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arXiv · 2207.12457

The minimal communication cost for simulating entangled qubits

Martin J. Renner·Marco Túlio Quintino
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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, $|\Psi_{AB}>=\sqrt{p}\ |00>+\sqrt{1-p}\ |11>$ (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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Martin J. Renner, Marco Túlio Quintino. 2022-07-25. The minimal communication cost for simulating entangled qubits. https://doi.org/10.22331/q-2023-10-24-1149

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