A condition for any realistic theory of quantum systems

Abstract

In quantum physics, the density operator completely describes the state. Instead, in classical physics the mean value of every physical quantity is evaluated by means of a probability distribution. We study the possibility to describe pure quantum states and events with classical probability distributions and conditional probabilities and prove that the distributions can not be quadratic functions of the quantum state. Some examples are considered. Finally, we deal with the exponential complexity problem of quantum physics and introduce the concept of classical dimension for a quantum system.

References in corpus (5)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Bohmian Mechanics and Quantum Field Theory
• Gaussian quantum Monte Carlo methods for fermions
• General implementation of all possible positive-operator-value measurements of single photon polarization states
• Classical phase-space descriptions of continuous-variable teleportation

Cited by in corpus (14)

• Negativity and contextuality are equivalent notions of nonclassicality
• Exponential complexity and ontological theories of quantum mechanics
• Nonnegative subtheories and quasiprobability representations of qubits
• Efficient Hidden-Variable Simulation of Measurements in Quantum Experiments
• Epistemic view of quantum states and communication complexity of quantum channels
• Q-functions as models of physical reality
• State space dimensionality in short memory hidden variable theories
• Communication complexity and the reality of the wave-function
• Epistemically restricted phase space representation, weak momentum value, and reconstruction of quantum wave function
• Measurement contextuality is implied by macroscopic realism
• Compressing the hidden variable space of a qubit
• Exponential communication gap between weak and strong classical simulations of quantum communication
• Efficient classical computation of expectation values in a class of quantum circuits with an epistemically restricted phase space representation
• Generalized Gleason theorem and finite amount of information for the context