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This study explores the feasibility of utilizing quantum error correction (QEC) to generate and store logical Bell states in heralded quantum entanglement protocols, crucial for quantum repeater networks. Two novel lattice surgery-based protocols (local and non-local) are introduced to establish logical Bell states between distant nodes using an intermediary node. In the local protocol, the intermediary node creates and directly transmits the logical Bell states to quantum memories. In contrast, the non-local protocol distributes auxiliary Bell states, merging boundaries between pre-existing codes in the quantum memories. We simulate the protocols using realistic experimental parameters, including cavity-enhanced atomic frequency comb quantum memories and multimode fiber-optic noisy channels. The study evaluates rotated and planar surface codes alongside Bacon-Shor codes for small code distances $(d = 3, 5)$ under standard and realistic noise models. We observe pseudo-thresholds, indicating that when physical error rates exceed approximately $p_{\text{err}} \sim 10^{-3}$, QEC codes do not provide any benefit over using unencoded Bell states. Moreover, to achieve an advantage over unencoded Bell states for a distance of $1 \, \mathrm{km}$ between the end node and the intermediary, gate error rates must be reduced by an order of magnitude $(0.1p_{\text{err}_H}$, $0.1p_{\text{err}_{CX}}$, and $0.1p_{\text{err}_M}$), highlighting the need for significant hardware improvements to implement logical Bell state protocols with quantum memories. Finally, both protocols were analyzed for their achieved rates, with the non-local protocol showing higher rates, ranging from $6.64 \, \mathrm{kHz}$ to $1.91 \, \mathrm{kHz}$, over distances of $1$ to $9 \, \mathrm{km}$ between the end node and the intermediary node.

We study the problem of joint communication and detection of wiretapping on an optical fiber from a quantum perspective. Our system model describes a communication link that is capable of transmitting data under normal operating conditions and raising a warning at the transmitter side in case of eavesdropping. It contributes to a unified modelling approach, based on which established quantum communication paradigms like quantum key distribution can be compared to other approaches offering similar functionality., Comment: 6 pages, 3 figures, to be presented at 2024 IEEE Global Communications Conference

Quantum Key Distribution (QKD) systems are infamously known for their high demand on hardware, their extremely low key generation rates and their lack of security resulting from a need for trusted nodes which is implied by the absence of quantum repeaters. While they theoretically offer unlimited security, they are therefore practically limited in several regards. In this work we focus on the lack of options to guarantee an end-to-end security service with the currently available technology and infrastructure and propose a novel protocol. We find that one of the stumbling stones on the path towards an end-to-end security service guaranteed by quantum key distribution may be removed by using this protocol. Our proposal combines several parallel instances of twinfield QKD followed by classical postprocessing and communication to allow Alice and Bob to share a secret key. This hybrid approach improves the key rate and range w.r.t. to previous QKD approaches at a contained cost in security. We show that a coalition of intermediary nodes between Alice and Bob is needed to break the new scheme, sharply outperforming the trusted node approach in terms of security. Furthermore, the protocols do not require complex quantum measurements on Alice and Bob's sides, thus being truly end-to-end.

Many quantum communication systems operate based on weak light pulses which by design are assumed to operate in isolation from regular data traffic. With the widespread availability and commercialization of these systems comes a need for seamless integration already at the physical layer. In particular for optical fiber links where wavelength division multiplexing (WDM) is the dominant data transmission technique this results in the propagation of very weak quantum signals against a strong data signal background. With this work, we present a novel theoretical approach that studies the evolution of co-propagating quantum and classical signals that are launched using WDM. The important factors that contribute to crosstalk, such as the launch power of the classical signal and the separation between the two signals in terms of wavelength, are comprehensively analyzed. Interestingly, calculations show that only the first two nearest channels from the classical channel experience noticeable crosstalk whereas other distant channels have negligible crosstalk effect. This reflects the WDM technique is in principle robust in the integration of weak quantum links into classical data traffic., Comment: 6 pages, 5 figures

We study the problem of joint communication and sensing for data transmission systems using optimal quantum instruments in order to transmit data and, at the same time, estimate environmental parameters. In particular we consider the specific but at the same time generic case of a noiseless bosonic classical-quantum channel where part of the transmitted light is reflected back to the transmitter. While sending messages to the receiver, the transmitter tries at the same time to estimate the reflectivity of the channel. Extending earlier results on similar but finite-dimensional systems, we are able to characterize optimal tradeoffs between communication and detection rates. We also compare quantum performance to analogous classical models, quantifying the quantum advantage., Comment: 6 pages, presented in Internet of Things World Forum 2024

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., Comment: 6 pages, 2 figures

Low latency and high data rate performance are essential in wireless communication systems. This paper explores trade-offs between latency and data rates for optical wireless communication. We introduce a latency-optimized model utilizing compound codes as one corner case and a data rate-optimized model employing channel estimation via pilot signals and feedback before data transmission. Trade-offs between the two extremes are displayed. Most importantly, we detail operating points that can only be reached when the receiver side of the link employs optimal quantum measurement strategies. Furthermore, we propose an IoT application in a robot factory as an example scenario. Our findings reveal a trade-off between latency and data rate driven by two basic algorithms: compound codes reduce latency at the cost of data rates, while channel estimation enhances data rates at the cost of latency., Comment: 6 pages, 2 figures

We propose an efficient decomposition scheme for a quantum receiver that attains the Helstrom bound in the low-photon regime for discriminating binary coherent states. Our method, which avoids feedback as used in Dolinar's case, breaks down nonlinear operations into basic gates used in continuous-variable quantum computation. We account for realistic conditions by examining the impact of photon loss and imperfect photon detection, including the presence of dark counts, while presenting squeezing as a technique to mitigate these noise sources and maintain the advantage over SQL. Our scheme motivates testing quantum advantages with cubic-phase gates and designing photonic quantum computers to optimize symbol-by-symbol measurements in optical communication., Comment: 8 pages, 7 figures

This work delivers a novel user-server authentication procedure exploiting the features of maximally entangled pairs in both an idealistic noiseless scenario and a moderately noisy one. Additionally, we leverage the specific features of our design, which are conveniently suited for inlaying it into the well known BB84 quantum communication protocol. We first define a trivial extension of our initial proposal allowing for such task (symmetric scheme) to then come up with what we denote as asymmetric scheme, better matching practicality. Furthermore, a realistic simulation of the user-server authentication protocol has been achieved by employing a noisy model for both transmission and storage, the latter relying on cavity-enhanced atomic-frequency comb (AFC) memories. While in a noiseless scenario our proposal is ensured to be airtight, considering a certain degree of noise poses a challenge when aiming to actually implement it. We have implemented a deep neural network to distinguish legitimate users from forgery attempts, outperforming a mere statistical approach designed for the same task. Such method achieved a success rate of 0.75 with storage times of $1$ $\mu s$ and a user-server distance of $10$ km., Comment: 11 pages, 5 figures

We present QuReed, an open-source quantum simulation framework designed to bridge gaps between quantum theory, experimental community and engineering. With Quantum Mechanics maturing and holding significant potential beyond quantum computing, the need for physically accurate simulations becomes critical. QuReed offers peer-reviewed simulation models, providing researchers and engineers with reliable tools for exploring quantum communication protocols and applications. By facilitating cross-talk between theory and experiments, QuReed aims to accelerate progress in the field and unlock the transformative power of quantum mechanics in the communications industry. Its user-friendly Python interface and comprehensive documentation ensure widespread accessibility and usability, making QuReed a valuable resource for advancing quantum communication technologies., Comment: Work in progress

Low latency and low power consumption are the main goals for our future networks. Fiber optics are already widely used for their faster speed. We want to investigate if optical decoding has further advantages to reaching future goals. We have investigated and compared the decoding latency and power consumption of an optical chip and its electronic counterpart built with MOSFETs. We have found that optical processing has a speed and power consumption benefit. For future networks and real-time applications, this can bring huge advantages over our current electronic processors., Comment: 6 pages, 7 figures, IEEE 9th World Forum on Internet of Things

In the context of optical signal processing, quantum and quantum-inspired machine learning algorithms have massive potential for deployment. One of the applications is in error correction protocols for the received noisy signals. In some scenarios, non-linear and unknown errors can lead to noise that bypasses linear error correction protocols that optical receivers generally implement. In those cases, machine learning techniques are used to recover the transmitted signal from the received signal through various estimation procedures. Since quantum machine learning algorithms promise advantage over classical algorithms, we expect that optical signal processing can benefit from these advantages. In this review, we survey several proposed quantum and quantum-inspired machine learning algorithms and their applicability with current technology to optical signal processing., Comment: European Wireless Conference (EW) 2023 - 6G Driving a Sustainable Growth

Nearest-neighbour clustering is a powerful set of heuristic algorithms that find natural application in the decoding of signals transmitted using the M-Quadrature Amplitude Modulation (M-QAM) protocol. Lloyd et al. proposed a quantum version of the algorithm that promised an exponential speed-up. We analyse the performance of this algorithm by simulating the use of a hybrid quantum-classical implementation of it upon 16-QAM and experimental 64-QAM data. We then benchmark the implementation against the classical k-means clustering algorithm. The choice of quantum encoding of the classical data plays a significant role in the performance, as it would for the hybrid quantum-classical implementation of any quantum machine learning algorithm. In this work, we use the popular angle embedding method for data embedding and the swap test for overlap estimation. The algorithm is emulated in software using Qiskit and tested on simulated and real-world experimental data. The discrepancy in accuracy from the perspective of the induced metric of the angle embedding method is discussed, and a thorough analysis regarding the angle embedding method in the context of distance estimation is provided. We detail an experimental optic fibre setup as well, from which we collect 64-QAM data. This is the dataset upon which the algorithms are benchmarked. Finally, some promising current and future directions for further research are discussed., Comment: 2023 IEEE Global Communications Conference: Selected Areas in Communications: Quantum Communications and Computing

Nearest-neighbour clustering is a simple yet powerful machine learning algorithm that finds natural application in the decoding of signals in classical optical-fibre communication systems. Quantum k-means clustering promises a speed-up over the classical k-means algorithm; however, it has been shown to not currently provide this speed-up for decoding optical-fibre signals due to the embedding of classical data, which introduces inaccuracies and slowdowns. Although still not achieving an exponential speed-up for NISQ implementations, this work proposes the generalised inverse stereographic projection as an improved embedding into the Bloch sphere for quantum distance estimation in k-nearest-neighbour clustering, which allows us to get closer to the classical performance. We also use the generalised inverse stereographic projection to develop an analogous classical clustering algorithm and benchmark its accuracy, runtime and convergence for decoding real-world experimental optical-fibre communication data. This proposed 'quantum-inspired' algorithm provides an improvement in both the accuracy and convergence rate with respect to the k-means algorithm. Hence, this work presents two main contributions. Firstly, we propose the general inverse stereographic projection into the Bloch sphere as a better embedding for quantum machine learning algorithms; here, we use the problem of clustering quadrature amplitude modulated optical-fibre signals as an example. Secondly, as a purely classical contribution inspired by the first contribution, we propose and benchmark the use of the general inverse stereographic projection and spherical centroid for clustering optical-fibre signals, showing that optimizing the radius yields a consistent improvement in accuracy and convergence rate.

This work explores entanglement-assisted communication, where quantum entanglement resources enable the transmission of classical information at an enhanced rate. We consider a scenario where entanglement is distributed ahead of time based on network traffic levels, and simulate a setting where idle nodes generate and store entanglement to later transmit messages at an accelerated rate. We analyze this communication model using noise models for quantum memory in various scenarios, and extend our investigation to a quantum-enhanced distributed computing environment, where entanglement storage enhances data transmission rates for cooperative data processing. We propose a protocol and demonstrate a distributed version of unsupervised clustering. Our results show that, for qubit channels, high rates of entanglement generation and modest storage requirements can surpass the classical limit with entanglement assistance., Comment: Accepted in IEEE QCE2023

Quantum information processing technology offers several communication strategies, which offer capacity advantages over classical technologies. However, advantages typically arise only in very particular communication scenarios which are of limited use in public networks. Most importantly, striking capacity advantages have so far been found only for cases where the system capacity is way below commercially interesting values. In this work we present a novel scenario where pre-shared entanglement offers arbitrarily high capacity advantages, and where at the same time data rates are compatible with future network demand. Our approach rests on the observation that the number of modes in multi-mode fiber can be increased solely by tuning of the refractive index, while maintaining the fiber diameter., Comment: 6 pages, 5 figure, European Wireless (IEEE) Conference

Optical fiber transmission systems form the backbone of today's communication networks and will be of high importance for future networks as well. Among the prominent noise effects in optical fiber is phase noise, which is induced by the Kerr effect. This effect limits the data transmission capacity of these networks and incurs high processing load on the receiver. At the same time, quantum information processing techniques offer more efficient solutions but are believed to be inefficient in terms of size, power consumption and resistance to noise. Here we investigate the concept of an all-optical joint detection receiver. We show how it contributes to enabling higher baud-rates for optical transmission systems when used as a pre-processor, even under high levels of noise induced by the Kerr effect., Comment: 6 pages, 3 figures; To be published in IEEE GLOBECOM 2022, see this https://globecom2022.ieee-globecom.org

Quantum communication technology offers several advanced strategies. However, their practical use is often times not yet well understood. In this work we therefore analyze the concept of a futuristic large-scale robotic factory, where each robot has a computing unit associated to it. The computing unit assists the robot with large computational tasks that have to be performed in real-time. Each robot moves randomly in a vicinity of its computing unit, and in addition both the robot and the unit can change location. To minimize latency, the connection is assumed as optical wireless. Due to the mobility, a permanent optimal assignment of frequency bands is assumed to increase communication latency and is therefore ruled out. Under such assumptions, we compare the different capacity scaling of different types of such architectures, where the one is built utilizing quantum communication techniques, and the other based on conventional design methods., Comment: 6 pages, 8 figures; To be published in IEEE GLOBECOM 2022, see https://globecom2022.ieee-globecom.org

We propose a new proof method for direct coding theorems for wiretap channels where the eavesdropper has access to a quantum version of the transmitted signal on an infinite-dimensional Hilbert space and the legitimate parties communicate through a classical channel or a classical input, quantum output (cq) channel. The transmitter input can be subject to an additive cost constraint, which specializes to the case of an average energy constraint. This method yields errors that decay exponentially with increasing block lengths. Moreover, it provides a guarantee of a quantum version of semantic security, which is an established concept in classical cryptography and physical layer security. Therefore, it complements existing works which either do not prove the exponential error decay or use weaker notions of security. The main part of this proof method is a direct coding result on channel resolvability which states that there is only a doubly exponentially small probability that a standard random codebook does not solve the channel resolvability problem for the cq channel. Semantic security has strong operational implications meaning essentially that the eavesdropper cannot use its quantum observation to gather any meaningful information about the transmitted signal. We also discuss the connections between semantic security and various other established notions of secrecy.

We consider all-optical network evolution from a quantum perspective. We show that a use of optimal quantum receivers allows an estimated $55\%$ decrease in energy consumption of all-optical amplifiers in network configurations that are typical today. We then compare data transmission capacities of quantum receivers with today's technology operating within the boundaries set by Shannon. We find that quantum receiver technology allows for a logarithmic scaling of the system capacity with the baud-rate, while Shannon-type systems are limited by the transmit power. Thus a natural quantum limit of classical data transmission emerges. Based on the above findings we argue for a new approach to optical communication network design, wherein in-line amplifiers are replaced by novel fiber supporting high spectral bandwidth to allow for noiseless data transmission in the quantum limit., Comment: This version has a significantly shortened abstract, and an expanded section on transmission at high baud-rates

We describe a method of investigating the near-term potential of quantum communication technology for communication networks from the perspective of current networks. For this, we integrate an instance of the quantum network simulator QuNetSim at the link layer into the communication network emulator ComNetsEmu. This novel augmented version of ComNetsEmu is thereby enabled to run arbitrary quantum protocols between any directly connected pair of network hosts. To give an example of the proposed method, we implement the link layer method of generating and storing entanglement while idle, to accelerate data transmission at later times using superdense coding.

Compound channel models offer a simple and straightforward way of analyzing the stability of decoder design under model variations. With this work we provide a coding theorem for a large class of practically relevant compound channel models. We give explicit formulas for the cases of the Gaussian classical-quantum compound channels with unknown noise, unknown phase and unknown attenuation. We show analytically how the classical compound channel capacity formula motivates nontrivial choices of the displacement parameter of the Kennedy receiver. Our work demonstrates the value of the compound channel model as a method for the design of receivers in quantum communication., Comment: 6 pages, 1 figure, accepted at ISIT - 2021 IEEE International Symposium on Information Theory

We analyse a communication scenario over a particular causal broadcast channel whose state depends on a modulo sum. The receivers of the broadcast receive channel state information and collaborate to determine the channel state as to decode their private messages. Further, the receivers of the broadcast can collude up to the minimum non-collusion condition to determine state information of the other non-colluding receivers. We analyse three resource scenarios for the receivers: receivers can share entanglement without classically communicating, can just use classical communication, or have both entanglement and classical communication. Using results from secure multi-party communication, we find that when the receivers can share entanglement and communicate classically, they can receive messages from the sender at a non-zero rate with verifiable secure collaboration. In the entanglement only case a positive capacity is not possible. In the classical communication case, a non-zero rate of communication is achievable but the communication complexity overhead grows quadratically in the number of receivers versus linear in the number of receivers with entanglement., Comment: 6 pages, 1 figure

As quantum internet technologies develop, the need for simulation software and education for quantum internet rises. QuNetSim aims to fill this need. QuNetSim is a Python software framework that can be used to simulate quantum networks up to the network layer. The goal of QuNetSim is to make it easier to investigate and test quantum networking protocols over various quantum network configurations and parameters. The framework incorporates many known quantum network protocols so that users can quickly build simulations and beginners can easily learn to implement their own quantum networking protocols., Comment: 11 pages, 6 figures. To appear in IEEE Transactions on Quantum Engineering

We introduce and analyse a multiple-access channel with two senders and one receiver, in the presence of i.i.d. noise coming from the environment. Partial side information about the environmental states allows the senders to modulate their signals accordingly. An adversarial jammer with its own access to information on environmental states and the modulation signals can jam a fraction of the transmissions. Our results show that for many choices of the system parameters, entanglement shared between the two senders allows them to communicate at non-zero rates with the receiver, while for the same parameters the system forbids any communication without entanglement-assistance, even if the senders have access to common randomness (local correlations). A simplified model displaying a similar behaviour but with a compound channel instead of a jammer is outlined to introduce basic aspects of the modeling. We complement these results by demonstrating that there even exist model parameters for which entanglement-assisted communication is no longer possible, but a hypothetical use of nonlocal no-signalling correlations between Alice and Bob could enable them to communicate to Charlie again., Comment: 15 pages, 3 figures. Compound channel model added to the document in Remark 1. Typos fixed. Accepted for puplication in IEEE Journal on Selected Areas in Information Theory

We study reliable communication in uncoordinated vehicular communication from the perspective of Shannon theory. Our system model for the information transmission is that of an Arbitrarily Varying Channel (AVC): One sender-receiver pair wants to communicate reliably, no matter what the input of a second sender is. The second sender is assumed to be uncoordinated and interfering, but is supposed to follow the rational goal of transmitting information otherwise. We prove that repetition coding can increase the capacity of such a system by relating the notion of symmetrizability of an arbitrarily varying channel to invertibility of the corresponding channel matrix. Explicit upper bounds on the number of repetitions needed to prevent system breakdown through diversity are provided. Further we introduce the notion of block-restricted jamming and present a lower and an upper bound on the maximum error capacity of the corresponding restricted AVC., Comment: 6 pages, conference, 2 figures, accepted to Proc. IEEE ICC, Shanghai, China, May 2019

We consider a model of communication via a fully quantum jammer channel with quantum jammer, quantum sender and quantum receiver, which we dub quantum arbitrarily varying channel (QAVC). Restricting to finite dimensional user and jammer systems, we show, using permutation symmetry and a de Finetti reduction, how the random coding capacity (classical and quantum) of the QAVC is reduced to the capacity of a naturally associated compound channel, which is obtained by restricting the jammer to i.i.d. input states. Furthermore, we demonstrate that the shared randomness required is at most logarithmic in the block length, using a random matrix tail bound. This implies a dichotomy theorem: either the classical capacity of the QAVC is zero, and then also the quantum capacity is zero, or each capacity equals its random coding variant., Comment: 5 pages, ISIT format (IEEEtra.cls)

We determine the secrecy capacities of AVQCs (arbitrarily varying quantum channels). Both secrecy capacity with average error probability and with maximal error probability are derived. Both derivations are based on one common code construction. The code we construct fulfills a stringent secrecy requirement, which is called the strong code concept. We determine when the secrecy capacity is a continuous function of the system parameters and completely characterize its discontinuity points both for average error criterion and for maximal error criterion. Furthermore, we prove the phenomenon "super-activation" for secrecy capacities of AVQCs, i.e., two quantum channels both with zero secrecy capacity, which, if used together, allow secure transmission with positive capacity. We also discuss the relations between the entanglement distillation capacity, the entanglement generating capacity, and the strong subspace transmission capacity for AVQCs., Comment: arXiv admin note: text overlap with arXiv:1702.03483

The question of robust direct communication in vehicular networks is discussed. In most state-of-the-art approaches, there is no central entity controlling channel access, so there may be arbitrary interference from other parties. Thus, a suitable channel model for Vehicle-to-X (V2X) communication is the Arbitrarily Varying Channel (AVC). Employing multiple antennas on a vehicle or sending over multiple frequencies to make use of diversity are promising approaches to combat interference. In this setup, an important question about diversity is how many antennas or orthogonal carrier frequencies are necessary in order to avoid system breakdown due to unknown interference in AVCs. For Binary Symmetric AVCs (AVBSC) and a physically meaningful identical state-constrained jammer, the deployment of a third, uncorrelated receiving antenna or the parallel transmission over three different orthogonal frequencies avoids symmetrizability and thus ensures positivity of the capacity of the overall communication channel. Furthermore, the capacity of the identical state-constrained composite AVBSC is continuous and shows super-activation, a phenomenon which was hitherto deemed impossible for classical communication without secrecy constraints. Subsuming, spatial and frequency diversity are enablers for reliable communication over communication channels with arbitrarily varying interference., Comment: 29 pages, 4 figures

Today, the internet makes tremendous amounts of data widely available. Often, the same information is behind multiple different available data sets. This lends growing importance to latent variable models that try to learn the hidden information from the available imperfect versions. For example, social media platforms can contain an abundance of pictures of the same person or object, yet all of which are taken from different perspectives. In a simplified scenario, one may consider pictures taken from the same perspective, which are distorted by noise. This latter application allows for a rigorous mathematical treatment, which is the content of this contribution. We apply a recently developed method of dependent component analysis to image denoising when multiple distorted copies of one and the same image are available, each being corrupted by a different and unknown noise process. In a simplified scenario, we assume that the distorted image is corrupted by noise that acts independently on each pixel. We answer completely the question of how to perform optimal denoising, when at least three distorted copies are available: First we define optimality of an algorithm in the presented scenario, and then we describe an aymptotically optimal universal discrete denoising algorithm (UDDA). In the case of binary data and binary symmetric noise, we develop a simplified variant of the algorithm, dubbed BUDDA, which we prove to attain universal denoising uniformly., Comment: 10 pages, 6 figures

We analyze arbitrarily varying classical-quantum wiretap channels.These channels are subject to two attacks at the same time: one passive (eavesdropping), and one active (jamming). We progress on previous works by introducing a reduced class of allowed codes that fulfills a more stringent secrecy requirement than earlier definitions. In addition, we prove that non-symmetrizability of the legal link is suficient for equality of the deterministic and the common randomness assisted secrecy capacities. At last, we focus on analytic properties of both secrecy capacities: We completely characterize their discontinuity points, and their super-activation properties., Comment: arXiv admin note: text overlap with arXiv:1606.01768, arXiv:1307.8007

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., Comment: arXiv admin note: text overlap with arXiv:1307.8007

We characterize the asymptotic performance of a class of positive operator valued measurements (POVMs) where the only task is to make measurements on independent and identically distributed quantum states on finite-dimensional systems. The POVMs we utilize here can be efficiently described in terms of a reasonably small set of parameters. Their analysis furthers the development of a quantum method of types. They deliver provably optimal performance in asymmetric hypothesis testing and in the transmission of classical messages over quantum channels. We now relate them to the recently developed $\alpha-z$ divergences $D_{\alpha,z}$ by giving an operational interpretation for the limiting case $\lim_{\alpha\to1}D_{\alpha,1-\alpha}$ in terms of probabilities for certain measurement outcomes. This explains one of the more surprising findings of [1] in terms of the theory of group representations. In addition, we provide a Cauchy-Binet type formula for unitary matrices which connects the underlying representation theoretic objects to partial sums of the entries of unitary matrices. At last, we concentrate on the special case of qubits. We are able to give a complete description of the asymptotic detection probabilities for all POVM elements described here. We take the opportunity to define a family of functions on pairs of semi-definite matrices which obeys the quantum generalizations of R\'enyi's axioms except from the generalized mean value axiom. This family is described by limiting values of $\alpha-z$ divergences for the extremal values of the parameter., Comment: 26 pages, no figures. Corrected affiliation and funding sources, as well as some typos

We study an analog of the well-known Gel'fand Pinsker Channel which uses quantum states for the transmission of the data. We consider the case where both the sender's inputs to the channel and the channel states are to be taken from a finite set (cq-channel with state information at the sender). We distinguish between causal and non-causal channel state information at the sender. The receiver remains ignorant, throughout. We give a single-letter description of the capacity in the first case. In the second case we present two different regularized expressions for the capacity. It is an astonishing and unexpected result of our work that a simple change from causal to non-causal channel state information at the encoder causes the complexity of a numerical computation of the capacity formula to change from trivial to seemingly difficult. Still, even the non-single letter formula allows one to draw nontrivial conclusions, for example regarding continuity of the capacity with respect to changes in the system parameters. The direct parts of both coding theorems are based on a special class of POVMs which are derived from orthogonal projections onto certain representations of the symmetric groups. This approach supports a reasoning that is inspired by the classical method of types. In combination with the non-commutative union bound these POVMs yield an elegant method of proof for the direct part of the coding theorem in the first case., Comment: 26 pages, no figures. Many typos corrected. More details added to the proofs. Added proof for the direct part of capacity theorem for causal encoding

We define the common randomness assisted capacity of an arbitrarily varying channel (AVWC) when the Eavesdropper is kept ignorant about the common randomness. We prove a multi-letter capacity formula for this model. We prove that, if enough common randomness is used, the capacity formula can be given a single-shot form again. We then consider the opposite extremal case, where no common randomness is available. It is known that the capacity of the system can be discontinuous under these circumstances. We prove here that it is still stable in the sense that it is continuous around its positivity points. We further prove that discontinuities can only arise if the legal link is symmetrizable and characterize the points where it is positive. These results shed new light on the design principles of communication systems with embedded security features. At last we investigate the effect of super-activation of the message transmission capacity of AVWCs under the average error criterion. We give a complete characterization of those AVWCs that may be super-activated. The effect is thereby also related to the (conjectured) super-activation of the common randomness assisted capacity of AVWCs with an eavesdropper that gets to know the common randomness. Super-activation is based on the idea of "wasting" a few bits of non-secret messages in order to enable provably secret transmission of a large bulk of data, a concept that may prove to be of further importance in the design of communication systems. In this work we provide further insight into this phenomenon by providing a class of codes that is capacity-achieving and does not convey any information to the Eavesdropper., Comment: Significant changes again: now 53 pages, 2 figures. Modified and corrected Lemma 3. Added insightful example related to Lemma 3. Extended proof of Theorem 2

This work is motivated by a question at the heart of unsupervised learning approaches: Assume we are collecting a number K of (subjective) opinions about some event E from K different agents. Can we infer E from them? Prima facie this seems impossible, since the agents may be lying. We model this task by letting the events be distributed according to some distribution p and the task is to estimate p under unknown noise. Again, this is impossible without additional assumptions. We report here the finding of very natural such assumptions - the availability of multiple copies of the true data, each under independent and invertible (in the sense of matrices) noise, is already sufficient: If the true distribution and the observations are modeled on the same finite alphabet, then the number of such copies needed to determine p to the highest possible precision is exactly three! This result can be seen as a counterpart to independent component analysis. Therefore, we call our approach 'dependent component analysis'. In addition, we present generalizations of the model to different alphabet sizes at in- and output. A second result is found: the 'activation' of invertibility through multiple parallel uses., Comment: 13 pages, 3 figures. Published in IEEE Transactions on Information Theory. Typo in Theorem 4 and Conjecture 1 corrected in this version

We give a complete characterization of the correlated random coding secrecy capacity of arbitrarily varying wiretap channels (AVWCs). We apply two alternative strong secrecy criteria, which both lead to the same multi-letter formula. The difference of these criteria lies in the treatment of correlated randomness, they coincide in the case of uncorrelated codes. On the basis of the derived formula, we show that the correlated random coding secrecy capacity is continuous as a function of the AVWC, in contrast to the discontinuous uncorrelated coding secrecy capacity. In the proof of the secrecy capacity formula for correlated random codes, we apply an auxiliary channel which is compound from the sender to the intended receiver and arbitrarily varying from the sender to the eavesdropper., Comment: 32 pages. With slight differences in Remarks 7-4) and Remark 17 submitted to IEEE Transactions on Information Theory

We prove coding theorems for two scenarios of cooperating encoders for the multiple access channel with two classical inputs and one quantum output. In the first scenario (ccq-MAC with common messages), the two senders each have their private messages, but would also like to transmit common messages. In the second scenario (ccq-MAC with conferencing encoders), each sender has its own set of messages, but they are allowed to use a limited amount of noiseless classical communication amongst each other prior to encoding their messages. This conferencing protocol may depend on each individual message they intend to send. The two scenarios are related to each other not only in spirit - the existence of near-optimal codes for the ccq-MAC with common messages is used for proving the existence of near-optimal codes for the ccq-MAC with conferencing encoders., Comment: 17 pages, no figures

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 classical-quantum wiretap channels. We prove the phenomenon super-activation for arbitrarily varying classical-quantum wiretap channels, i.e., if we use two arbitrarily varying classical-quantum wiretap channels, both with zero deterministic secrecy capacity together, they allow perfect secure transmission.

We investigate the action of the depolarising (qubit) channel on permutation invariant input states. More specifically, we raise the question on which invariant subspaces the output of the depolarising channel, given such special input, is supported. An answer is given for equidistributed states on isotypical subspaces, also called symmetric Werner states. Horns problem and two of the corresponding inequalities are invoked as a method of proof., Comment: 7 pages, no figures

As our main result we show that, in order to achieve the randomness assisted message - and entanglement transmission capacities of a finite arbitrarily varying quantum channel it is not necessary that sender and receiver share (asymptotically perfect) common randomness. Rather, it is sufficient that they each have access to an unlimited amount of uses of one part of a correlated bipartite source. This access might be restricted to an arbitrary small (nonzero) fraction per channel use, without changing the main result. We investigate the notion of common randomness. It turns out that this is a very costly resource - generically, it cannot be obtained just by local processing of a bipartite source. This result underlines the importance of our main result. Also, the asymptotic equivalence of the maximal- and average error criterion for classical message transmission over finite arbitrarily varying quantum channels is proven. At last, we prove a simplifed symmetrizability condition for finite arbitrarily varying quantum channels., Comment: 25 pages, no figures. Considerably revised version, accepted for publication in J. Math. Phys

We consider compound as well as arbitrarily varying classical-quantum channel models. For classical-quantum compound channels, we give an elementary proof of the direct part of the coding theorem. A weak converse under average error criterion to this statement is also established. We use this result together with the robustification and elimination technique developed by Ahlswede in order to give an alternative proof of the direct part of the coding theorem for a finite classical-quantum arbitrarily varying channels with the criterion of success being average error probability. Moreover we provide a proof of the strong converse to the random coding capacity in this setting.The notion of symmetrizability for the maximal error probability is defined and it is shown to be both necessary and sufficient for the capacity for message transmission with maximal error probability criterion to equal zero. Finally, it is shown that the connection between zero-error capacity and certain arbitrarily varying channels is, just like in the case of quantum channels, only partially valid for classical-quantum channels., Comment: 37 pages, 0 figures. Accepted for publication in the LNCS Volume in Memory of Rudolf Ahlswede. Includes a section on certain differences between classical and classical-quantum channels regarding their zero-error capacities

We give a proof of the multi-party typicality conjecture for the first nontrivial case when there are only two parties. The conjecture itself is motivated by the study of multi-party state merging protocols on quantum systems. Our approach is based on fundamental group-theoretical properties, thereby providing an opportunity to study the problem from a more systematic perspective. Our proof also covers an extended multiparty typicality conjecture that we state in this work. This extended multiparty typicality conjecture is formulated using arbitrary $k$-norms instead of only the $2$-norm as in the original conjecture., Comment: 17 pages, no figures. Typos removed, extended introduction. Generalized problem statement

We investigate entanglement transmission over an unknown channel in the presence of a third party (called the adversary), which is enabled to choose the channel from a given set of memoryless but non-stationary channels without informing the legitimate sender and receiver about the particular choice that he made. This channel model is called arbitrarily varying quantum channel (AVQC). We derive a quantum version of Ahlswede's dichotomy for classical arbitrarily varying channels. This includes a regularized formula for the common randomness-assisted capacity for entanglement transmission of an AVQC. Quite surprisingly and in contrast to the classical analog of the problem involving the maximal and average error probability, we find that the capacity for entanglement transmission of an AVQC always equals its strong subspace transmission capacity. These results are accompanied by different notions of symmetrizability (zero-capacity conditions) as well as by conditions for an AVQC to have a capacity described by a single-letter formula. In he final part of the paper the capacity of the erasure-AVQC is computed and some light shed on the connection between AVQCs and zero-error capacities. Additionally, we show by entirely elementary and operational arguments motivated by the theory of AVQCs that the quantum, classical, and entanglement-assisted zero-error capacities of quantum channels are generically zero and are discontinuous at every positivity point., Comment: 49 pages, no figures, final version of our papers arXiv:1010.0418v2 and arXiv:1010.0418. Published "Online First" in Communications in Mathematical Physics, 2012

We determine the optimal achievable rate at which entanglement can be reliably transmitted when the memoryless channel used during transmission is unknown both to sender and receiver. To be more precise, we assume that both of them only know that the channel belongs to a given set of channels. Thus, they have to use encoding and decoding schemes that work well for the whole set., Comment: To appear in the proceedings of ISIT 2009