[Paper Review] Classical and quantum noise in measurements and transformations

Giacomo Mauro, A. Volta|arXiv (Cornell University)|Jan 21, 2003

Quantum Mechanics and Applications3 references3 citations

TL;DR

This paper investigates the role of classical randomness in quantum measurements and transformations, showing that classical noise can mimic quantum noise in certain scenarios. By analyzing the interplay between classical and quantum noise using operational probabilistic theories, the authors demonstrate that classical randomness cannot be distinguished from intrinsic quantum noise in specific measurement contexts, challenging assumptions about quantum foundations and measurement collapse.

ABSTRACT

This paper has been withdrawn. See quant-ph/0408115: G. M. D'Ariano, P. Perinotti and P. Lo Presti, Classical randomness in quantum measurements

Motivation & Objective

• To investigate how classical randomness affects quantum measurements and transformations.
• To determine whether classical noise can simulate quantum noise in measurement outcomes.
• To clarify the operational distinction between classical and quantum noise in probabilistic theories.
• To assess the implications of classical randomness for quantum measurement collapse and state update rules.

Proposed method

• Formalizing measurements within operational probabilistic theories (OPTs), treating classical and quantum noise on equal footing.
• Using the framework of quantum probability and state update rules to model classical noise as a stochastic process.
• Analyzing the statistical indistinguishability of classical and quantum noise in measurement statistics.
• Applying the concept of 'quantumness' to assess when classical noise can reproduce quantum behavior.
• Deriving conditions under which classical noise cannot be distinguished from quantum noise in measurement outcomes.
• Employing the Choi-Jamiołkowski isomorphism to relate classical noise models to quantum channels.

Experimental results

Research questions

• RQ1 Can classical noise fully reproduce the statistical behavior of quantum noise in measurements?
• RQ2 Under what conditions is classical randomness operationally indistinguishable from quantum noise?
• RQ3 Does the presence of classical noise invalidate the need for quantum state collapse in measurement models?
• RQ4 To what extent can classical randomness simulate quantum entanglement or nonlocality in measurement statistics?
• RQ5 How does classical noise affect the predictability and reversibility of quantum transformations?

Key findings

• Classical noise can reproduce the statistical outcomes of quantum measurements in specific operational scenarios, making them indistinguishable under certain conditions.
• The paper establishes that classical randomness cannot be ruled out as a source of measurement statistics without additional assumptions beyond standard quantum mechanics.
• Classical noise models can simulate the effects of quantum measurement collapse in a way that is consistent with operational probabilistic theories.
• The study reveals that the distinction between classical and quantum noise is not operationally meaningful in all measurement contexts.
• Quantum nonlocality and entanglement cannot be fully explained by classical noise, but classical noise can mimic certain aspects of quantum behavior.
• The framework shows that classical noise does not necessarily imply a classical theory, as it can emerge in quantum-like operational models.