The minimal communication cost for simulating entangled qubits

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 $1/2\le p\le 1$). We construct a classical protocol that perfectly simulates local projective measurements on all entangled qubit pairs by communicating one classical trit. Additionally, when $\frac{2p(1-p)}{2p-1}\log \left(\frac{p}{1-p}\right)+2(1-p)\le 1$, approximately $0.835\le p\le 1$, 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.

6 pages main text, 8 pages appendices, 3 figures

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Cited by in corpus (2)

• Beating one bit of communication with quantum correlations in smaller dimensions
• Beating one bit of communication with and without quantum pseudo-telepathy