Complexity and multi-functional variants of the Quantum-to-Quantum Bernoulli Factories

Fuente: arXiv
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Main Authors: Hoch, Francesco, Giordani, Taira, Carvacho, Gonzalo, Spagnolo, Nicolò, Sciarrino, Fabio
Format: Preprint
Published: 2025
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author Hoch, Francesco
Giordani, Taira
Carvacho, Gonzalo
Spagnolo, Nicolò
Sciarrino, Fabio
author_facet Hoch, Francesco
Giordani, Taira
Carvacho, Gonzalo
Spagnolo, Nicolò
Sciarrino, Fabio
contents A Bernoulli factory is a model for randomness manipulation that transforms an initial Bernoulli random variable into another Bernoulli variable by applying a predetermined function relating the output bias to the input one. In literature, quantum-to-quantum Bernoulli factory schemes have been proposed, which encode both the input and output variables using qubit amplitudes. This fundamental concept can serve as a subroutine for quantum algorithms that involve Bayesian inference and Monte Carlo methods, or that require data encryption, like in blind quantum computation. In this work, we present a characterisation of the complexity of the quantum-to-quantum Bernoulli factory by providing a lower bound on the required number of qubits needed to implement the protocol, an upper bound on the success probability and the quantum circuit that saturates the bounds. We also formalise and analyse two different variants of the original problem that address the possibility of increasing the number of input biases or the number of functions implemented by the quantum-to-quantum Bernoulli factory. The obtained results can be used as a framework for randomness manipulation via such an approach.
format Preprint
id arxiv_https___arxiv_org_abs_2512_10810
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Complexity and multi-functional variants of the Quantum-to-Quantum Bernoulli Factories
Hoch, Francesco
Giordani, Taira
Carvacho, Gonzalo
Spagnolo, Nicolò
Sciarrino, Fabio
Quantum Physics
A Bernoulli factory is a model for randomness manipulation that transforms an initial Bernoulli random variable into another Bernoulli variable by applying a predetermined function relating the output bias to the input one. In literature, quantum-to-quantum Bernoulli factory schemes have been proposed, which encode both the input and output variables using qubit amplitudes. This fundamental concept can serve as a subroutine for quantum algorithms that involve Bayesian inference and Monte Carlo methods, or that require data encryption, like in blind quantum computation. In this work, we present a characterisation of the complexity of the quantum-to-quantum Bernoulli factory by providing a lower bound on the required number of qubits needed to implement the protocol, an upper bound on the success probability and the quantum circuit that saturates the bounds. We also formalise and analyse two different variants of the original problem that address the possibility of increasing the number of input biases or the number of functions implemented by the quantum-to-quantum Bernoulli factory. The obtained results can be used as a framework for randomness manipulation via such an approach.
title Complexity and multi-functional variants of the Quantum-to-Quantum Bernoulli Factories
topic Quantum Physics
url https://arxiv.org/abs/2512.10810