Abstract
The locking effect is a phenomenon that 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 locking protocol harnesses this effect in a cryptographic context, whereby one party can encode bits into 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.
- Received 30 July 2013
DOI:https://doi.org/10.1103/PhysRevX.4.011016
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Published by the American Physical Society
Popular Summary
Quantum cryptography, including the task of quantum key distribution (QKD), is one of the major contemporary areas of application of quantum mechanics. In QKD, the goal is to transmit a secret key between the two communicating parties, and the successfully shared key is then used to encrypt a message communicated through a public channel, which a third party has practically no chance of decrypting. A fundamental drawback, however, is that the key and the message must have equal length. This means that the distribution of secret keys must be done at bit rates comparable to standard communication technology, but reaching those bit rates is still a major challenge for current quantum technology.
A conceptually different approach has been proposed to circumvent this challenge, based on the phenomenon of quantum data locking (QDL). Because of a strong form of the quantum-mechanical uncertainty principle, a small secret key can be used to “lock” an exponentially longer message, if this message is suitably encoded into a quantum system. The encrypted message is then secure against any hacking or interfering attempt of a third party who performs a quantum measurement to learn about the message. To find useful applications, however, QDL must be proven to be robust against noise. In this paper, we place the concept of noisy QDL on a solid theoretical ground for the first time.
Many fundamental questions about noisy QDL were open. How should the locking capacity of a quantum channel (such as a fiber optic cable for photon-based information transmission) be defined? Are there noisy quantum channels with nonzero locking capacity? If yes, is such a channel required to preserve quantum entanglement or is “quantum discord,” a less stringent form of quantum correlation, sufficient? Can the locking capacity of a quantum channel surpass its capacity for transmitting information securely against an adversary with access to a quantum memory? Is QDL possible with coherent states? We address all of these questions with complete or partial answers, including a concrete definition of the locking capacity of a noisy quantum channel and a rigorous bound on that capacity.
From a fundamental perspective, our paper sets out the locking capacity of a quantum channel as one that is unique to quantum information theory. Schemes for QDL could very well allow for secure communication of data at much higher rates than is possible with QKD, as long as malicious adversaries do not have access to fully functional quantum computers and reliable quantum storage.
