Recently, a close connection was established between nonlocality, Bell experiments, quantum communication, and quantum cryptography, on the one side, and quantum logic gates, quantum computing, and quantum logic, on the other. [C.H. Bennett et al., Phys. Rev. Lett. 76, 722 (1996)] All of them, Bell experiments, quantum communication/cryptographic schemes, and quantum computers use entangled systems as their inputs and the detection efficiences of the latter were so far very low (under 10 experiments carried out so far relied only on (nanoseconds) coincidental detections and that made them inconclusive in principle. [E. Santos, Phys. Rev. Lett. 66, 1388 (1995); Phys. Lett. A 212, 10 (1996)]. Recently we discovered a new kind of entanglement [M. Pavicic and J. Summhammer, Phys. Rev. Lett. 73, 3191 (1994)] and a new preselective scheme of entangling independent systems [M. Pavicic, J. Opt. Soc. Am. B 12, 821 (1995)] which should enable over 70 main hypothesis of the proposed project is that preselection of entangled photon pairs can be used for designing quantum logic gates for quantum computers, for obtaining user-ready input pairs in quantum cryptography and quantum communication, as well as for a long-wanted loophole-free Bell experiment, on the one hand, and that the algebraic representation of quantum logic (new desarguesian orthomodular lattices) can provide necessary algorithms for quantum computers, on the other. The aim of the project is to carry out all the elements from the hypothesis. Our basic methods will be our theory of the spin-correlated interferometry. [M. Pavicic, Physical Review A, 50, 3486 (1994)] and our new representation of quantum logic [M. Pavicic, Int. J. Theor. Phys. 32, 1481 (1993)]. First feasible loophole-free Bell experiment and a feasible interaction-free experiment with over 95 so far) are expected as first testable results. An objective indicator of the importance and influence of a branch is the number of papers in the leading journals, e.g., Phys. Rev. Lett., Phys. Rev. A, J. Opt. Soc. Am. B, and App. Phys. B. Only Phys. Rev. Lett. with the highest impact factor, 7.2 of all physical journals published more than 20 papers in the branches of quantum computers, cryptography, and communication (Bell experiments, quantum interferometry, etc.). On the other hand, we published in all the above journals recently. Therefore, the proposal may be ranked as important.

Recent foundational investigations and experiments in quantum mechanics and quantum optics significantly contributed to quantum communication and computation technology. The advances were mostly related to the intensity interference and were stimulated by a tremendous increase in the detection technique. It is therefore essential to develop models of quantum entanglement and quantum nonlocality which underlie quantum communication and computation and this is our main objective. In doing so, we use the standard quantum optical methods as well as new algebraico-probabilistic ones.

Lately, important developments have been made in the field of quantum logic, quantum gates, and preparation of entangled states. This has sharply increased the interest in a possible physical realization of quantum computers, quantum communication, and quantum cryptography. The goal of this project is to develop a method for preparing preselected entangled states and to develop logical structures underlying quantum mechanical computation. Preselected entangled states will enable realizable quantum gates and quantum cryptographic pairs and quantum structures will provide quantum algorithms.

The proposed project is compatible with the priority Information and Communication Technologies in the following way. Preselected entangled photon states may be used as input states for quantum computers and cryptographic communication. Devices for their preparation can be used as quantum gates for quantum computers. Quantum structures (quantum logic, orthomodular lattices, desarguesian lattices, probabilistic representations of these lattices, etc.) can be used as algorithms for quantum computers. Quantum computers are a kind of information technology under development and cryptographic communication is a kind of communication technology under development. Classical computer technology is coming to its limits: quantum tunneling between neighbouring circuits will soon limit further shrinking and this, together with the relativistic upper signal velocity, will also soon limit further increase in the speed. Quantum computers, however, can significantly increase these limits by the way they work; e.g., they do not calculate inteference, they perform interference. It is therefore essential to start designing quantum computers as the next generation of the computer technology. As for the quantum cryptography, it is absolutely superior to the classical cryptography because eavesdropping a quantum encrypted message is impossible in principle. Putting together quantum computers and quantum cryptography this reads: hacking of a quantum computer network is impossible in principle.

First of all, the results of the research can be applied in further theoretical development of quantum intensity interfereometry, quantum logic, orthomodular lattice theory, and the theory of quantum computers and of quantum cryptography. Then, calculated preparation of preselected entangled photon state can be used for designing a loophole-free Bell experiment which is the simplest version of a quantum computer and which can be carried out by means of the existing detection technology. That would be a first conclusive Bell-Einstein-Podolsky-Rosen experiment carried out without supplementary assumptions (i.e., a ``loophole-free'' one) in the World so far. The preselection scheme which will be used, includes the concept of a gate so that one will be able to apply the set-up for a realization of quantum gates. We emphasize that such four photon entanglement and preselection scheme are our discoveries which have not been previously reported in the literature. The Bell pairs obtained by the preselection scheme can be used as user-ready pairs in quantum cryptography which has got a unique property to be unbreakable in principle: eavesdroping of a message destroys the message. Preselected single photons appear in our scheme unpolarized and therefore the scheme can be used as a source of precisely directed unpolarized single photons which is not possible with previous sources: e.g., photons emitted from an atom in a cascade process are emitted in all possible directions.

In the background of the proposed project recent developments of the following four fields are interwoven:

(1) quantum computer theory;

(2) quantum cryptography and nonlocality;

(3) quantum intensity interferometry;

(4) quantum logic.

(1) In 1995 several important results were achieved:

a) it was proved that the von Neumann quantum entropy is equal to the number of qubits (spin-1/2 subsystems, quantum bits) within the density matrix [B. Schumacher, Quantum coding, Phys. Rev. A 51, 2738 (1995)];

b) it was shown that quantum gates operating on just two bits are sufficient for constructing quantum computer circuits [A. Berenco et al., Conditional quantum dynamics and logic gates, Phys. Rev. Lett. 74, 4083 (1995)];

c) it was shown that quantum computer does prime factoring in polynomial time (classical computer takes exponential time) [A. Ekert et al., Shor's quantum algorithm for factorizing numbers, preprint, Math. Dept., Plymouth Univ., UK (1995)].

It is therefore essential to design physically realizable quantum gates. The first two have already been proposed: one with CQED (cavity quantum electrodynamics) technique [T. Sleator et al., Realizable universal quantum gates, Phys. Rev. Lett. 74, 4087 (1995)] and the other with cold ions [J.I. Cirac et al., Quantum computations with cold trapped ions, Phys. Rev. Lett. 74, 4091 (1995)].

(2) Quantum cryptography, quantum nonlocality, and the Bell experiments are closely related since all of them are based on entangled states. Both Bell experiments and cryptographic schemes relied on coincidental counts within nanoseconds. For a practical realization of a cryptographic communication this is a serious problem and for Bell experiments this turned out to be an additional assumption which made all experiments carried out so far inconclusive. [E. Santos, Does quantum mechanics violate the Bell inequalities? Phys. Rev. Lett. 66, 1388 (1995)]. The reason for that were postselection and detection loopholes [E. Santos, Unreliability of performed tests of Bell’s inequality using parametric down-converted photons, Phys. Lett. A 212, 10 (1996)]. So, a number of loophole-free experiments have been proposed recently [R.T. Jones et al., Quantum mechanics and Bell’s inequalities, Phys. Rev. Lett. 72, 267 (1994); M. Pavicic, Spin-correlated interferometry with beam splitters: preselection of spin-correlated photons, J. Opt. Soc. Am. B 12, 821 (1995)]. On the other hand, quantum cryptography conjectured that it should be possible to entangle independent already entangled pairs of systems [C.H. Bennett, Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70, 1895 (1993)]. We proved the conjecture for the spin space [M. Pavicic and J. Summhammer, Interferometry with Two Pairs of Spin Correlated Photons, Phys. Rev. Lett. 73, 3191 (1994)]. A direct consequence of this result was that quantum nonlocality is a property of selection and not of an entanglement at a common origin [M. Pavicic, Preselection with certainty of photons in a singlet state from a set of independent photons, Int. J. Theor. Phys. 34, 1653 (1995)]. Taken together, switching from postselection to preselection experiments can solve both problems.

(3) Quantum intensity interference (interference of the fourth order) is the main tool of the most considered experiments. In the past ten years a number of novel effects which differ essentially from the usual amplitude interference (of the second order) have been discovered. For our project the essential effect is that the interference makes unpolarized independent photons entangled in polarization [M. Pavicic, Spin correlated interferometry for polarized and unpolarized photons on a beam splitter, Phys. Rev.A 50, 3486 (1994)].

(4) Quantum logic became a vast branch of both physics and mathematics.[M. Pavicic, Bibliography on quantum logics and related structures, Int. J. Theor. Phys. 31, 373 (1995)].

I was the principal investigator of the former project Algebraico-Probabilistic Structures of Quantum Mechanics (1-03-176). We will use the following two of its results:

(1) Starting from two independent entangled photon pairs, one can preselect two photons from different pairs into the singlet state by an interference performed by the other two photons from these different pairs;

(2) The unique bi-implication was proved to characterize quantum logic and its YES-NO representation of quantum logic.

(1) will be used for quantum gates and quantum cryptography,

(2) for quantum algorithms.

(1) Formulated the spin correlated interferometry of the fourth order for independent polarized as well as unpolarized photons. Ref. [5] of Sec. 30.1;

(2) Formulated the spin interferometry and spin entanglement for independent photon pairs. [6];

(3) Formulated a way to spin-entangled independent photon pairs emerging unpolarized from two beam-splitters and established a procedure for recording unequal superpositions without loss of detection counts. [8]

(4) Formulated a way to preselect with certainty a subset of photon pairs in the singlet state out of a set of completely random, unpolarized, and independent photons without directly interacting with them. [7];

(5) Proved: If the unique bi-implication within an ortholattice is equal to one whenever their elements are equal, then the ortholattice is orthomodular [3]; (6) Proved soundness and completeness for a new YES-NO representation of quantum logic [4]; (7) Proposed a loophole-free experiment with photons of different colours[9]

Ref. [12] was used by P. Busch and P.J. Lahti, Found. Phys. 19, No. 6 (1989) and reviewed by S. Weigert, Phys.Rev. A, 7689 (1992)

[13] reviewed by A.. Dvurecenskij, Math. Rev. #88k:03132

[14] rev. by A. Barchielli, Math. Rev. #92b:81019

[2] rev. by K. Matsuno, Math. Rev. #92b:81019

[3] used by D.J. Moore, Helv. Phys. Acta 66, 471 (1993) and rev. by J. Hamhalter, Math. Rev. #94g:81013//

[5] from 30.1 was extensively used in order to formulate a classical counterpart (50 effect (100 Correlations in Unpolarized Light, Opt. Comm. 112, 85 (1994). [6] was used by P.G. Kwiat et al., Phys. Rev. Lett. 75, 4337 (1995), T.B. Pittman, Phys. Lett. A 204, 193 (1995), and H. Weinfurter et al., in Quantum Interferometry II, ICTP, Trieste (1996).

[8] rev. by P. Hariharan and B.C. Sanders, Progress in Optics (1996).

The main hypothesis of the proposed project is that preselection of entangled photon pairs can be used for designing quantum logic binary gates for quantum computers, for obtaining user-ready input pairs in quantum cryptography and quantum communication, as well as for a long-wanted loophole-free Bell experiment, on the one hand, and that the algebraic representation of quantum logic (new desarguesian orthomodular lattices) can provide necessary algorithms for quantum computers, on the other.

An indicator of the importance and meaning of a particular branch is the number of papers published in the leading journals of the field, e.g., Phys.Rev.Lett., Phys.Rev.A, J.Opt.Soc.Am.B, and App.Phys.B. Only Phys. Rev. Lett. with the highest impact factor, 7.2 of all physical journals published in 1995 more than 20 papers in the branches of quantum computers, quantum cryptography, and quantum communication (Bell experiments, quantum intensity interference, etc.) as opposed to <10 in 1993. On the other hand, I published papers in all these journals. Thus, the project can be ranked as important.

Main aims of the projects are:

(1) to design and calculate in all realistic details a loophole-free Bell experiment using downconversion in two type-II nonlinear crystals fed by a subpicosecond laser; the set up will preselect independent photons into (non)maximally entangled pairs on an asymmetrical beam splitter;

(2) to implement preselected entangled photon pairs scheme as user-ready inputs for quantum communication and cryptography;

(3) to investigate whether a preselection scheme can be carried out with monolithic total internal reflection resonators with quantum tunneling for inputs and outputs and whether one can use such resonators as quantum gates in quantum computer circuits; (4) to obtain new algebraic varietes of desarguesian orthomodular lattices, i.e, new representations of quantum logic and corresponding algorithms for quantum computing.

Referring to the points from the previous section the methods will be as follows:

(1) to describe downconversion we shall use its theory as elaborated in L. Mandel and E. Wolf, Optical Coherence and Quantum Optics, Cambridge University Press (1995); to describe the interference of the fourth order at an asymmetrical beam splitter we shall use its theory as introduced and elaborated in M. Pavicic, Spin Correlated Interferometry for Polarized and Unpolarized Photons on a Beam Splitter, Physical Review A, 50, 3486-3491 (1994);

(2) to describe spatial distribution of photons downconverted in type-II nonlinear crystals we shall use the elaboration from A. Joobeur, B.E.A. Saleh, and M.C. Teich, Physical Review A 50, 3349-3361 (1994);

(3) to describe MOTIRR (monolithic total-internal-reflection resonator) and FTIR (frustrated total internal reflection, i.e., optical tunneling) we shall use its theory as elaborated in S. Schiller and R.I. Byer, Quadruply Resonant Optical Parametric Oscillation in a Monolithic Total-Internal-Reflection Resonator, Journal of the Optical Society of America B, 10, 1696-1707 (1993); to describe quantum gates we might use some ideas from D.P. Di Vincenzo, Two-Bit Gates Are Universal for Quantum Computation, Physical Review A 51, 1015-1022 (1995);

(3) to obtain new algebraic varieties of quantum logic and orthomodular lattices we shall use standard quantum logic, i.e., lattice theory methods as elaborated in P. Ptak and Pulmannova, Orthomodular Structures as Quantum Logics, Kluwer, Dordrecht, Holland (1991) as well as our new representation of quantum logic as introduced and elaborated in M. Pavicic, Non-Ordered Quantum Logic and Its Yes-No Representation, International Journal of Theoretical Physics, 32, 1481-1505 (1993).

First, the elaboration of the preselection set-up will be made. Spatio-temporal distribution of photons downconverted from type-II crystals will be calculated by means of wave packet and the lowered visibility of the intensity interference by means of integration over the dimensions of the pinholes in front of the detectors. Thereupon, various experimental parameters will be introduced and evaluated. This elaboration will enable us to complete points (1) and (2) from the last but one section. As for point (3) of Sec. Methods we shall first calculate resonance with monolithic total internal reflection resonators with quantum tunneling for inputs and outputs for pulse lasers using Gaussian wave packets and then for cw (continuous wave) lasers in order to determine the main properties of such resonators and whether one can use such resonators as quantum gates in quantum computer circuits. In the end, we shall try to obtain new algebraic varietes of desarguesian orthomodular lattices, i.e., new representations of quantum logic and corresopnding algorithms for quantum computing.

A pilot study concerning points (1) and (2) of Sec. Methods has been made under the title Event-Ready Entanglement Preparation and presented at the workshop and conference Quantum Interferometry II in the International Centre for Theoretical Physics in Trieste at the beginning of March this year where I was invited as an invited speaker. Since at this conference gathered practically all leading workers from the branches concerning this project it was a proper opportunity to discuss possible elaborations of the afore mentioned points. The prevailing opinion was that the project should be feasible.

As for point (3) of Sec. Methods , during my stay at Humboldt-Universitaet zu Berlin, Germany, Nichtklassische Strahlung, Max-Planck-Ges., last year I did calculations together with Prof. Harry Paul which show that this part is feasible too.

Point (1) of Sec. Methods can be used to carry out an experiment. That would be a first conclusive Bell experiment carried out so far. Next, we intend to apply the calculations obtained in point (3) of Sec. Methods on the so-called interaction-free experiment. That would also be possible to carry out experimentally. At the same time that would be a first interaction-free experiment with the efficiency over 50 could be over 95

quantum cryptography, nonlocality, quantum logic gates, quantum logic, Bell experiment, interference of the fourth order, quantum communication, intensity interferometry, quantum computers, orthomodular lattices

[1] M. Pavicic, A New Axiomatization of Unified Quantum Logic, International Journal of Theoretical Physics, 31, 753-1766 (1992).

[2] M. Pavicic, On a Formal Difference between the Individual and Statistical Interpretation of Quantum Mechanics, Physics Letters A, 174, 353-357 (1993).

[3] M. Pavicic, Non-Ordered Quantum Logic and Its Yes-No Representation, International Journal of Theoretical Physics, 32, 1481-1505 (1993).

[4] M. Pavicic, Probabilistic Forcing in Quantum Logic, International Journal of Theoretical Physics, 32, 1965-1979 (1993).

[5] M. Pavicic, Spin Correlated Interferometry for Polarized and Unpolarized Photons on a Beam Splitter, Physical Review A, 50, 3486-3491 (1994).

[6] M. Pavicic and J. Summhammer, Interferometry with Two Pairs of Spin Correlated Photons, Physical Review Letters, 73, 3191-3194 (1994).

[7] M. Pavicic, Preselection with Certainty of Photons in a Singlet State from a Set of Independent Photons, International Journal of Theoretical Physics, 34, 1653-1665 (1995).

[8] M. Pavicic, Spin-Correlated Interferometry with Beam Splitters: Preselection of Spin-Correlated Photons, Journal of the Optical Society of America B, 12, 821-828 (1995).

[9] M. Pavicic, Closure of the Enhancement and Detection Loopholes in the Bell Theorem by the Fourth Order Interference with Photons of Different Colours, Physics Letters A, 209, 255-260 (1995).

[10] M. Pavicic, Preselected Sub-Poissonian Correlations, in D. Han, K.C. Peng, Y.S. Kim, and V.I. Man’ko (eds.), Fourth International Conference on Squeezed States and Uncertainty Relations, NASA Conference Publication 3322, USA (1996), pp. 325-330.

[11] M. Pavicic, When Do Position and Momentum Distributions Determine the Quantum Mechanical State? Physics Letters A, 118, 5-7 (1986).

[12] M. Pavicic, Complex Gaussians and the Pauli Non-Uniqueness, Physics Letters A 122, 280-282 (1987).

[13] M. Pavicic, Minimal Quantum Logic with Merged Implications, International Journal of Theoretical Physics 26, 845-852 (1987).

[14] M. Pavicic, A Relative Frequency Criterion for the Repeatability of Quantum Measurements, Nuovo Cimento, 105 B, 1103-1112 (1990); Ibid., 106 B, 105-106 (1991).

[15] M. Pavicic, Quantum Malus Law for Composite Systems as a Hidden-Variable Theory, Physical Review D, 42, 3594-3595 (1990).