No Arabic abstract
This work considers the distribution of a secret key over an optical (bosonic) channel in the regime of high photon efficiency, i.e., when the number of secret key bits generated per detected photon is high. While in principle the photon efficiency is unbounded, there is an inherent tradeoff between this efficiency and the key generation rate (with respect to the channel bandwidth). We derive asymptotic expressions for the optimal generation rates in the photon-efficient limit, and propose schemes that approach these limits up to certain approximations. The schemes are practical, in the sense that they use coherent or temporally-entangled optical states and direct photodetection, all of which are reasonably easy to realize in practice, in conjunction with off-the-shelf classical codes.
Graph based codes such as low density parity check (LDPC) codes have been shown promising for the information reconciliation phase in quantum key distribution (QKD). However, existing graph coding schemes have not fully utilized the properties of the QKD channel. In this work, we first investigate the channel statistics for discrete variable (DV) QKD based on energy-time entangled photons. We then establish a so-called balanced modulation scheme that is promising for this channel. Based on the modulation, we propose a joint local-global graph coding scheme that is expected to achieve good error-correction performance.
The fading wire-tap channel is investigated, where the source-to-destination channel and the source-to-wire-tapper channel are corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information is assumed to be known at both the transmitter and the receiver. The parallel wire-tap channel with independent subchannels is first studied, which serves as an information-theoretic model for the fading wire-tap channel. The secrecy capacity of the parallel wire-tap channel is established. This result is then specialized to give the secrecy capacity of the fading wire-tap channel, which is achieved with the source node dynamically changing the power allocation according to the channel state realization. An optimal source power allocation is obtained to achieve the secrecy capacity.
We consider the problem of oblivious transfer (OT) over OFDM and MIMO wireless communication systems where only the receiver knows the channel state information. The sender and receiver also have unlimited access to a noise-free real channel. Using a physical layer approach, based on the properties of the noisy fading channel, we propose a scheme that enables the transmitter to send obliviously one-of-two files, i.e., without knowing which one has been actually requested by the receiver, while also ensuring that the receiver does not get any information about the other file.
We study the problem of strong coordination of the actions of two nodes $X$ and $Y$ that communicate over a discrete memoryless channel (DMC) such that the actions follow a prescribed joint probability distribution. We propose two novel random coding schemes and a polar coding scheme for this noisy strong coordination problem, and derive inner bounds for the respective strong coordination capacity region. The first scheme is a joint coordination-channel coding scheme that utilizes the randomness provided by the DMC to reduce the amount of local randomness required to generate the sequence of actions at Node $Y$. Based on this random coding scheme, we provide a characterization of the capacity region for two special cases of the noisy strong coordination setup, namely, when the actions at Node $Y$ are determined by Node $X$ and when the DMC is a deterministic channel. The second scheme exploits separate coordination and channel coding where local randomness is extracted from the channel after decoding. The third scheme is a joint coordination-channel polar coding scheme for strong coordination. We show that polar codes are able to achieve the established inner bound to the noisy strong coordination capacity region and thus provide a constructive alternative to a random coding proof. Our polar coding scheme also offers a constructive solution to a channel simulation problem where a DMC and shared randomness are employed together to simulate another DMC. Finally, by leveraging the random coding results for this problem, we present an example in which the proposed joint scheme is able to strictly outperform the separate scheme in terms of achievable communication rate for the same amount of injected randomness into both systems. Thus, we establish the sub-optimality of the separation of strong coordination and channel coding with respect to the communication rate over the DMC.
Quantum key distribution (QKD) is one of the most important subjects in quantum information theory. There are two kinds of QKD protocols, prepare-measure protocols and entanglement-based protocols. For long-distance communications in noisy environments, entanglement-based protocols might be more reliable since they could be assisted with distillation procedures to prevent from noises. In this paper, we study the entanglement-based QKD over certain noisy channels and present schemes against collective noises, including collective dephasing and collective rotation, Pauli noises, amplitude damping noises, phase damping noises and mixtures of them. We focus on how to implement QKD protocols over noisy channels as in noiseless ones without errors. We also analyze the efficiency of the schemes, demonstrating that they could be more efficient than the standard entanglement-based QKD scheme.