The minimal communication cost for simulating entangled qubits

Martin J. Renner1,2 and Marco Túlio Quintino3,2,1

1University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology (VCQ), Boltzmanngasse 5, 1090 Vienna, Austria
2Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
3Sorbonne Université, CNRS, LIP6, F-75005 Paris, France

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Abstract

We analyze the amount of classical communication required to reproduce the statistics of local projective measurements on a general pair of entangled qubits, $|\Psi_{AB}\rangle=\sqrt{p}\ |00\rangle+\sqrt{1-p}\ |11\rangle$ (with $1/2\leq p \leq 1$). We construct a classical protocol that perfectly simulates local projective measurements on all entangled qubit pairs by communicating one classical trit. Additionally, when $\frac{2p(1-p)}{2p-1} \log{\left(\frac{p}{1-p}\right)}+2(1-p)\leq1$, approximately $0.835 \leq p \leq 1$, we present a classical protocol that requires only a single bit of communication. The latter model even allows a perfect classical simulation with an average communication cost that approaches zero in the limit where the degree of entanglement approaches zero ($p \to 1$). This proves that the communication cost for simulating weakly entangled qubit pairs is strictly smaller than for the maximally entangled one.

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Cited by

[1] Armin Tavakoli, "The classical price tag of entangled qubits", Quantum Views 7, 76 (2023).

[2] István Márton, Erika Bene, Péter Diviánszky, and Tamás Vértesi, "Beating one bit of communication with and without quantum pseudo-telepathy", arXiv:2308.10771, (2023).

[3] Peter Sidajaya, Aloysius Dewen Lim, Baichu Yu, and Valerio Scarani, "Neural Network Approach to the Simulation of Entangled States with One Bit of Communication", Quantum 7, 1150 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2024-05-21 16:06:22) and SAO/NASA ADS (last updated successfully 2024-05-21 16:06:24). The list may be incomplete as not all publishers provide suitable and complete citation data.

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