arXiv subjects

Mani Zartab

Publications and source records attributed to Mani Zartab.

4 recordsLinked to original sources

arXiv2026

Neural Network Learning of One-Bit Protocols for Qubit Measurement Simulation

Communication complexity provides a natural framework for quantifying the classical resources required to reproduce quantum statistics. In the qubit prepare-and-measure scenario, two classical bits have been shown to be necessary and sufficient to simulate arbitrary qubit states and arbi- trary quantum measurements exactly. However, this result does not exclude the possibility that restricted families of measurements may admit accurate 1-bit classical approximations. We use a neural network procedure to demonstrate that a single bit can achieve high average accuracy for specific measurement families. A performance analysis of our neural network reveals that symmet- ric measurements with uniformly weighted elements, such as those forming regular polyhedra, are particularly amenable to this restricted communication. By analyzing the patterns learned by the neural network, we derive an analytical protocol that is extremely accurate for finite information- ally complete symmetric configurations and becomes exact in the limit of a continuous isotropic measurement.

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arXiv2025

Prepare-and-measure and entanglement simulation beyond qubits

For two non-communicating parties, quantum theory can give rise to probability distributions of outcomes that no local classical model can reproduce without communication. However, in the case of two-dimensional systems ($d=2$), it is known that allowing a finite amount of classical communication to shared classical resources makes it possible to simulate these quantum correlations. Whether such a simulation remains possible in higher dimensions is still an open question. In this work, we identify the key features of the exact classical protocol in $d=2$, and use them to construct robust approximate protocols in higher dimensions. We assess their performance through a randomized numerical study based on the Total Variation Distance. Our approach exactly reproduces the quantum probability distributions for $d=2$, and performs very well compared to existing protocols for higher dimensions, being the most robust protocol in all cases studied. These results offer new insights into the analytical structure of classical protocols in higher dimensions.

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arXiv2025

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

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.

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arXiv2023

Filter functions for the Glauber-Sudarshan $P$-function regularization

The phase-space quasi-probability distribution formalism for representing quantum states provides practical tools for various applications in quantum optics such as identifying the nonclassicality of quantum states. We study filter functions that are introduced to regularize the Glauber-Sudarshan $P$ function. We show that the quantum map associated with a filter function is completely positive and trace preserving and hence physically realizable if and only if the Fourier transform of this function is a probability density distribution. We also derive a lower bound on the fidelity between the input and output states of a physical quantum filtering map. Therefore, based on these results, we show that any quantum state can be approximated, to arbitrary accuracy, by a quantum state with a regular Glauber-Sudarshan $P$ function. We propose applications of our results for estimating the output state of an unknown quantum process and estimating the outcome probabilities of quantum measurements.

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