3/s water was lost. Such conditions required reservoir repair within a short time frame of approximately 10 days during which the power plant was shut down. When the reservoir was emptied, a resistivity sounding (Wenner electrodes arrangement at five depth levels) was conducted on the reservoir bottom and clay blanket. An alternative concept has also been considered - the construction of a new reservoir area that has similar hydrogeological conditions. The solution for the possible impact of groundwater (air) “pressure” could be the construction of a horizontal “vent” in the deepest part of the palaeodepression, where the bedrock karstification is the most intensive and the interrelation between groundwater and air pressure on the overburden is possible. The reservoir bottom impermeability could be resolved with a clay blanket or with synthetic materials
Recursive proof of the Bell-Kochen-Specker theorem in any dimension
We present a method to obtain sets of vectors proving the Bell-Kochen-Specker
theorem in dimension from a similar set in dimension (). As an application of the method we find the smallest proofs known in
dimension five (29 vectors), six (31) and seven (34), and different sets
matching the current record (36) in dimension eight.Comment: LaTeX, 7 page
Probability Measures and projections on Quantum Logics
The present paper is devoted to modelling of a probability measure of logical
connectives on a quantum logic (QL), via a -map, which is a special map on
it. We follow the work in which the probability of logical conjunction,
disjunction and symmetric difference and their negations for non-compatible
propositions are studied.
We study such a -map on quantum logics, which is a probability measure
of a projection and show, that unlike classical (Boolean) logic, probability
measure of projections on a quantum logic are not necessarilly pure
projections.
We compare properties of a -map on QLs with properties of a probability
measure related to logical connectives on a Boolean algebra
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