Communication Tasks with Infinite QuantumClassical Separation
Abstract
Quantum resources can be more powerful than classical resources—a quantum computer can solve certain problems exponentially faster than a classical computer, and computing a function of two parties' inputs can be done with exponentially less communication with quantum messages than with classical ones. Here we consider a task between two players, Alice and Bob where quantum resources are infinitely more powerful than their classical counterpart. Alice is given a string of length n , and Bob's task is to exclude certain combinations of bits that Alice might have. If Alice must send classical messages, then she must reveal nearly n bits of information to Bob, but if she is allowed to send quantum bits, the amount of information she must reveal goes to zero with increasing n . Next, we consider a version of the task where the parties may have access to entanglement. With this assistance, Alice only needs to send a constant number of bits, while without entanglement, the number of bits Alice must send grows linearly with n . The task is related to the PuseyBarrettRudolph theorem which arises in the context of the foundations of quantum theory.
 Publication:

Physical Review Letters
 Pub Date:
 July 2015
 DOI:
 10.1103/PhysRevLett.115.030504
 arXiv:
 arXiv:1407.8217
 Bibcode:
 2015PhRvL.115c0504P
 Keywords:

 03.67.Hk;
 03.65.Ta;
 03.65.Ud;
 03.67.Ac;
 Quantum communication;
 Foundations of quantum mechanics;
 measurement theory;
 Entanglement and quantum nonlocality;
 Quantum algorithms protocols and simulations;
 Quantum Physics
 EPrint:
 V4: Added affiliation V3: Slight changes to match journal version. V2: Slight modification in entanglement assisted setting  Alice must now abort rather than Bob. Improved proofs in appendices