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When are Popescu-Rohrlich boxes and random access codes equivalent?

Andrzej Grudka1, Karol Horodecki2, Michał Horodecki3

  • 1Faculty of Physics, Adam Mickiewicz University, 61-614 Poznań, Poland.

Physical Review Letters
|September 20, 2014
PubMed
Summary
This summary is machine-generated.

We explore the relationship between Popescu-Rohrlich (PR) boxes and random access codes (RACs). We show that nonsignaling random access codes can simulate PR boxes, establishing their equivalence.

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Area of Science:

  • Quantum information science
  • Foundations of quantum mechanics

Background:

  • Popescu-Rohrlich (PR) boxes are supraquantum resources violating Bell inequalities maximally.
  • Random access codes (RACs) allow a receiver to choose one of two bits from a sender.
  • A PR box with one bit of communication can simulate a RAC.

Purpose of the Study:

  • To investigate the converse: whether a RAC can simulate a PR box.
  • To introduce the 'racbox' concept for studying this interconvertibility.
  • To determine the conditions under which RACs and PR boxes are equivalent.

Main Methods:

  • Introduction of the 'racbox' as a resource offering RAC functionality with one bit of communication.
  • Analysis of the simulation capabilities of nonsignaling and signaling racboxes.
  • Derivation of a resource inequality relating racboxes and PR boxes.

Main Results:

  • Nonsignaling racboxes can simulate PR boxes, demonstrating their equivalence.
  • A signaling racbox example is provided that cannot simulate a PR box.
  • A resource inequality between racboxes and PR boxes is established and shown to be saturated.

Conclusions:

  • Nonsignaling racboxes and PR boxes are shown to be equivalent supraquantum resources.
  • The study highlights the importance of signaling properties in resource interconversion.
  • The derived resource inequality provides a quantitative measure of the relationship between these resources.