The Experts below are selected from a list of 372630 Experts worldwide ranked by ideXlab platform
Andrew Klapper - One of the best experts on this subject based on the ideXlab platform.
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On $q$-nearly bent Boolean functions
arXiv: Combinatorics, 2019Co-Authors: Zhixiong Chen, Andrew KlapperAbstract:For each non-constant Boolean function $q$, Klapper introduced the notion of $q$-transforms of Boolean functions. The {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable from $q$ by nonsingular linear Change of Basis. In this work we discuss the existence of $q$-nearly bent functions, a new family of Boolean functions characterized by the $q$-transform. Let $q$ be a non-affine Boolean function. We prove that any balanced Boolean functions (linear or non-linear) are $q$-nearly bent if $q$ has weight one, which gives a positive answer to an open question (whether there exist non-affine $q$-nearly bent functions) proposed by Klapper. We also prove a necessary condition for checking when a function isn't $q$-nearly bent.
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A New Transform Related to Distance From a Boolean Function
IEEE Transactions on Information Theory, 2016Co-Authors: Andrew KlapperAbstract:We introduce a new transform on Boolean functions generalizing the Walsh–Hadamard transform. For Boolean functions $q$ and $f$ , the $q$ -transform of $f$ measures the proximity of $f$ to the set of functions obtained from $q$ by Change of Basis. This has implications for security against certain algebraic attacks. In this paper, we derive the expected value and second moment (Parseval’s equation) of the $q$ -transform, leading to a notion of $q$ -bentness. We also develop a Poisson summation formula, which leads to a proof that the $q$ -transform is invertible.
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a new transform related to distance from a boolean function extended abstract
International Conference on Sequences and Their Applications, 2014Co-Authors: Andrew KlapperAbstract:We introduce a new transform on Boolean functions generalizing the Walsh-Hadamard transform. For Boolean functions \(q\) and \(f\), the q-transform of f measures the proximity of \(f\) to the set of functions obtained from \(q\) by Change of Basis. This has implications for security against certain algebraic attacks. In this paper we derive the expected value and second moment (Parseval’s equation) of the \(q\)-transform, leading to a notion of \(q\)-bentness. We also develop a Poisson Summation Formula, which leads to a proof that the \(q\)-transform is invertible.
Thomas Vidick - One of the best experts on this subject based on the ideXlab platform.
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self testing of a single quantum device under computational assumptions
Conference on Innovations in Theoretical Computer Science, 2021Co-Authors: Tony Metger, Thomas VidickAbstract:Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system’s state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a Change of Basis applied to both the device’s state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
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self testing of a single quantum device under computational assumptions
arXiv: Quantum Physics, 2020Co-Authors: Tony Metger, Thomas VidickAbstract:Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations. This usually requires the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a Change of Basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement inside a single quantum device. We achieve this using techniques introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
Bassam Bamieh - One of the best experts on this subject based on the ideXlab platform.
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discovering the fourier transform a tutorial on circulant matrices circular convolution and the dft
arXiv: Signal Processing, 2018Co-Authors: Bassam BamiehAbstract:How could the Fourier transform be discovered if one didn't know it? In the case of the Discrete Fourier Transform (DFT), we show how it arises naturally out of analysis of circulant matrices. In particular, the DFT can be derived as the Change of Basis that simultaneously diagonalizes all circulant matrices. Thus the DFT arises naturally from a linear algebra question. Rather than thinking of the DFT as a signal transform, it is more natural to think of it as a Change of Basis that renders a certain set of linear operations into a simple, diagonal form.
G J Milburn - One of the best experts on this subject based on the ideXlab platform.
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the quantum mellin transform
arXiv: Quantum Physics, 2007Co-Authors: J Twamley, G J MilburnAbstract:We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to ``Hyperbolic phase space''. We show that this new unitary Change of Basis from the position x on the half line to the Hyperbolic momentum $p_\eta$, transforms the wavefunction via a Mellin transform on to the critial line $s=1/2-ip_\eta$. We utilise this new transform to find quantum wavefunctions whose Hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann Zeta function. We finally give possible physical realisations to perform an indirect measurement of the Hyperbolic momentum of a quantum system on the half-line.
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the quantum mellin transform
New Journal of Physics, 2006Co-Authors: J Twamley, G J MilburnAbstract:We uncover a new type of unitary operation for quantum mechanics on the half-line which yields a transformation to 'hyperbolic phase space' (η, pη). We show that this new unitary Change of Basis from the position x on the half line to the hyperbolic momentum pη, transforms the wavefunction via a Mellin transform on to the critical line s = 1/2−ipη. We utilize this new transform to find quantum wavefunctions whose hyperbolic momentum representation approximate a class of higher transcendental functions, and in particular, approximate the Riemann–Zeta function. We finally give possible physical realizations to perform an indirect measurement of the hyperbolic momentum of a quantum system on the half-line.
Tony Metger - One of the best experts on this subject based on the ideXlab platform.
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self testing of a single quantum device under computational assumptions
Conference on Innovations in Theoretical Computer Science, 2021Co-Authors: Tony Metger, Thomas VidickAbstract:Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations, and plays an important role in device-independent quantum information processing as well as quantum complexity theory. Prior works on self-testing require the assumption that the system’s state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a Change of Basis applied to both the device’s state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement, a property usually closely associated with two separated subsystems, inside a single quantum device. To achieve this, we build on techniques first introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.
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self testing of a single quantum device under computational assumptions
arXiv: Quantum Physics, 2020Co-Authors: Tony Metger, Thomas VidickAbstract:Self-testing is a method to characterise an arbitrary quantum system based only on its classical input-output correlations. This usually requires the assumption that the system's state is shared among multiple parties that only perform local measurements and cannot communicate. Here, we replace the setting of multiple non-communicating parties, which is difficult to enforce in practice, by a single computationally bounded party. Specifically, we construct a protocol that allows a classical verifier to robustly certify that a single computationally bounded quantum device must have prepared a Bell pair and performed single-qubit measurements on it, up to a Change of Basis applied to both the device's state and measurements. This means that under computational assumptions, the verifier is able to certify the presence of entanglement inside a single quantum device. We achieve this using techniques introduced by Brakerski et al. (2018) and Mahadev (2018) which allow a classical verifier to constrain the actions of a quantum device assuming the device does not break post-quantum cryptography.