Physics – Quantum Physics
Scientific paper
2011-10-26
Phys. Rev. A 84, 060303(R) (2011)
Physics
Quantum Physics
corrected some minor typos
Scientific paper
10.1103/PhysRevA.84.060303
A process of preparation, transmission and subsequent projective measurement of a qubit can be simulated by a classical model with only two bits of communication and some amount of shared randomness. However no model for n qubits with a finite amount of classical communication is known at present. A lower bound for the communication cost can provide useful hints for a generalization. It is known for example that the amount of communication must be greater than c 2^n, where c~0.01. The proof uses a quite elaborate theorem of communication complexity. Using a mathematical conjecture known as the "double cap conjecture", we strengthen this result by presenting a geometrical and extremely simple derivation of the lower bound 2^n-1. Only rank-1 projective measurements are involved in the derivation.
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