Quantum enigma machines and the locking capacity of a quantum channel

Abstract

The locking effect is a phenomenon which is unique to quantum information theory and represents one of the strongest separations between the classical and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking protocol harnesses this effect in a cryptographic context, whereby one party can encode n bits into n qubits while using only a constant-size secret key. The encoded message is then secure against any measurement that an eavesdropper could perform in an attempt to recover the message, but the protocol does not necessarily meet the composability requirements needed in quantum key distribution applications. In any case, the locking effect represents an extreme violation of Shannon's classical theorem, which states that information-theoretic security holds in the classical case if and only if the secret key is the same size as the message. Given this intriguing phenomenon, it is of practical interest to study the effect in the presence of noise, which can occur in the systems of both the legitimate receiver and the eavesdropper. This paper formally defines the locking capacity of a quantum channel as the maximum amount of locked information that can be reliably transmitted to a legitimate receiver by exploiting many independent uses of a quantum channel and an amount of secret key sublinear in the number of channel uses. We provide general operational bounds on the locking capacity in terms of other well-known capacities from quantum Shannon theory. We also study the important case of bosonic channels, finding limitations on these channels' locking capacity when coherent-state encodings are employed and particular locking protocols for these channels that might be physically implementable.

37 pages

References in corpus (8)

• Randomizing quantum states: Constructions and applications
• Quantum Communication With Zero-Capacity Channels
• A Sharp Fannes-type Inequality for the von Neumann Entropy
• Quantum Capacities of Bosonic Channels
• Degradability of Bosonic Gaussian channels
• The private classical capacity with a symmetric side channel and its application to quantum cryptography
• Extensive nonadditivity of privacy
• Quantum Capacity Approaching Codes for the Detected-Jump Channel

Cited by in corpus (20)

• Advances in Quantum Cryptography
• Entropic Uncertainty Relations and their Applications
• A Quantum Enigma Machine: Experimentally Demonstrating Quantum Data Locking
• Superadditivity of private information for any number of uses of the channel
• Group transformations and entangled-state quantum gates with directionally unbiased linear-optical multiports
• Quantum-locked key distribution at nearly the classical capacity rate
• Robust quantum data locking from phase modulation
• Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination
• Experimental quantum data locking
• Quantum cryptography beyond key distribution: theory and experiment
• Quantum data locking for high-rate private communication
• Continuous-variable quantum enigma machines for long-distance key distribution
• Photonic quantum data locking
• Quantum data hiding in the presence of noise
• Error-tolerant oblivious transfer in the noisy-storage model
• Non-convexity of private capacity and classical environment-assisted capacity of a quantum channel
• "Pretty strong" converse for the private capacity of degraded quantum wiretap channels
• Fault tolerant quantum data locking
• Simultaneous superadditivity of the direct and complementary channel capacities
• Classical State Masking over a Quantum Channel