### Abstract

We analyze the amount of classical communication required to reproduce the statistics of local projective measurements on a general pair of entangled qubits, |Ψ>=sqrt(p) |00>+sqrt(1−p) |11> (with 1/2≤p≤1). We construct a classical protocol that perfectly simulates local projective measurements on all entangled qubit pairs by communicating one classical trit. Additionally, when 2p(1−p)2p−1log(p1−p)+2(1−p)≤1, approximately 0.835≤p≤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→1). This proves that the communication cost for simulating weakly entangled qubit pairs is strictly smaller than for the maximally entangled one.

Publication

The minimal communication cost for simulating entangled qubits

We analyze the amount of classical communication required to reproduce the statistics of local projective measurements on a general pair of entangled qubits, |Ψ>=sqrt(p) |00>+sqrt(1−p) |11> (with 1/2≤p≤1). We construct a classical protocol that perfectly simulates local projective measurements on all entangled qubit pairs by communicating one classical trit. Additionally, when 2p(1−p)2p−1log(p1−p)+2(1−p)≤1, approximately 0.835≤p≤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→1). This proves that the communication cost for simulating weakly entangled qubit pairs is strictly smaller than for the maximally entangled one.