No-Go Theorem for Generic Simulation of Qubit Channels with Finite Classical Resources

Fuente: arXiv
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Main Authors: Naik, Sahil Gopalkrishna, Zartab, Mani, Gisin, Nicolas, Banik, Manik
Format: Preprint
Published: 2025
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author Naik, Sahil Gopalkrishna
Zartab, Mani
Gisin, Nicolas
Banik, Manik
author_facet Naik, Sahil Gopalkrishna
Zartab, Mani
Gisin, Nicolas
Banik, Manik
contents The mathematical framework of quantum theory, though fundamentally distinct from classical physics, raises the question of whether quantum processes can be efficiently simulated using classical resources. For instance, a sender (Alice) possessing the classical description of a qubit state can simulate the action of a qubit channel through finite classical communication with a receiver (Bob), enabling Bob to reproduce measurement statistics for any observable on the state. In this work, we contend that a more general simulation requires reproducing statistics of joint measurements, potentially involving entangled effects, on Alice's system and an additional system held by Bob, even when Bob's system state is unknown or entangled with a larger system. Within this broad framework, we prove that no finite amount of classical messaging, regardless of how many rounds are used or how large each message can be, can reproduce a perfect qubit channel, highlighting an inescapable barrier in quantum channel simulation with classical resources. We also establish that entangled effects crucially underlies this no-go result. However, for noisy qubit channels, such as those with depolarizing noise, we demonstrate that general simulation is achievable with finite communication. Notably, the required communication increases as the noise decreases, revealing an intricate relationship between the noise in the channel and the resources necessary for its classical simulation.
format Preprint
id arxiv_https___arxiv_org_abs_2501_15807
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle No-Go Theorem for Generic Simulation of Qubit Channels with Finite Classical Resources
Naik, Sahil Gopalkrishna
Zartab, Mani
Gisin, Nicolas
Banik, Manik
Quantum Physics
The mathematical framework of quantum theory, though fundamentally distinct from classical physics, raises the question of whether quantum processes can be efficiently simulated using classical resources. For instance, a sender (Alice) possessing the classical description of a qubit state can simulate the action of a qubit channel through finite classical communication with a receiver (Bob), enabling Bob to reproduce measurement statistics for any observable on the state. In this work, we contend that a more general simulation requires reproducing statistics of joint measurements, potentially involving entangled effects, on Alice's system and an additional system held by Bob, even when Bob's system state is unknown or entangled with a larger system. Within this broad framework, we prove that no finite amount of classical messaging, regardless of how many rounds are used or how large each message can be, can reproduce a perfect qubit channel, highlighting an inescapable barrier in quantum channel simulation with classical resources. We also establish that entangled effects crucially underlies this no-go result. However, for noisy qubit channels, such as those with depolarizing noise, we demonstrate that general simulation is achievable with finite communication. Notably, the required communication increases as the noise decreases, revealing an intricate relationship between the noise in the channel and the resources necessary for its classical simulation.
title No-Go Theorem for Generic Simulation of Qubit Channels with Finite Classical Resources
topic Quantum Physics
url https://arxiv.org/abs/2501.15807