Distributed Private Randomness Distillation

Abstract

We develop the resource theory of private randomness extraction in the distributed and device-dependent scenario. We begin by introducing the notion of independent random bits, which are bipartite states containing ideal private randomness for each party, and motivate the natural set of free operations. As a conceptual tool, we introduce Virtual Quantum State Merging, which is essentially the flip side of Quantum State Merging, without communication. We focus on the bipartite case and find the rate regions achievable in different settings. Surprisingly, it turns out that local noise can boost randomness extraction. As a consequence of our analysis, we resolve a long-standing problem by giving an operational interpretation for the reverse coherent information (up to a constant term $\log d$) as the number of private random bits obtained by sending quantum states from one honest party (server) to another one (client) via the eavesdropped quantum channel.

6+12 pages, 1 figure. Improved presentation, more details in the technical proofs, updated references. Accepted for publication in PRL

References in corpus (11)

• Distillation of secret key and entanglement from quantum states
• Quantum information can be negative
• Coding Theorem and Strong Converse for Quantum Channels
• Performance and structure of single-mode bosonic codes
• Direct and Reverse Secret-Key Capacities of a Quantum Channel
• Extensive nonadditivity of privacy
• Continuous-variable entanglement distillation over a pure loss channel with multiple quantum scissors
• Upper bounds on secret key agreement over lossy thermal bosonic channels
• Quantum state redistribution based on a generalized decoupling
• Secure uniform random number extraction via incoherent strategies
• Conditional channel simulation

Cited by in corpus (15)

• Entropy of a quantum channel
• Witnessing Negative Conditional Entropy
• A-unital Operations and Quantum Conditional Entropy
• Stream privacy amplification for quantum cryptography
• Finite Block Length Analysis on Quantum Coherence Distillation and Incoherent Randomness Extraction
• Decoupling by local random unitaries without simultaneous smoothing, and applications to multi-user quantum information tasks
• Fermionic one-body entanglement as a thermodynamic resource
• Teleportation fidelity of quantum repeater networks
• Optimal allocation of quantum resources
• Limitations for private randomness repeaters
• Upper bounds on the leakage of private data and operational approach to markovianity
• Bounding conditional entropy of bipartite states with Bell operators
• Quantum information theory and Fourier multipliers on quantum groups
• Teleportation Fidelity of Binary Tree Quantum Repeater Networks
• Does Quantum Information Require Additional Structure?