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arXiv:1410.4748 · New Journal of Physics

Quantum data locking for high-rate private communication

Cosmo Lupo, Seth Lloyd

Published Mar 12, 2015• 20 citations
arXivHTMLPDF

Abstract

We show that, if the accessible information is used as a security quantifier, quantum channels with a certain symmetry can convey private messages at a tremendously high rate, as high as less than one bit below the rate of non-private classical communication. This result is obtained by exploiting the quantum data locking effect. The price to pay to achieve such a high private communication rate is that accessible information security is in general not composable. However, composable security holds against an eavesdropper who is forced to measure her share of the quantum system within a finite time after she gets it.

DOI
10.1088/1367-2630/17/3/033022

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We show that, if the accessible information is used as a security quantifier, quantum channels with a certain symmetry can convey private messages at a tremendously high rate, as high as less than one bit below the rate of non-private classical communication. This result is obtained by exploiting the quantum data locking effect. The price to pay to achieve such a high private communication rate is that accessible information security is in general not composable. However, composable security holds against an eavesdropper who is forced to measure her share of the quantum system within a finite time after she gets it.
Quantum data locking is a protocol that allows for a small secret key to (un)lock an exponentially larger amount of information, hence yielding the strongest violation of the classical one-time pad encryption in the quantum setting. This violation mirrors a large gap existing between two security criteria for quantum cryptography quantified by two entropic quantities: the Holevo information and the accessible information. We show that the latter becomes a sensible security criterion if an upper bound on the coherence time of the eavesdropper's quantum memory is known. Under this condition, we introduce a protocol for secret key generation through a memoryless qudit channel. For channels with enough symmetry, such as the d-dimensional erasure and depolarizing channels, this protocol allows secret key generation at an asymptotic rate as high as the classical capacity minus one bit.
Quantum cryptography was designed to provide a new approach to the problem of distributing keys for private-key cryptography. The principal idea is that security can be ensured by exploiting the laws of quantum physics and, in particular, by the fact that any attempt to measure a quantum state will change it uncontrollably. This change can be detected by the legitimate users of the communication channel and so reveal to them the presence of an eavesdropper. In this paper I explain (briefly) how quantum key distribution works and some of the progress that has been made towards making this a viable technology. With the principles of quantum communication and quantum key distribution firmly established, it is perhaps time to consider how efficient it can be made. It is interesting to ask, in particular, how many bits of information might reasonably be encoded securely on each photon. The use of photons entangled in their time of arrival might make it possible to achieve data rates in excess of 10 bits per photon.
A classical one-time pad allows two parties to send private messages over a public classical channel-an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.
Quantum cryptography allows for unconditionally secure communication against an eavesdropper endowed with unlimited computational power and perfect technologies, who is only constrained by the laws of physics. We review recent results showing that, under the assumption that the eavesdropper can store quantum information only for a limited time, it is possible to enhance the performance of quantum key distribution in both a quantitative and qualitative fashion. We consider quantum data locking as a cryptographic primitive and discuss secure communication and key distribution protocols. For the case of a lossy optical channel, this yields the theoretical possibility of generating secret key at a constant rate of 1 bit per mode at arbitrarily long communication distances.
It is a common belief that quantum key distribution systems are the one and only information-theoretically secure physical layer security protocol that enables secure data transmission without a need for the legitimate parties to have any channel knowledge. It is also known that this high security profile results in severe rate restrictions for the parties utilizing the quantum key distribution systems. This observation raises the question of whether quantifying the level of ignorance of the legitimate parties with regard to the channel parameters may enable us to navigate the large gray zone between insecure but highly performant systems on the one side and perfectly secure but highly non-performant systems on the other side. Indeed, by proving a capacity formula for the bosonic compound wiretap channel using the binary phase shift keying alphabet, we are able to quantify in this work exactly how channel uncertainty penalizes data transmission rates.
We investigate how a classical private key can be used by two players, connected by an insecure one-way quantum channel, to perform private communication of quantum information. In particular we show that in order to transmit n qubits privately, 2n bits of shared private key are necessary and sufficient. This result may be viewed as the quantum analogue of the classical one-time pad encryption scheme. From the point of view of the eavesdropper, this encryption process can be seen as a randomization of the original state. We thus also obtain strict bounds on the amount of entropy necessary for randomizing n qubits.