The Burau Representation is Unitary [PDF]
Proceedings of the American Mathematical Society, 1984 A slight modification of the Burau representation of the braid group is shown to be unitary relative to an explicitly defined Hermitian form. This gives a partial answer to the problem of identifying the image of the Burau representation and provides a tool for attacking the question of whether or not the Burau representation is faithful.
Craig C. Squier
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Minimal unitary representation of SO*(8) = SO(6,2) and its SU(2) deformations as massless 6D conformal fields and their supersymmetric extensions [PDF]
, 2010 We study the minimal unitary representation (minrep) of SO(6,2) over an Hilbert space of functions of five variables, obtained by quantizing its quasiconformal realization.
Arkani-Hamed +68 more
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Direct dialling of Haar random unitary matrices [PDF]
New Journal of Physics, 2017 Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics.
Nicholas J Russell +3 more
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Modeling Quantum Behavior in the Framework of Permutation Groups
EPJ Web of Conferences, 2018 Quantum-mechanical concepts can be formulated in constructive finite terms without loss of their empirical content if we replace a general unitary group by a unitary representation of a finite group.
Kornyak Vladimir
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Null infinity and unitary representation of the Poincare group [PDF]
Journal of High Energy Physics, 2019 Following Pasterski-Shao-Strominger we construct a new basis of states in the single-particle Hilbert space of massless particles as a linear combination of standard Wigner states.
Shamik Banerjee
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Representation Class and Geometrical Invariants of Quantum States under Local Unitary Transformations [PDF]
, 2007 We investigate the equivalence of bipartite quantum mixed states under local unitary transformations by introducing representation classes from a geometrical approach.
Chen K. +6 more
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Unitary (semi)causal quantum-circuit representation of black hole evaporation [PDF]
European Physical Journal C: Particles and FieldsA general structure of unitary evolution (evaporation) of the black hole, respecting causality imposed by the event horizon (semicausality), has been derived and presented in the language of quantum circuits.
Bogusław Broda
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The Explicit Form of the Unitary Representation of the Poincaré Group for Vector-Valued Wave Functions (Massive and Massless), with Applications to Photon Localization and Position Operators [PDF]
MathematicsWe geometrically derive the explicit form of the unitary representation of the Poincaré group for vector-valued wave functions and use it to apply speed-of-light boosts to a simple polarization basis to end up with a Hawton–Baylis photon position ...
Arkadiusz Jadczyk
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On families of twisted power partial isometries
Karpatsʹkì Matematičnì Publìkacìï, 2022 We consider families of power partial isometries satisfying twisted commutation relations with deformation parameters $\lambda_{ij}\in\mathbb C$, $|\lambda_{ij}|=1$.
V.L. Ostrovskyi +2 more
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Detecting mixed-unitary quantum channels is NP-hard [PDF]
Quantum, 2020 A quantum channel is said to be a $\textit{mixed-unitary}$ channel if it can be expressed as a convex combination of unitary channels. We prove that, given the Choi representation of a quantum channel $\Phi$, it is NP-hard with respect to polynomial-time
Colin Do-Yan Lee, John Watrous
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