The minimal communication cost for simulating entangled qubits

Quantum 7, 1149 (2023).

https://doi.org/10.22331/q-2023-10-24-1149

We analyze the amount of classical communication required to reproduce the statistics of local projective measurements on a general pair of entangled qubits, $|Psi_{AB}rangle=sqrt{p} |00rangle+sqrt{1-p} |11rangle$ (with $1/2leq p leq 1$). 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.