DeepAI AI Chat
Log In Sign Up

Quantum Random Access Codes for Boolean Functions

by   João F. Doriguello, et al.

An np↦m random access code (RAC) is an encoding of n bits into m bits such that any initial bit can be recovered with probability at least p, while in a quantum RAC (QRAC), the n bits are encoded into m qubits. Since its proposal, the idea of RACs was generalized in many different ways, e.g. allowing the use of shared entanglement (called entanglement-assisted random access code, or simply EARAC) or recovering multiple bits instead of one. In this paper we generalize the idea of RACs to recovering the value of a given Boolean function f on any subset of fixed size of the initial bits, which we call f-random access codes. We study and give protocols for f-random access codes with classical (f-RAC) and quantum (f-QRAC) encoding, together with many different resources, e.g. private or shared randomness, shared entanglement (f-EARAC) and Popescu-Rohrlich boxes (f-PRRAC). The success probability of our protocols is characterized by the noise stability of the Boolean function f. Moreover, we give an upper bound on the success probability of any f-QRAC with shared randomness that matches its success probability up to a multiplicative constant (and f-RACs by extension), meaning that quantum protocols can only achieve a limited advantage over their classical counterparts.


page 1

page 2

page 3

page 4


Quantum Teleportation with One Classical Bit

Quantum teleportation allows one to transmit an arbitrary qubit from poi...

New entanglement-assisted MDS quantum codes from constacyclic codes

Construction of good quantum codes via classical codes is an important t...

Entanglement-assisted quantum MDS codes from constacyclic codes with large minimum distance

The entanglement-assisted (EA) formalism allows arbitrary classical line...

Two families of Entanglement-assisted quantum MDS codes from constacyclic codes

Entanglement-assisted quantum error correcting codes (EAQECCs) can be de...

Communication Complexity of Private Simultaneous Quantum Messages Protocols

The private simultaneous messages model is a non-interactive version of ...

Universal codes in the shared-randomness model for channels with general distortion capabilities

We put forth new models for universal channel coding. Unlike standard co...

Dimensionality Distinguishers

The celebrated Clauser, Horne, Shimony and Holt (CHSH) game model helps ...