Due to Csiszar and Koerner, the private capacity of classical wiretap channels has a single-letter characterization in terms of the private information. For quantum wiretap channels, however, it is known that regularization of the private information is necessary to reach the capacity. Here, we study hybrid classical-quantum wiretap channels in order to resolve to what extent quantum effects are needed to witness non-additivity phenomena in quantum Shannon theory. For wiretap channels with quantum inputs but classical outputs, we prove that the characterization of the capacity in terms of the private information stays single-letter. Hence, entangled input states are of no asymptotic advantage in this setting. For wiretap channels with classical inputs, we show by means of explicit examples that the private information already becomes non-additive when either one of the two receivers becomes quantum (with the other receiver staying classical). This gives non-additivity examples that are not caused by entanglement and illustrates that quantum adversaries are strictly different from classical adversaries in the wiretap model.
We determine the capacity of the classical compound quantum wiretapper channel with channel state information at the transmitter. Moreover we derive a lower bound on the capacity of this channel without channel state information and determine the capacity of the classical quantum compound wiretap channel with channel state information at the transmitter.
We derive a lower bound on the capacity of classical-quantum arbitrarily varying wiretap channel and determine the capacity of the classicalquantum arbitrarily varying wiretap channel with channel state information at the transmitter.
We establish Ahlswede dichotomy for arbitrarily varying classical-quantum wiretap channels. This means that either the deterministic secrecy capacity of an arbitrarily varying classical-quantum wiretap channel is zero or it equals its randomness-assisted secrecy capacity. We analyze the secrecy capacity of arbitrarily varying classical-quantum wiretap channels when the sender and the receiver use various resources. It turns out that having randomness, common randomness, and correlation as resources are very helpful for achieving a positive deterministic secrecy capacity of arbitrarily varying …
We determine the secrecy capacity of the compound channel with quantum wiretapper and channel state information at the transmitter. Moreover, we derive a lower bound on the secrecy capacity of this channel without channel state information and determine the secrecy capacity of the compound classical-quantum wiretap channel with channel state information at the transmitter. We use this result to derive a new proof for a lower bound on the entanglement generating capacity of compound quantum channel. We also derive a new proof for the entanglement generating capacity of compound quantum channel …
In the vein of the recent "pretty strong" converse for the quantum and private capacity of degradable quantum channels [Morgan/Winter, IEEE Trans. Inf. Theory 60(1):317-333, 2014], we use the same techniques, in particular the calculus of min-entropies, to show a pretty strong converse for the private capacity of degraded classical-quantum-quantum (cqq-)wiretap channels, which generalize Wyner's model of the degraded classical wiretap channel. While the result is not completely tight, leaving some gap between the region of error and privacy parameters for which the converse bound holds, and a …
We consider the problem of semantic security via classical-quantum and quantum wiretap channels and use explicit constructions to transform a non-secure code into a semantically secure code, achieving capacity by means of biregular irreducible functions. Explicit parameters in finite regimes can be extracted from theorems. We also generalize the semantic security capacity theorem, which shows that a strongly secure code guarantees a semantically secure code with the same secrecy rate, to any quantum channel, including the infinite-dimensional and non-Gaussian ones.
We determine the secrecy capacities under common randomness assisted coding of arbitrarily varying classical-quantum wiretap channels.Furthermore, we determine the secrecy capacity of a mixed channel model which is compound from the sender to the legal receiver and varies arbitrarily from the sender to the eavesdropper. As an application we examine when the secrecy capacity is a continuous function of the system parameters and show that resources, i.e., having access to a perfect copy of the outcome of a random experiment. are helpful for channel stability.
In this paper, we want to derive achievable secrecy rate regions for quantum interference channel with classical inputs under one-shot setting. The main idea to this end is to use the combination of superposition and rate splitting for encoding scheme and constructing a decoding scheme based on simultaneous decoding.
Secrecy issues of free-space optical links realizing information theoretically secure communications as well as high transmission rates are discussed. We numerically study secrecy communication rates of optical wiretap channel based on on-off keying modulation under typical conditions met in satellite-ground links. It is shown that under reasonable degraded conditions on a wiretapper, information theoretically secure communications should be possible in a much wider distance range than a range limit of quantum key distribution, enabling secure optical links between geostationary earth orbit sa…
Determining the ultimate classical information carrying capacity of electromagnetic waves requires quantum-mechanical analysis to properly account for the bosonic nature of these waves. Recent work has established capacity theorems for bosonic single-user and broadcast channels, under the presumption of two minimum output entropy conjectures. Despite considerable accumulated evidence that supports the validity of these conjectures, they have yet to be proven. In this paper, it is shown that the second conjecture suffices to prove the classical capacity of the bosonic wiretap channel, which in …
The theory of quantum cryptography aims to guarantee unconditional information-theoretic security against an omnipotent eavesdropper. In many practical scenarios, however, the assumption of an all-powerful adversary is excessive and can be relaxed considerably. In this paper we study secret key distillation across a lossy and noisy quantum wiretap channel between Alice and Bob, with a separately parameterized realistically lossy quantum channel to the eavesdropper Eve. We show that under such restricted eavesdropping, the key rates achievable can exceed the secret key distillation capacity aga…
A usual code for quantum wiretap channel requires an auxiliary random variable subject to the perfect uniform distribution. However, it is difficult to prepare such an auxiliary random variable. We propose a code that requires only an auxiliary random variable subject to a non-uniform distribution instead of the perfect uniform distribution. Further, we evaluate the exponential decreasing rate of leaked information and derive its equivocation rate. For practical constructions, we also discuss the security when our code consists of a linear error correcting code.
In this paper, we want to investigate classical-quantum multiple access wiretap channels (CQ-MA-WTC) under one-shot setting. In this regard, we analyze the CQ-MA-WTC using simultaneous position-based decoder for reliable decoding and using a newly introduced technique in order to decode securely. Also, for the sake of comparison, we analyze the CQ-MA-WTC using Sen's one-shot joint typicality lemma for reliable decoding. The simultaneous position-based decoder tends to a multiple hypothesis testing problem. Also, using convex splitting to analyze the privacy criteria in a simultaneous scenario …
We prove an upper bound on the private capacity of the single-mode noiseless bosonic wiretap channel. Combined with a previous lower bound, we obtain the low photon-number asymptotic expression for the private capacity. We then show that the multiple-mode noiseless bosonic wiretap channel is equivalent to parallel single-mode channels, hence the single-mode bounds can be applied. Finally, we consider multiple-spatial-mode propagation through atmospheric turbulence, and derive a private-capacity lower bound that only requires second moments of the channel matrix.
In this work we study the problem of communication over the quantum wiretap channel. For this channel there are three parties Alice (sender), Bob (legitimate receiver) and Eve (eavesdropper). We obtain upper and lower bounds on the amount of information Alice can communicate to Bob such that Eve gets to know as little information as possible about the transmitted messages. Our bounds are in terms of quantum hypothesis testing divergence and smooth max quantum relative entropy. To obtain our result we prove a one-shot version of the quantum covering lemma along with operator Chernoff bound for …
We prove additivity of the minimum output entropy and the Holevo capacity for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. The physical significance of these channels and their relations to other known channels is also discussed.
Additivity of the Holevo capacity is proved for product channels, under the condition that one of the channels is in a certain class of unital qubit channels, with the other completely arbitrary. This qubit class includes the depolarizing channel. As a byproduct this proves that the Holevo bound is the ultimate information capacity of such qubit channels (assuming no prior entanglement between sender and receiver). Additivity of minimal entropy and multiplicativity of p-norms are also proved under the same assumptions.
We consider bistochastic quantum channels generated by unitary representations of the discret group. The proof of the additivity conjecture for the quantum depolarizing channel $Φ$ based on the decreasing property of the relative entropy is given. We show that the additivity conjecture is true for the channel $Ξ=Ψ\circ Φ$, where $Ψ$ is the phase damping.
Additivity of minimal entropy output is proven for the class of quantum channels $Λ_t (A):=t A^{T}+(1-t)τ(A)$ in the parameter range $-2/(d^2-2)\le t \le 1/(d+1)$.
Additivity of quantum communication channel is discussed in terms of Poisson process to show it is additive in probability. Poisson process is shown to be responsible for entanglement which is a rare event.
Additivity of the minimal output entropy for the family of transpose depolarizing channels introduced by Fannes et al. [quant-ph/0410195] is considered. It is shown that using the method of our previous paper [quant-ph/0403072] allows us to prove the additivity for the range of the parameter values for which the problem was left open in [quant-ph/0410195]. Together with the result of [quant-ph/0410195], this covers the whole family of transpose depolarizing channels.
We give an elementary self-contained proof that the minimal entropy output of arbitrary products of channels $ρ\mapsto \frac{1}{d-1}(1-ρ^T)$ is additive.
The minimum entropy output is computed for rotationally invariant quantum channels acting on spin-1/2 and spin-1 systems. For the case of two parallel such channels and initial entangled (singlet) state the entropy of the output is higher then the doubled minimal entropy output of the single channel. This gives a certain moral support to the additivity hypothesis. Another related simple function of the channel (minimum entropy gain) is shown to be additive in general.
In this paper we give several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity. To this end a characteristic property of the optimal ensemble for such a channel is derived, generalizing the maximal distance property. It is shown that the additivity conjecture for constrained channels holds true for certain nontrivial classes of channels. Recently P. Shor showed that conjectured additivity properties for several quantum information quantities are in fact equivalent. After giving an algebraic…
We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel for a given channel so that they share the above additivity properties; we can reduce the conjectures for all channels to those for unital channels.
We present a constructive example of violation of additivity of minimum output Rényi entropy for each p>2. The example is provided by antisymmetric subspace of a suitable dimension. We discuss possibility of extension of the result to go beyond p>2 and obtain additivity for p=0 for a class of entanglement breaking channels.
The continuity properties of the convex closure of the output entropy of infinite dimensional channels and their applications to the additivity problem are considered. The main result of this paper is the statement that the superadditivity of the convex closure of the output entropy for all finite dimensional channels implies the superadditivity of the convex closure of the output entropy for all infinite dimensional channels, which provides the analogous statements for the strong superadditivity of the EoF and for the additivity of the minimal output entropy. The above result also provides in…
