Quantum Advantage for Shared Randomness Generation

Abstract

Sharing correlated random variables is a resource for a number of information theoretic tasks such as privacy amplification, simultaneous message passing, secret sharing and many more. In this article, we show that to establish such a resource called shared randomness, quantum systems provide an advantage over their classical counterpart. Precisely, we show that appropriate albeit fixed measurements on a shared two-qubit state can generate correlations which cannot be obtained from any possible state on two classical bits. In a resource theoretic set-up, this feature of quantum systems can be interpreted as an advantage in winning a two players co-operative game, which we call the `non-monopolize social subsidy' game. It turns out that the quantum states leading to the desired advantage must possess non-classicality in the form of quantum discord. On the other hand, while distributing such sources of shared randomness between two parties via noisy channels, quantum channels with zero capacity as well as with classical capacity strictly less than unity perform more efficiently than the perfect classical channel. Protocols presented here are noise-robust and hence should be realizable with state-of-the-art quantum devices.

Accepted in Quantum

References in corpus (16)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Non-Markovianity: Characterization, Quantification and Detection
• Reference frames, superselection rules, and quantum information
• Quantum technologies with hybrid systems
• Quantum Illumination with Gaussian States
• The Communication Cost of Simulating Bell Correlations
• Interpreting quantum discord through quantum state merging
• Operational interpretations of quantum discord
• 'Designer atoms' for quantum metrology
• Linking Quantum Discord to Entanglement in a Measurement
• Gigahertz decoy quantum key distribution with 1 Mbit/s secure key rate
• Local deterministic model of singlet state correlations based on relaxing measurement independence
• Optimal approach to quantum communication using dynamic programming
• Type-independent Characterization of Spacelike Separated Resources
• Entangleability of cones
• Role of quantum discord in quantum communication

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