Continuous-variable quantum enigma machines for long-distance key distribution

Quantum physics allows for unconditionally secure communication through insecure communication channels. The achievable rates of quantum-secured communication are fundamentally limited by the laws of quantum physics and in particular by the properties of entanglement. For a lossy communication line, this implies that the secret-key generation rate vanishes at least exponentially with the communication distance. We show that this fundamental limitation can be violated in a realistic scenario where the eavesdropper can store quantum information for only a finite, yet arbitrarily long, time. We consider communication through a lossy bononic channel (modeling linear loss in optical fibers) and we show that it is in principle possible to achieve a constant rate of key generation of one bit per optical mode over arbitrarily long communication distances.Comment: 13 pages. V2: new title, new result on active attacks, increased rigour in the security proo

Quantum-locked key distribution at nearly the classical capacity rate

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.Comment: v2 is close to the published version and contains only the key distribution protocols (4+5 pages), an extended version of the direct communication protocol is posted in arXiv:1410.4748 Comments always welcom

Quantum Data Locking for Secure Communication against an Eavesdropper with Time-Limited Storage

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.United States. Army Research Office (United States. Defense Advanced Research Projects Agency. Quiness Program (W31P4Q-12-1-0019

Methods for Estimating Capacities and Rates of Gaussian Quantum Channels

Optimization methods aimed at estimating the capacities of a general Gaussian channel are developed. Specifically evaluation of classical capacity as maximum of the Holevo information is pursued over all possible Gaussian encodings for the lossy bosonic channel, but extension to other capacities and other Gaussian channels seems feasible. Solutions for both memoryless and memory channels are presented. It is first dealt with single use (single-mode) channel where the capacity dependence from channel's parameters is analyzed providing a full classification of the possible cases. Then it is dealt with multiple uses (multi-mode) channel where the capacity dependence from the (multi-mode) environment state is analyzed when both total environment energy and environment purity are fixed. This allows a fair comparison among different environments, thus understanding the role of memory (inter-mode correlations) and phenomenon like superadditivity of the capacity. The developed methods are also used for deriving transmission rates with heterodyne and homodyne measurements at the channel output. Classical capacity and transmission rates are presented within a unique framework where the rates can be treated as logarithmic approximations of the capacity.Comment: 39 pages, 30 figures. New results and graphs were added. Errors and misprints were corrected. To appear in IEEE Trans. Inf. T

Quantum data hiding in the presence of noise

When classical or quantum information is broadcast to separate receivers, there exist codes that encrypt the encoded data such that the receivers cannot recover it when performing local operations and classical communication, but they can decode reliably if they bring their systems together and perform a collective measurement. This phenomenon is known as quantum data hiding and hitherto has been studied under the assumption that noise does not affect the encoded systems. With the aim of applying the quantum data hiding effect in practical scenarios, here we define the data-hiding capacity for hiding classical information using a quantum channel. Using this notion, we establish a regularized upper bound on the data hiding capacity of any quantum broadcast channel, and we prove that coherent-state encodings have a strong limitation on their data hiding rates. We then prove a lower bound on the data hiding capacity of channels that map the maximally mixed state to the maximally mixed state (we call these channels "mictodiactic"---they can be seen as a generalization of unital channels when the input and output spaces are not necessarily isomorphic) and argue how to extend this bound to generic channels and to more than two receivers.Comment: 12 pages, accepted for publication in IEEE Transactions on Information Theor

Robust quantum data locking from phase modulation

Quantum data locking is a unique quantum phenomenon that allows a relatively short key to (un)lock an arbitrarily long message encoded in a quantum state, in such a way that an eavesdropper who measures the state but does not know the key has essentially no information about the encrypted message. The application of quantum data locking in cryptography would allow one to overcome the limitations of the one-time pad encryption, which requires the key to have the same length as the message. However, it is known that the strength of quantum data locking is also its Achilles heel, as the leakage of a few bits of the key or the message may in principle allow the eavesdropper to unlock a disproportionate amount of information. In this paper we show that there exist quantum data locking schemes that can be made robust against information leakage by increasing the length of the shared key by a proportionate amount. This implies that a constant size key can still encrypt an arbitrarily long message as long as a fraction of it remains secret to the eavesdropper. Moreover, we greatly simplify the structure of the protocol by proving that phase modulation suffices to generate strong locking schemes, paving the way to optical experimental realizations. Also, we show that successful data locking protocols can be constructed using random codewords, which very well could be helpful in discovering random codes for data locking over noisy quantum channels.Comment: A new result on the robustness of quantum data locking has been adde