A Concise Guide to Complex Hadamard Matrices

Experimental realization of any discrete unitary operator

Reck, M., Zeilinger, A., Bernstein, H. J., & Bertani, P. (1994) · Physical Review Letters · doi:10.1103/physrevlett.73.58 · Cited by 2,155 · see citing works

Commutator of the Quark Mass Matrices in the Standard Electroweak Model and a Measure of Maximal CP Nonconservation

Jarlskog, C. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.1039 · Cited by 1,657 · see citing works

Optimal state-determination by mutually unbiased measurements

Wootters, W. K., & Fields, B. D. (1989) · Annals of Physics · doi:10.1016/0003-4916(89)90322-9 · Cited by 1,458 · see citing works

Geometrical description of quantal state determination

Ivonovic, I. D. (1981) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/14/12/019 · Cited by 732 · see citing works

Fuglede’s conjecture is false in 5 and higher dimensions

Tao, T. (2004) · Mathematical Research Letters · doi:10.4310/mrl.2004.v11.n2.a8 · Cited by 392 · see citing works

LX. Thoughts on inverse orthogonal matrices, simultaneous signsuccessions, and tessellated pavements in two or more colours, with applications to Newton's rule, ornamental tile-work, and the theory of numbers

Sylvester, J. J. (1867) · The London Edinburgh and Dublin Philosophical Magazine and Journal of Science · doi:10.1080/14786446708639914 · Cited by 341 · see citing works

Constructions of Mutually Unbiased Bases

Klappenecker, A., & Rötteler, M. (2004) · Lecture Notes in Computer Science · doi:10.1007/978-3-540-24633-6_10 · Cited by 288 · see citing works

On Orthogonal Arrays

Seiden, E., & Zemach, R. (1966) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177699280 · Cited by 285 · see citing works

All teleportation and dense coding schemes

Werner, R. F. (2001) · Journal of Physics A: Mathematical and General · doi:10.1088/0305-4470/34/35/332 · Cited by 270 · see citing works

All Teleportation and Dense Coding SchemesPreprint

Werner, R. F. (2000) · Cited by 261 · see citing works

Generalized Hadamard matrices

Butson, A. T. (1962) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-1962-0142557-0 · Cited by 228 · see citing works

Hadamard’s determinant theorem and the sum of four squares

Williamson, J. H. (1944) · Duke Mathematical Journal · doi:10.1215/s0012-7094-44-01108-7 · Cited by 215 · see citing works

Hadamard Matrices and Their Applications

Agaian, S. С. (1985) · Lecture notes in mathematics · doi:10.1007/bfb0101073 · Cited by 201 · see citing works

Equiangular lines, mutually unbiased bases, and spin models

Godsil, C. D., & Roy, A. (2008) · European Journal of Combinatorics · doi:10.1016/j.ejc.2008.01.002 · Cited by 170 · see citing works

On SIC-POVMs and MUBs in Dimension 6Preprint

Grassl, M. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0406175 · Cited by 150 · see citing works

Complex Hadamard matrices and the Spectral Set Conjecture

Kolountzakis, M. N., & Matolcsi, M. (2004) · RACO (Revistes Catalanes amb Accés Obert) (Consorci de Serveis Universitaris de Catalunya) · doi:10.48550/arxiv.math/0411512 · Cited by 147 · see citing works

A Hadamard matrix of order 428

Kharaghani, H., & Tayfeh‐Rezaie, B. (2004) · Journal of Combinatorial Designs · doi:10.1002/jcd.20043 · Cited by 145 · see citing works

Fuglede’s conjecture fails in dimension 4

Matolcsi, M. (2005) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-05-07874-3 · Cited by 144 · see citing works

How to ascertain the values of sigmax , σy , and σz of a spin-1/2particle

Vaidman, L., Aharonov, Y., & Albert, D. Z. (1987) · Physical Review Letters · doi:10.1103/physrevlett.58.1385 · Cited by 128 · see citing works

Some results on the parametrization of complex Hadamard matrices

Diţă, P. (2004) · Journal of Physics A Mathematical and General · doi:10.1088/0305-4470/37/20/008 · Cited by 111 · see citing works

Group representations, error bases and quantum codes

Lab., N. (. S. L. A. N., Knill, E. H., & USDOE, W. (1996) · doi:10.2172/378680 · Cited by 106 · see citing works

A faster way to count the solutions of inhomogeneous systems of algebraic equations, with applications to cyclic n-roots

Björck, G., & Fröberg, R. (1991) · Journal of Symbolic Computation · doi:10.1016/s0747-7171(08)80153-8 · Cited by 103 · see citing works

Minimal rephasing-invariantCP-violating parameters with Dirac and Majorana fermions

Nieves, J. F., & Pal, P. B. (1987) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.36.315 · Cited by 97 · see citing works

Partial λ-Geometries and Generalized Hadamard Matrices Over Groups

Drake, D. A. (1979) · Canadian Journal of Mathematics · doi:10.4153/cjm-1979-062-1 · Cited by 95 · see citing works

The mean king's problem: prime degrees of freedom

Englert, B.-G., & Aharonov, Y. (2001) · Physics Letters A · doi:10.1016/s0375-9601(01)00271-7 · Cited by 94 · see citing works

Beyond stabilizer codes .I. Nice error bases

Klappenecker, A., & Rötteler, M. (2002) · IEEE Transactions on Information Theory · doi:10.1109/tit.2002.800471 · Cited by 81 · see citing works

The mean king's problem: Prime degrees of freedom

Englert, B., & Aharonov, Y. (2001) · CERN Document Server (European Organization for Nuclear Research) · Cited by 75 · see citing works

Rephasing-invariant parametrizations of generalized Kobayashi-Maskawa matrices

Bjorken, J. D., & Dunietz, I. (1987) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.36.2109 · Cited by 74 · see citing works

Mutually unbiased bases and orthogonal decompositions of Lie algebras

Boykin, P. O., Sitharam, M., Tiep, P. H., & Wocjan, P. (2007) · Quantum Information and Computation · doi:10.26421/qic7.4-6 · Cited by 68 · see citing works

Birkhoff’s Polytope and Unistochastic Matrices, N = 3 and N = 4

Bengtsson, I., Ericsson, Å., Kuś, M., Tadej, W., & Życzkowski, K. (2005) · Communications in Mathematical Physics · doi:10.1007/s00220-005-1392-8 · Cited by 66 · see citing works

Complex Hadamard matrices

Wallis, J. S. (1973) · Linear and Multilinear Algebra · doi:10.1080/03081087308817024 · Cited by 63 · see citing works

Relations Among Generalized Hadamard Matrices, Relative Difference Sets, and Maximal Length Linear Recurring Sequences

Butson, A. T. (1963) · Canadian Journal of Mathematics · doi:10.4153/cjm-1963-005-3 · Cited by 57 · see citing works

Hamiltonian theory of a symmetric multiport

Jex, I., Stenholm, S., & Zeilinger, A. (1995) · Optics Communications · doi:10.1016/0030-4018(95)00078-m · Cited by 53 · see citing works

Simulation and reversal of n -qubit Hamiltonians using Hadamard matrices

Leung, D. (2002) · Journal of Modern Optics · doi:10.1080/09500340110109674 · Cited by 44 · see citing works

New classes of finite unimodular sequences with unimodular Fourier transforms. Circulant Hadamard matrices with complex entries

Björck, G., & Saffari, B. (1995) · Cited by 37 · see citing works

Switching Operations for Hadamard Matrices

Orrick, W. P. (2008) · SIAM Journal on Discrete Mathematics · doi:10.1137/050641727 · Cited by 35 · see citing works

Real Mutually Unbiased BasesPreprint

Boykin, P. O., Sitharam, M., Tarifi, M., & Wocjan, P. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0502024 · Cited by 30 · see citing works

Existence of continuous families of complex hadamard matrices of certain prime dimensions and related results

Petrescu, M., & Popa, S. (1997) · Cited by 30 · see citing works

On the non-existence of generalized Hadamard matrices

Winterhof, A. (2000) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(99)00147-0 · Cited by 29 · see citing works

Cocyclic Generalised Hadamard Matrices and Central Relative Difference Sets

Perera, A. A. I., & Horadam, K. J. (1998) · Designs Codes and Cryptography · doi:10.1023/a:1008367718018 · Cited by 27 · see citing works

A finiteness result for commuting squares of matrix algebrasPreprint

Nicoară, R. (2004) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0404301 · Cited by 25 · see citing works

On the reconstruction of a unitary matrix from its moduli

Auberson, G., Martin, A., & Mennessier, G. (1991) · Communications in Mathematical Physics · doi:10.1007/bf02099133 · Cited by 25 · see citing works

A sensitive algorithm for detecting the inequivalence of Hadamard matrices

Fang, K., & Ge, G. (2003) · Mathematics of Computation · doi:10.1090/s0025-5718-03-01539-4 · Cited by 20 · see citing works

A generalised Hadamard transform

(18043900), K. H. (2005) · RMIT Research Repository (RMIT University Library) · Cited by 19 · see citing works

On the asymptotic existence of complex Hadamard matrices

Craigen, R., Holzmann, W. H., & Kharaghani, H. (1997) · Journal of Combinatorial Designs · doi:10.1002/(sici)1520-6610(1997)5:5 · Cited by 16 · see citing works

Complex Hadamard matrices related to Bent sequences

Matsufuji, S., & Suehiro, N. (1996) · IEEE Transactions on Information Theory · doi:10.1109/18.485734 · Cited by 16 · see citing works

Error correcting codes associated with complex Hadamard matrices

Heng, I., & Cooke, C. H. (1998) · Applied Mathematics Letters · doi:10.1016/s0893-9659(98)00059-7 · Cited by 15 · see citing works

Conjectures about Hadamard matrices

Beder, J. H. (1998) · Journal of Statistical Planning and Inference · doi:10.1016/s0378-3758(98)00020-2 · Cited by 14 · see citing works

Permutation equivalence classes of kronecker products of unitary Fourier matrices

Tadej, W. (2006) · Linear Algebra and its Applications · doi:10.1016/j.laa.2006.03.004 · Cited by 14 · see citing works

Generation of Inequivalent Generalized Bell Bases

Wójcik, A., Grudka, A., & Chhajlany, R. W. (2003) · Quantum Information Processing · doi:10.1023/b:qinp.0000004124.68257.d9 · Cited by 13 · see citing works

New Tales of the Mean KingPreprint

Klappenecker, A., & Roetteler, M. (2005) · arXiv (Cornell University) · doi:10.48550/arxiv.quant-ph/0502138 · Cited by 10 · see citing works

Generalized Hadamard Matrices

Hayden, J. L. (1997) · Designs Codes and Cryptography · doi:10.1023/a:1008245910019 · Cited by 9 · see citing works

GLOBAL FITS TO THE CABIBBO–KOBAYASHI–MASKAWA MATRIX: UNITARITY CONDITION METHOD VERSUS STANDARD UNITARITY TRIANGLES APPROACH

Diţă, P. (2005) · Modern Physics Letters A · doi:10.1142/s0217732305017974 · Cited by 7 · see citing works

Universal linear optics

Carolan, J., Harrold, C., Sparrow, C., Martín-López, E., Russell, N. J., Silverstone, J. W., Shadbolt, P. J., Matsuda, N., Oguma, M., Itoh, M., et al. (2015) · Science · doi:10.1126/science.aab3642 · Cited by 1,093 · see citing works

ON MUTUALLY UNBIASED BASES

Durt, T., Englert, B., Bengtsson, I., & Życzkowski, K. (2010) · International Journal of Quantum Information · doi:10.1142/s0219749910006502 · Cited by 715 · see citing works

Interacting quantum observables : categorical algebra and diagrammatics

Coecke, B., & Duncan, R. (2008) · Strathprints: The University of Strathclyde institutional repository (University of Strathclyde) · Cited by 345 · see citing works

Single-scan multidimensional magnetic resonance

Tal, A., & Frydman, L. (2010) · Progress in Nuclear Magnetic Resonance Spectroscopy · doi:10.1016/j.pnmrs.2010.04.001 · Cited by 278 · see citing works

Decoherence in quantum walks – a review

KENDON, V. (2007) · Mathematical Structures in Computer Science · doi:10.1017/s0960129507006354 · Cited by 252 · see citing works

Decoherence in quantum walks - a review

Kendon, V (2006) · CERN Document Server (European Organization for Nuclear Research) · Cited by 243 · see citing works

Absolutely maximally entangled states, combinatorial designs, and multiunitary matrices

Goyeneche, D., Alsina, D. A., Latorre, J. I., Riera, A., & Życzkowski, K. (2015) · Physical Review A · doi:10.1103/physreva.92.032316 · Cited by 161 · see citing works

Majorization entropic uncertainty relations

Puchała, Z., Rudnicki, Ł., & Życzkowski, K. (2013) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/46/27/272002 · Cited by 159 · see citing works

Genuinely multipartite entangled states and orthogonal arrays

Goyeneche, D., & Życzkowski, K. (2014) · Physical Review A · doi:10.1103/physreva.90.022316 · Cited by 157 · see citing works

Maximum velocity quantum circuits

Claeys, P. W., & Lamacraft, A. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.033032 · Cited by 127 · see citing works

Mutually unbiased bases and Hadamard matrices of order six

Bengtsson, I., Bruzda, W., Ericsson, Å., Larsson, J.-Å., Tadej, W., & Życzkowski, K. (2007) · Journal of Mathematical Physics · doi:10.1063/1.2716990 · Cited by 130 · see citing works

Recurrence and Pólya Number of Quantum Walks

Štefaňák, M., Jex, I., & Kiss, T. (2008) · Physical Review Letters · doi:10.1103/physrevlett.100.020501 · Cited by 118 · see citing works

Three Ways to Look at Mutually Unbiased Bases

Bengtsson, I. (2007) · AIP conference proceedings · doi:10.1063/1.2713445 · Cited by 118 · see citing works

Constructing mutually unbiased bases in dimension six

BRIERLEY, S. D., & Weigert, S. (2009) · Physical Review A · doi:10.1103/physreva.79.052316 · Cited by 116 · see citing works

WAVE-PARTICLE DUALITY IN MULTI-PATH INTERFEROMETERS: GENERAL CONCEPTS AND THREE-PATH INTERFEROMETERS

Englert, B., Kaszlikowski, D., Kwek, L. C., & Chee, W. H. (2008) · International Journal of Quantum Information · doi:10.1142/s0219749908003220 · Cited by 110 · see citing works

Quantum Incompatibility Witnesses

Carmeli, C., Heinosaari, T., & Toigo, A. (2019) · Physical Review Letters · doi:10.1103/physrevlett.122.130402 · Cited by 102 · see citing works

Interference of identical particles from entanglement to boson-sampling

Tichy, M. C. (2014) · Journal of Physics B Atomic Molecular and Optical Physics · doi:10.1088/0953-4075/47/10/103001 · Cited by 95 · see citing works

Five Open Problems in Quantum Information Theory

Horodecki, P., Rudnicki, Ł., & Życzkowski, K. (2022) · PRX Quantum · doi:10.1103/prxquantum.3.010101 · Cited by 134 · see citing works

Many-particle interference beyond many-boson and many-fermion statistics

Tichy, M. C., Tiersch, M., Mintert, F., & Buchleitner, A. (2012) · New Journal of Physics · doi:10.1088/1367-2630/14/9/093015 · Cited by 82 · see citing works

A generalized Pauli problem and an infinite family of MUB-triplets in dimension 6

Jaming, P., Matolcsi, M., Móra, P., Szöllősi, F., & Weiner, M. (2009) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/42/24/245305 · Cited by 73 · see citing works

A Multiplier-Free Generator for Polyphase Complete Complementary Codes

Das, S., Budisin, S., Majhi, S., Liu, Z., & Guan, Y. L. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2017.2780050 · Cited by 64 · see citing works

An angular momentum approach to quadratic Fourier transform, Hadamard matrices, Gauss sums, mutually unbiased bases, the unitary group and the Pauli group

Kibler, M. (2009) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/42/35/353001 · Cited by 58 · see citing works

Unification of different views of decoherence and discord

Coles, P. J. (2012) · Physical Review A · doi:10.1103/physreva.85.042103 · Cited by 57 · see citing works

Maximum coherence in the optimal basis

Hu, M., Shen, S., & Fan, H. (2017) · Physical Review A · doi:10.1103/physreva.96.052309 · Cited by 58 · see citing works

Four-photon indistinguishability transition

Tichy, M. C., Lim, H., Ra, Y.-S., Mintert, F., Kim, Y.-H., & Buchleitner, A. (2011) · Physical Review A · doi:10.1103/physreva.83.062111 · Cited by 52 · see citing works

Coined quantum walks on percolation graphs

Leung, G., Knott, P., Bailey, J., & Kendon, V. M. (2010) · New Journal of Physics · doi:10.1088/1367-2630/12/12/123018 · Cited by 49 · see citing works

Maximal coherence in a generic basis

Yao, Y., Dong, G., Ge, L., Li, M., & Sun, C. P. (2016) · Physical Review A · doi:10.1103/physreva.94.062339 · Cited by 51 · see citing works

Coherifying quantum channels

Korzekwa, K., Czachórski, S., Puchała, Z., & Życzkowski, K. (2018) · New Journal of Physics · doi:10.1088/1367-2630/aaaff3 · Cited by 51 · see citing works

Construction and the ergodicity properties of dual unitary quantum circuits

Borsi, M., & Pozsgay, B. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.106.014302 · Cited by 48 · see citing works

Distinguishability of generic quantum states

Puchała, Z., Pawela, Ł., & Życzkowski, K. (2016) · Physical Review A · doi:10.1103/physreva.93.062112 · Cited by 48 · see citing works

Orthogonal maximal abelian * -subalgebras of the 6×6 matrices

Beauchamp, K. A., & Nicoară, R. (2008) · Linear Algebra and its Applications · doi:10.1016/j.laa.2007.10.023 · Cited by 45 · see citing works

Quantum Latin squares and unitary error bases

Vicary, J., & Musto, B. (2016) · Apollo (University of Cambridge) · doi:10.17863/cam.52830 · Cited by 44 · see citing works

Biunitary constructions in quantum information

Reutter, D., & Vicary, J. (2019) · doi:10.21136/hs.2019.04 · Cited by 40 · see citing works

Exact local correlations in kicked chains

Gutkin, B., Braun, P. A., Akila, M., Waltner, D., & Guhr, T. (2020) · Physical review. B./Physical review. B · doi:10.1103/physrevb.102.174307 · Cited by 40 · see citing works

Defect of a unitary matrix

Tadej, W., & Życzkowski, K. (2008) · Linear Algebra and its Applications · doi:10.1016/j.laa.2008.02.036 · Cited by 39 · see citing works

Complex equiangular Parseval frames and Seidel matrices containing 𝑝th roots of unity

Bodmann, B. G., & Elwood, H. J. (2010) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-2010-10435-5 · Cited by 38 · see citing works

From SICs and MUBs to Eddington

Bengtsson, I. (2010) · Journal of Physics: Conference Series · doi:10.1088/1742-6596/254/1/012007 · Cited by 37 · see citing works

Parametrizing complex Hadamard matrices

Szöllősi, F. (2007) · European Journal of Combinatorics · doi:10.1016/j.ejc.2007.06.009 · Cited by 37 · see citing works

The limited role of mutually unbiased product bases in dimension 6

McNulty, D., & Weigert, S. (2012) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8113/45/10/102001 · Cited by 37 · see citing works

Three-parameter complex Hadamard matrices of order 6

Karlsson, B. R. (2010) · Linear Algebra and its Applications · doi:10.1016/j.laa.2010.08.020 · Cited by 36 · see citing works

Complex Hadamard matrices of order 6: a four-parameter familyPreprint

Szöllősi, F. (2010) · Cited by 35 · see citing works

Tight frames, Hadamard matrices and Zauner’s conjecture

Appleby, M., Bengtsson, I., Flammia, S. T., & Goyeneche, D. (2019) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ab25ad · Cited by 34 · see citing works

Complementarity in Quantum Systems

Petz, D. (2006) · Cited by 34 · see citing works

Mutually unbiased maximally entangled bases in $$\mathbb {C}^d\otimes \mathbb {C}^{kd}$$ C d ⊗ C k d

Tao, Y.-H., Nan, H., Zhang, J., & Fei, S.-M. (2015) · Quantum Information Processing · doi:10.1007/s11128-015-0980-6 · Cited by 33 · see citing works

Generalizations of Pauli channels

Ohno, H., & Petz, D. (2009) · Acta Mathematica Academiae Scientiarum Hungaricae · doi:10.1007/s10474-009-8171-5 · Cited by 33 · see citing works

Complementarity in quantum systems

Petz, D. (2007) · Reports on Mathematical Physics · doi:10.1016/s0034-4877(07)00010-9 · Cited by 33 · see citing works

Five open problems in quantum informationPreprint

Horodecki, P., Rudnicki, Ł., & Życzkowski, K. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2002.03233 · Cited by 33 · see citing works

Exotic complex Hadamard matrices and their equivalence

Szöllősi, F. (2010) · Cryptography and Communications · doi:10.1007/s12095-010-0021-3 · Cited by 32 · see citing works

Improved multiuser MIMO unitary precoding using partial channel state information and insights from the riemannian manifold

Kim, I., Park, S., Love, D. J., & Sung, K. (2009) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2009.071384 · Cited by 32 · see citing works

New Parametric Discrete Fourier and Hartley Transforms, and Algorithms for Fast Computation

Bouguezel, S., Ahmad, M., & Swamy, M. N. S. (2010) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2010.2072151 · Cited by 31 · see citing works

Representations of quantum permutation algebras

Banica, T., Bichon, J., & Schlenker, J. (2009) · Journal of Functional Analysis · doi:10.1016/j.jfa.2009.04.013 · Cited by 30 · see citing works

Diagonal unitary entangling gates and contradiagonal quantum states

Lakshminarayan, A., Puchała, Z., & Życzkowski, K. (2014) · Physical Review A · doi:10.1103/physreva.90.032303 · Cited by 29 · see citing works

Block- ZXZ synthesis of an arbitrary quantum circuit

Vos, A. D., & Baerdemacker, S. D. (2016) · Physical Review A · doi:10.1103/physreva.94.052317 · Cited by 29 · see citing works

Towards a Classification of 6 × 6 Complex Hadamard Matrices

Matolcsi, M., & Szöllősi, F. (2008) · Open Systems & Information Dynamics · doi:10.1142/s1230161208000092 · Cited by 29 · see citing works

Quantum Correlations in the Minimal Scenario

Thinh, L. P., Meroni, C., Sturmfels, B., Werner, R. F., & Ziegler, T. (2023) · Quantum · doi:10.22331/q-2023-03-16-947 · Cited by 28 · see citing works

Entropic uncertainty relations from equiangular tight frames and their applications

Rastegin, A. E. (2023) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2022.0546 · Cited by 26 · see citing works

Constructions of Complex Hadamard Matrices via Tiling Abelian Groups

Matolcsi, M., Réffy, J., & Szöllősi, F. (2007) · Open Systems & Information Dynamics · doi:10.1007/s11080-007-9050-6 · Cited by 26 · see citing works

FBG-Based Weak Coherent State and Entanglement-Assisted Multidimensional QKD

Djordjević, I. B. (2018) · IEEE photonics journal · doi:10.1109/jphot.2018.2860524 · Cited by 25 · see citing works

Block-circulant matrices with circulant blocks, Weil sums, and mutually unbiased bases. II. The prime power case

Combescure, M. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3078420 · Cited by 25 · see citing works

Pilot Contamination in Massive MIMO Induced by Timing and Frequency Errors

Yang, F., Cai, P., Qian, H. L., & Luo, X. (2018) · IEEE Transactions on Wireless Communications · doi:10.1109/twc.2018.2825982 · Cited by 25 · see citing works

Volume of the set of unistochastic matrices of order 3 and the mean Jarlskog invariant

Dunkl, C. F., & Życzkowski, K. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3272543 · Cited by 23 · see citing works

A two-parameter family of complex Hadamard matrices of order 6 induced by hypocycloids

Szöllősi, F. (2009) · Proceedings of the American Mathematical Society · doi:10.1090/s0002-9939-09-10102-8 · Cited by 23 · see citing works

A New Class of Reciprocal–Orthogonal Parametric Transforms

Bouguezel, S., Ahmad, M. O., & Swamy, M. N. S. (2008) · IEEE Transactions on Circuits and Systems I Regular Papers · doi:10.1109/tcsi.2008.2002923 · Cited by 23 · see citing works

A hybrid data-driven method for fast approximation of practical dynamic security region boundary of power systems

Liu, Y., Shi, X.-J., & Xu, Y. H. (2019) · International Journal of Electrical Power & Energy Systems · doi:10.1016/j.ijepes.2019.105658 · Cited by 23 · see citing works

Detecting entanglement can be more effective with inequivalent mutually unbiased bases

Hiesmayr, B. C., McNulty, D., Baek, S., Roy, S. S., Bae, J., & Chruściński, D. (2021) · New Journal of Physics · doi:10.1088/1367-2630/ac20ea · Cited by 22 · see citing works

Unbiased bases (Hadamards) for six-level systems: Four ways from Fourier

Skinner, A. J., Newell, V. A., & Sánchez, R. D. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3059166 · Cited by 22 · see citing works

Stochastic local operations with classical communication of absolutely maximally entangled states

Burchardt, A., & Raissi, Z. (2020) · Physical Review A · doi:10.1103/physreva.102.022413 · Cited by 21 · see citing works

COMPLEMENTARITY AND THE ALGEBRAIC STRUCTURE OF FOUR-LEVEL QUANTUM SYSTEMS

Petz, D., Szántó, A., & Weiner, M. (2009) · Infinite Dimensional Analysis Quantum Probability and Related Topics · doi:10.1142/s0219025709003598 · Cited by 21 · see citing works

Quantum groups and Hadamard matricesPreprint

Banica, T., & Nicoara, R. (2006) · arXiv (Cornell University) · doi:10.48550/arxiv.math/0610529 · Cited by 21 · see citing works

Conditions for optimal input states for discrimination of quantum channels

Jenčová, A., & Plávala, M. (2016) · Journal of Mathematical Physics · doi:10.1063/1.4972286 · Cited by 20 · see citing works

The Kronecker product in terms of Hubbard operators and the Clebsch–Gordan decomposition of

Enríquez, M., & Rosas-Ortiz, Ó. (2013) · Annals of Physics · doi:10.1016/j.aop.2013.08.016 · Cited by 20 · see citing works

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Lampio, P. H. J., Östergård, P. R. J., & Szöllősi, F. (2019) · Mathematics of Computation · doi:10.1090/mcom/3453 · Cited by 20 · see citing works

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Rampp, M. A., Rather, S. A., & Claeys, P. W. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.033271 · Cited by 19 · see citing works

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Banica, T., Nechita, I., & Życzkowski, K. (2012) · Open Systems & Information Dynamics · doi:10.1142/s1230161212500242 · Cited by 19 · see citing works

Construction of mutually unbiased maximally entangled bases through permutations of Hadamard matrices

Xu, D. (2017) · Quantum Information Processing · doi:10.1007/s11128-017-1534-x · Cited by 18 · see citing works

Matrices of fidelities for ensembles of quantum states and the Holevo quantity

Fannes, M., de Melo, F., Roga, W., & Życzkowski, K. (2012) · Quantum Information and Computation · doi:10.26421/qic12.5-6-8 · Cited by 20 · see citing works

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Gutkin, B., Braun, P. A., Akila, M., Waltner, D., & Guhr, T. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2001.01298 · Cited by 18 · see citing works

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Banica, T., & Bichon, J. (2015) · International Mathematics Research Notices · doi:10.1093/imrn/rnv102 · Cited by 17 · see citing works

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Sommers, G. M., Gopalakrishnan, S., Gullans, M. J., & Huse, D. A. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.064311 · Cited by 17 · see citing works

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Claeys, P. W., Lamacraft, A., & Vicary, J. (2024) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad653f · Cited by 17 · see citing works

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Vos, A. D., & Baerdemacker, S. D. (2013) · Open Systems & Information Dynamics · doi:10.1142/s1230161213500042 · Cited by 17 · see citing works

Algebraic complementarity in quantum theory

Petz, D. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3276681 · Cited by 17 · see citing works

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Chterental, O., & Djoković, D. Ž. (2007) · Linear Algebra and its Applications · doi:10.1016/j.laa.2007.09.022 · Cited by 17 · see citing works

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Vos, A. D., & Baerdemacker, S. D. (2016) · Cited by 17 · see citing works

Exactly solvable quantum many-body dynamics from space-time duality

Bertini, B., Claeys, P. W., & Prosen, T. (2025) · Reviews of Modern Physics · doi:10.1103/yx73-dk86 · Cited by 16 · see citing works

Hadamard matrices from mutually unbiased bases

Diţă, P. (2010) · Journal of Mathematical Physics · doi:10.1063/1.3456082 · Cited by 15 · see citing works

Families of complex Hadamard matrices

Sá, N. B. E., & Bengtsson, I. (2013) · Linear Algebra and its Applications · doi:10.1016/j.laa.2012.10.029 · Cited by 15 · see citing works

Two-parameter complex Hadamard matrices for N=6

Karlsson, B. R. (2009) · Journal of Mathematical Physics · doi:10.1063/1.3198230 · Cited by 15 · see citing works

The quaternary complex Hadamard matrices of orders 10, 12, and 14

Lampio, P. H. J., Szöllősi, F., & Östergård, P. R. J. (2012) · Discrete Mathematics · doi:10.1016/j.disc.2012.10.001 · Cited by 15 · see citing works

Quantum Key Distribution Highly Sensitive to EavesdroppingPreprint

BRIERLEY, S. D. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0910.2578 · Cited by 15 · see citing works

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Mestyán, M., Pozsgay, B., & Wanless, I. M. (2024) · SciPost Physics · doi:10.21468/scipostphys.16.1.010 · Cited by 14 · see citing works

Generalized graph states based on Hadamard matrices

Cui, S. X., Yu, N., & Zeng, B. (2015) · Journal of Mathematical Physics · doi:10.1063/1.4926427 · Cited by 14 · see citing works

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Image encryption using the reciprocal-orthogonal parametric transform

Bouguezel, S., Ahmad, M. O., & Swamy, M. N. S. (2010) · IEEE International Symposium on Circuits and Systems proceedings · doi:10.1109/iscas.2010.5537110 · Cited by 14 · see citing works

Matrix product constraints by projection methods

Elser, V. (2016) · Journal of Global Optimization · doi:10.1007/s10898-016-0466-9 · Cited by 14 · see citing works

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Higham, N. J., & Mikaitis, M. (2021) · Numerical Algorithms · doi:10.1007/s11075-021-01226-2 · Cited by 13 · see citing works

Unbiased complex Hadamard matrices and bases

Best, D., & Kharaghani, H. (2010) · Cryptography and Communications · doi:10.1007/s12095-010-0029-8 · Cited by 14 · see citing works

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Claeys, P. W., & Lamacraft, A. (2024) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad776a · Cited by 13 · see citing works

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Szöllősi, F. (2007) · European Journal of Combinatorics · doi:10.1016/j.ejc.2007.06.009 · Cited by 37 · see citing works

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Matolcsi, M., & Szöllősi, F. (2008) · Open Systems & Information Dynamics · doi:10.1142/s1230161208000092 · Cited by 29 · see citing works

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Construction, classification and parametrization of complex Hadamard matrices

Szöllősi, F. (2012) · Open Research (Auckland University of Technology) · doi:10.60644/3263