Quantum teleportation for nonmaximal entangled states in the. Constructing mutually unbiased bases from quantum latin. We introduce orthogonal quantum latin squares, which restrict to traditional orthogonal latin squares, and investigate their application in quantum information science. Keywords postquantum cryptography, noncommutative cryptography, symmetric groups, permutations, diffiehellman key exchange, elgamal cipher, combinatorial analysis. An efficient algorithm for eigenvalue problem of latin. Even at the end of the 1700s thomas jeffersons adoption of the vi genere cipher by the u. Mutually unbiased bases, orthogonal latin squares, and hiddenvariable models tomasz paterek,1 borivoje dakic,1,2 and caslav brukner1,2 1institute for quantum optics and quantum information, austrian academy of sciences, boltzmanngasse 3, a1090 vienna, austria. Every quantum latin square is also a quantum latin isometry square. An improved quantum inspired evolutionary algorithm is proposed for solving mixed discretecontinuous nonlinear problems in engineering design. In usual quantum information theory, the ideal resources are maximal entangled states. The focus of this paper is the extension of this property to quantum latin squares, by way of the following new definition. Mutually unbiased bases, orthogonal latin squares, and hidden.
Orthogonal quantum latin squares definition a pair of quantum latin squares are orthogonal when the pointwise inner product of any row from one with any row from the other yielding a single 1 and with the rest being 0. Find all latin squares of side 4 in standard form with respect to the sequence 1. We use quantum latin squares to build maximally entangled bases, and show how a pair of mutually unbiased maximally. The construction combines the designtheoretic objects s, knets which can be constructed from w mutually orthogonal latin squares of order s and vice versa and generalized hadamard matrices of size s. Jamison dept of mathematical sciences, university of memphis october 15 october 16. Eggermont called diagonal latin squares infinitelymultimagic squares in a 2004 talk. We use quantum latin squares to build maximally entangled bases, and show how a pair of mutually unbiased maximally entangled bases can be constructed in square dimension from orthogonal quantum.
A class of quantum ldpc codes derived from latin squares and. Bimagic squares corresponding to p2 begin at orders 8 and 9, trimagic for p3 begin at order 12, etc. In january 1999, sarah flannery, a sportsloving teenager from blarney in county cork, ireland, was awarded irelands young scientist of the year for her extraordinary research and discoveries in internet cryptography. For the past three decades, latin squares techniques have been widely used in many statistical applications. The proposed latin square quantum inspired evolutionary algorithm lsqea combines latin squares and quantum inspired genetic algorithm qga. Some unexpected connections with the theory of quantum latin squares are explored, and we introduce and study a sinkhornlike algorithm used to randomly generate quantum latin squares.
Any sicpovm defines a complex hadamard matrix in every dimension. Much effort has been devoted to latin square design. Multiparty quantum key agreement protocol with bell states and single particles. Our main results use quantum latin squares to give a new construction of unitary error. Latin squares in experimental design lei gao michigan state university december 10, 2005 abstract. Our protein bars our vegan, plantbased, gluten free, soy free, non gmo. In the ancient chinese board game go a player can capture the stones of an opponent by occupying all orthogonallyadjacent points. Through nsta, youll find leading resources for excellence in teaching and learning and experience growth through robust professional development. The above latin square is not the multiplication table of a group, because for this square. International conference on quantum physics and nuclear engineering march 1416, 2016 london, uk scientific tracks abstracts. Tackling problems in quantum entanglement and channels via. This kind of cryptography was slow to gain acceptance. The symbol m, for instance, is used for both an uppercase m and an uppercase. However, as shown in the present study, nonmaximal entangled states have potentiality to be useful resources.
Developing construction techniques for uebs has been a major activity in quantum computation, with three primary methods proposed. We show that quantum latin squares can be seen as weakened versions of mutuallyunbiased bases mubs. We introduce quantum latin squares, combinatorial quantum objects which generalize classical latin squares. Quantum latin squares and unitary error bases core. In this paper, we consider the eigenproblems for latin squares in a bipartite minmaxplus system. Constructing mutually unbiased bases from quantum latin squares benjamin musto department of computer science university of oxford benjamin. It is easy to see that classical latin squares are exactly the ordinary latin squares studied in combinatorics 6, and so the theory of quantum latin squares extends this classical theory. A maximally entangled basis meb for a bipartite system represented by a tensor product hilbert space h. Fractional latin squares, simplex algebras, and generalized. Quantum information processing 2017 hosted by microsoft.
We present a new method for constructing a ueb from a quantum latin square equipped with extra data. Constructing mutually unbiased bases from quantum latin squares benjamin musto benjamin. The only essential topics concerning latin squares and quasigroups are given in section 2, since these mathematical constructions are not generally known. There are at most n 1 mutually orthogonal latin squares of order n. In board games such as chess which feature a grid of squares, orthogonal is used to mean in the same rowrank or columnfile. Quantum ldpc codes derived from combinatorial objects and. The proposed algorithm is implemented in matlab, using maxplus algebra toolbox.
Quantum latin isometry squares we now define a generalisation of quantum latin square. A quantum latin isometry square d h j of order n is an nbyn grid of isometries. The following day, her story began appearing in irish papers and soon after was splashed across the front page of the london times, complete with a photo of. Its a perpetual wonder that mathematical theories developed with no useful purpose in mind except to satisify a mathematical curiosity, often and most unexpectedly apply not only to other parts of mathematics but to other sciences and real world problems.
Pdf latin squares and their applications to cryptography. H, is an orthonormal basis such that each basis state is maximally entangled. There is a standard notion of orthogonality for classical latin squares 10. A classical latin square is a quantum latin square for which every element of the array is in the computational basis. Furthermore, we believe that the m level entangled states are a kind of realistic entangled states in quantum physical systems.
Request pdf a class of quantum ldpc codes derived from latin squares and combinatorial design in this paper we construct a class of regular low density parity check ldpc codes derived from. Formalization of quantum protocols using coq 66 honda. This is the counterpart to squares which are diagonally adjacent. Rogers observed before 2007 that latin squares are multisemimagic for rows and columns. Many concepts of combinatorial designs, such as orthogonal arrays, hadamard matrices and orthogonal latin squares etc. Introduction ostquantum cryptography pqc is a relatively new cryptologic trend 1, 2 that acquired a nist status 3, 4. We characterize completely the unitary operators preserving diagonal, blockdiagonal, and tensor product algebras. New construction of mutually unbiased bases in square.
On bipartite unitary matrices generating subalgebra. Qip 2017 was hosted in seattle, washington by the quarc group at microsoft research in redmond and the university of washington. Classical and quantum design theory tam as tasn adi bme, institute of mathematics. Classical and quantum design theory analizis tanszek.
Fermionic quantum theory and superselection rules for operational probabilistic theories. Constructing mutually unbiased bases from quantum latin squares. Pdf orthogonality for quantum latin isometry squares. International journal of theoretical physics, volume 0, issue. Dedicated to the unification of the latest physics research, this journal seeks to map the direction of future research by presenting original work in traditional physics like general relativity, quantum theory with relativistic quantum field theory, as used. Construction of mutually unbiased bases using mutually orthogonal latin squares. A class of quantum ldpc codes derived from latin squares and combinatorial design salah a. Quantum physics and logic 2015 department of computer. There is a standard notion of orthogonality for classical latin squares 11. Improved quantuminspired evolutionary algorithm for. Quantum latin squares quantum latin arrangements quantum orthogonal arrays mathematics quantum mechanics. A class of quantum ldpc codes derived from latin squares.
Analysis of quantum entanglement in quantum programs using stabilizer formalism 21 tosini, dariano, manessi, perinotti. For each square found determine whether or not it is the multiplication table of a group. The remaining greek majuscules can be produced with ordinary latin letters. Fractional latin squares, simplex algebras, and generalized quotients article in journal of statistical planning and inference 862. Conference proceedings scientific tracks abstracts lasers. We use quantum latin squares to build maximally entangled bases, and show how a pair of mutually unbiased maximally entangled bases can be constructed in square dimension from orthogonal quantum latin squares. Jan 14, 2017 20th annual conference on quantum information processing.
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