Quantum-to-Quantum Bernoulli Factory

Abstract

Given a coin with unknown bias $p\in [0,1]$, can we exactly simulate another coin with bias $f(p)$? The exact set of simulable functions has been well characterized 20 years ago. In this paper, we ask the quantum counterpart of this question: Given the quantum coin $|p⟩=\sqrt{p}|0⟩+\sqrt{1-p}|1⟩$, can we exactly simulate another quantum coin $|f(p)⟩=\sqrt{f(p)}|0⟩+\sqrt{1-f(p)}|1⟩$? We give the full characterization of simulable quantum state $k_0(p)|0⟩+k_1(p)|1⟩$ from quantum coin $|p⟩=\sqrt{p}|0⟩+\sqrt{1-p}|1⟩$, and present an algorithm to transform it. Surprisingly, we show that simulable sets in the quantum-to-quantum case and classical-to-classical case have no inclusion relationship with each other.

7 pages, 2 figures

References in corpus (3)

• Creating superpositions that correspond to efficiently integrable probability distributions
• Speed-up via Quantum Sampling
• Experimental Quantum Randomness Processing

Cited by in corpus (6)

• ON states as resource units for universal quantum computation with photonic architectures
• An Experimental Quantum Bernoulli Factory
• Modular Quantum-to-Quantum Bernoulli Factory in an Integrated Photonic Processor
• Polarization-encoded photonic quantum-to-quantum Bernoulli factory based on a quantum dot source
• General Quantum Bernoulli Factory: Framework Analysis and Experiments
• Complexity and multi-functional variants of the Quantum-to-Quantum Bernoulli Factories