The minimal communication cost for simulating entangled qubits

Tue, 24 Oct 2023 00:00:00 +0000

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.

Classical Cost of Transmitting a Qubit

Wed, 01 Mar 2023 00:00:00 +0000

We consider general prepare-and-measure scenarios in which Alice can transmit qubit states to Bob, who can perform general measurements in the form of positive operator-valued measures (POVMs). We show that the statistics obtained in any such quantum protocol can be simulated by the purely classical means of shared randomness and two bits of communication. Furthermore, we prove that two bits of communication is the minimal cost of a perfect classical simulation. In addition, we apply our methods to Bell scenarios, which extends the well-known Toner and Bacon protocol. In particular, two bits of communication are enough to simulate all quantum correlations associated to arbitrary local POVMs applied to any entangled two-qubit state.

Martin Renner | LIP6 - Équipe QI

The minimal communication cost for simulating entangled qubits

Classical Cost of Transmitting a Qubit