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Application of Quantum Process Calculus to Higher Dimensional Quantum Protocols [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We describe the use of quantum process calculus to describe and analyze quantum communication protocols, following the successful field of formal methods from classical computer science.
Simon J. Gay, Ittoop Vergheese Puthoor
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Almost periodic functions in quantum calculus [PDF]
Electronic Journal of Differential Equations, 2018 In this article, we introduce the concepts of Bochner and Bohr almost periodic functions in quantum calculus and show that both concepts are equivalent.
Martin Bohner, Jaqueline G. Mesquita
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Generalized Ostrowski-Gruss Like Inequality on Time Scales [PDF]
Sahand Communications in Mathematical Analysis, 2023 In this paper, we present a generalization of the Montgomery Identity to various time scale versions, including the discrete case, continuous case, and the case of quantum calculus.
Faraz Mehmood +2 more
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Quantum stochastic calculus with maximal operator domains. [PDF]
, 2004 Quantum stochastic calculus is extended in a new formulation in which its stochastic integrals achieve their natural and maximal domains. Operator adaptedness, conditional expectations and stochastic integrals are all defined simply in terms of the ...
Lindsay, J. Martin, Attal, Stéphane
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Some self-adjoint quantum semimartingales [PDF]
, 2006 It is proved that the quantum stochastic gauge integral preserves self-adjointness of vacuum-adapted processes. This fact, together with bounded perturbations and the link between the Hudson–Parthasarathy calculus and vacuum-adapted theory, is used to ...
Belton, Alexander C. R.
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Depicting qudit quantum mechanics and mutually unbiased qudit theories [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We generalize the ZX calculus to quantum systems of dimension higher than two. The resulting calculus is sound and universal for quantum mechanics. We define the notion of a mutually unbiased qudit theory and study two particular instances of these ...
André Ranchin
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Qutrit Dichromatic Calculus and Its Universality [PDF]
Electronic Proceedings in Theoretical Computer Science, 2014 We introduce a dichromatic calculus (RG) for qutrit systems. We show that the decomposition of the qutrit Hadamard gate is non-unique and not derivable from the dichromatic calculus.
Quanlong Wang, Xiaoning Bian
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Covariantization of quantized calculi over quantum groups [PDF]
Mathematica Bohemica, 2020 We introduce a method for construction of a covariant differential calculus over a Hopf algebra $A$ from a quantized calculus $da=[D,a]$, $a\in A$, where $D$ is a candidate for a Dirac operator for $A$.
Seyed Ebrahim Akrami, Shervin Farzi
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Quantum Control in the Unitary Sphere: Lambda-S1 and its Categorical Model [PDF]
Logical Methods in Computer Science, 2022 In a recent paper, a realizability technique has been used to give a semantics of a quantum lambda calculus. Such a technique gives rise to an infinite number of valid typing rules, without giving preference to any subset of those.
Alejandro Díaz-Caro, Octavio Malherbe
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Superdense Coding with GHZ and Quantum Key Distribution with W in the ZX-calculus [PDF]
Electronic Proceedings in Theoretical Computer Science, 2012 Quantum entanglement is a key resource in many quantum protocols, such as quantum teleportation and quantum cryptography. Yet entanglement makes protocols presented in Dirac notation difficult to verify.
Anne Hillebrand
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