We formulate a model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately---but to arbitrary precision---described by Schr\"odinger's equation and $H$ . The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wave function. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. We analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.We formulate a model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian $H$ acting on $n$ qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately---but to arbitrary precision---described by Schr\"odinger's equation and $H$. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wave function. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. We analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.

arXiv:2207.09465Physical Review AJul 26, 20234 citations

Large Deviations for Quantum Spin Systems

Karel Netočný, Frank Redig

arXiv:math-ph/0404018Journal of Statistical PhysicsOct 28, 200449 citations

Large Deviation Strategy for Inverse Problem II

Izumi Ojima, Kazuya Okamura

In the earlier paper [1], we have proposed the large deviation strategy (LDS) and discussed its first level. By efficient use of the central measure, we will establish a quantum version of Sanov's theorem, the Bayesian escort predictive state and the widely applicable information criteria for quantum states in LDS second level. Finally, these results are re-examined in the context of quantum estimation theory, and organized as quantum model selection, i.e., a quantum version of model selection.In the earlier paper [1], we have proposed the large deviation strategy (LDS) and discussed its first level. By efficient use of the central measure, we will establish a quantum version of Sanov's theorem, the Bayesian escort predictive state and the widely applicable information criteria for quantum states in LDS second level. Finally, these results are re-examined in the context of quantum estimation theory, and organized as quantum model selection, i.e., a quantum version of model selection.

Open Systems & Information DynamicsSep 1, 20122 citations

Large Deviations in Quantum Information Theory

Rudolf Ahlswede, Vladimir M. Blinovsky

Problems of Information TransmissionOct 1, 20035 citations

We formulate a model in which quantum mechanics emerges from classical mechanics. Given a local Hamiltonian

H

acting on

n

qubits, we define a local classical model with an additional spatial dimension whose boundary dynamics is approximately---but to arbitrary precision---described by Schr\"odinger's equation and

H

. The bulk consists of a lattice of classical bits that propagate towards the boundary through a circuit of stochastic matrices. The bits reaching the boundary are governed by a probability distribution whose deviation from the uniform distribution can be interpreted as the quantum-mechanical wave function. Bell nonlocality is achieved because information can move through the bulk much faster than the boundary speed of light. We analytically estimate how much the model deviates from quantum mechanics, and we validate these estimates using computer simulations.