The Magical Number Seven: An Unexpected Dimensional Threshold in Quantum Communication Complexity

Abstract

Entanglement-assisted classical communication and transmission of a quantum system are the two quantum resources for information processing. Many information tasks can be performed using either quantum resource. However, this equivalence is not always present since entanglement assisted classical communication is known to sometimes be the better performing resource. Here, we show not only the opposite phenomenon; that there exists tasks for which transmission of a quantum system is a more powerful resource than entanglement assisted classical communication, but also that such phenomena can have a surprisingly strong dependence on the dimension of Hilbert space. We introduce a family of communication complexity problems parametrized by dimension of Hilbert space and study the performance of each quantum resource. We find that for low dimensions, the two resources perform equally well, whereas for dimension seven and above, the equivalence is suddenly broken and transmission of a quantum system becomes more powerful than entanglement assisted classical communication. Moreover, we find that transmission of a quantum system may even outperform classical communication assisted by the stronger-than-quantum correlations obtained from the principle of Macroscopic Locality.

References in corpus (6)

• Bounding the set of quantum correlations
• Secret Sharing with a Single d-level Quantum System
• Bounding the set of finite dimensional quantum correlations
• Quantum communication complexity advantage implies violation of a Bell inequality
• Properties of dimension witnesses and their semi-definite programming relaxations
• Relation between semi- and fully-device-independent protocols

Cited by in corpus (16)

• High-dimensional quantum communication: benefits, progress, and future challenges
• Enabling computation of correlation bounds for finite-dimensional quantum systems via symmetrisation
• Semidefinite programming relaxations for quantum correlations
• Preparation contextuality as an essential feature underlying quantum communication advantage
• High-dimensional quantum communication complexity beyond strategies based on Bell's theorem
• Correlations in entanglement-assisted prepare-and-measure scenarios
• Informationally restricted quantum correlations
• Informationally restricted correlations: a general framework for classical and quantum systems
• Complementarity between entanglement-assisted and quantum distributed random access code
• Does violation of a Bell inequality always imply quantum advantage in a communication complexity problem?
• Bounding and simulating contextual correlations in quantum theory
• Higher dimensional communication complexity problems: classical protocols vs quantum ones based on Bell's Theorem or prepare-transmit-measure schemes
• Device independent witness of arbitrary dimensional quantum systems employing binary outcome measurements
• Hiding Ignorance Using High Dimensions
• Multiparty quantum random access codes
• Bound entanglement-assisted prepare-and-measure scenarios based on four-dimensional quantum messages