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 As a service to the community I explain the error in some detail.Comment: The original paper (v. 1 and 2) was retracted from Phys.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 ($n$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 $n$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 n>3n>3

We present a method to obtain sets of vectors proving the Bell-Kochen-Specker theorem in dimension $n$ from a similar set in dimension $d$ ($3\leq d<n\leq 2d$). 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 $G$-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 $G$-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 $G$-map on QLs with properties of a probability measure related to logical connectives on a Boolean algebra