Dynamics of a qubit as a classical stochastic process with time-correlated noise: minimal measurement invasiveness

Abstract

So far it has been shown that the quantum dynamics cannot be described as a classical Markov process unless the number of classical states is uncountably infinite. In this paper, we present a stochastic model with time-correlated noise that exactly reproduces any unitary evolution of a qubit and requires just four classical states. The invasive updating of just one bit during a measurement accounts for the quantum violation of the Leggett-Garg inequalities. Unlike in a pilot wave theory, the stochastic forces governing the jumps among the four states do not depend on the quantum state, but only on the unitary evolution. This model is used to derive a local hidden variable model, augmented by one bit of classical communication, for simulating entangled Bell states.

Minor changes. Added hyperlinks in the bibliography

References in corpus (3)

• The Communication Cost of Simulating Bell Correlations
• Exponential complexity and ontological theories of quantum mechanics
• State space dimensionality in short memory hidden variable theories

Cited by in corpus (29)

• Leggett-Garg Inequalities
• Are quantum states real?
• The Leggett-Garg Inequalities and No-Signalling in Time: A Quasi-Probability Approach
• Experimental detection of quantum coherent evolution through the violation of Leggett-Garg-type inequalities
• Coherence and non-classicality of quantum Markov processes
• Comparing Conditions for Macrorealism: Leggett-Garg Inequalities vs No-Signaling in Time
• Study of temporal quantum correlations in decohering B and K meson systems
• Decoherence and maximal violations of the Leggett-Garg inequality
• Exploration of an augmented set of Leggett-Garg inequalities using a noninvasive continuous-in-time velocity measurement
• Enhanced violations of Leggett-Garg inequalities in an experimental three-level system
• Epistemic view of quantum states and communication complexity of quantum channels
• Detecting violations of macrorealism when the original Leggett-Garg inequalities are satisfied
• Ambiguous measurements, signalling and violations of Leggett-Garg inequalities
• A quasi-probability for the arrival time problem with links to backflow and the Leggett-Garg inequalities
• Leggett-Garg tests of macrorealism: checks for non-invasiveness and generalizations to higher-order correlators
• Subtleties of witnessing quantum coherence in non-isolated systems
• Leggett-Garg Correlation Functions from Non-Invasive Velocity Measurement Continuous in Time
• Communication complexity and the reality of the wave-function
• Necessary and sufficient conditions for macrorealism using two and three-time Leggett-Garg inequalities
• Algebraic maximum violation of the Leggett-Garg inequality in a two-level system under PT symmetric dynamics
• Entropic Leggett-Garg inequality in neutrinos and B (K) meson systems
• $\psi$-epistemic interpretations of quantum theory have a measurement problem
• Violation of Leggett-Garg type inequalities in a driven two level atom interacting with a squeezed thermal reservoir
• Deccoherent Histories and Measurement of Temporal Correlation Functions for Leggett-Garg Inequalities
• Exponential communication gap between weak and strong classical simulations of quantum communication
• Effect of memory on the violation of Leggett-Garg inequality
• Stochastic Mechanics Without Ad Hoc Quantization: Theory And Applications To Semiclassical Gravity
• Assessing the dynamical assumptions in Tsirelson inequality tests of non-classicality in harmonic oscillators
• Connecting Commutativity and Classicality for Multi-Time Quantum Processes