The Experts below are selected from a list of 309 Experts worldwide ranked by ideXlab platform
Mark M. Wilde - One of the best experts on this subject based on the ideXlab platform.
-
Relative entropy of steering: on its definition and properties
Journal of Physics A, 2017Co-Authors: Eneet Kaur, Mark M. WildeAbstract:In [Gallego and Aolita, Physical Review X 5, 041008 (2015)], the authors proposed a definition for the relative entropy of steering and showed that the resulting quantity is a convex steering monotone. Here we advocate for a different definition for relative entropy of steering, based on well grounded concerns coming from quantum Shannon Theory. We prove that this modified relative entropy of steering is a convex steering monotone. Furthermore, we establish that it is uniformly continuous and faithful, in both cases giving quantitative bounds that should be useful in applications. We also consider a restricted relative entropy of steering which is relevant for the case in which the free operations in the resource Theory of steering have a more restricted form (the restricted operations could be more relevant in practical scenarios). The restricted relative entropy of steering is convex, monotone with respect to these restricted operations, uniformly continuous, and faithful.
-
quantum information Theory concepts in quantum Shannon Theory
2013Co-Authors: Mark M. WildeAbstract:In these first few chapters, our aim is to establish a firm grounding so that we can address some fundamental questions regarding information transmission over quantum channels. This area of study has become known as “quantum Shannon Theory” in the broader quantum information community, in order to distinguish this topic from other areas of study in quantum information science. In this text, we will use the terms “quantum Shannon Theory” and “quantum information Theory” somewhat interchangeably. We will begin by briefly overviewing several fundamental aspects of the quantum Theory. Our study of the quantum Theory, in this chapter and future ones, will be at an abstract level, without giving preference to any particular physical system such as a spin-1/2 particle or a photon. This approach will be more beneficial for the purposes of our study, but, here and there, we will make some reference to actual physical systems to ground us in reality. You may be wondering, what is quantum Shannon Theory and why do we name this area of study as such? In short, quantum Shannon Theory is the study of the ultimate capability of noisy physical systems, governed by the laws of quantum mechanics, to preserve information and correlations. Quantum information theorists have chosen the name quantum Shannon Theory to honor Claude Shannon, who single-handedly founded the field of classical information Theory, with a groundbreaking 1948 paper (Shannon, 1948).
-
classical Shannon Theory
2013Co-Authors: Mark M. WildeAbstract:We cannot overstate the importance of Shannon's contribution to modern science. His introduction of the field of information Theory and his solutions to its two main theorems demonstrate that his ideas on communication were far beyond the other prevailing ideas in this domain around 1948. In this chapter, our aim is to discuss Shannon's two main contributions in a descriptive fashion. The goal of this high-level discussion is to build up the intuition for the problem domain of information Theory and to understand the main concepts before we delve into the analogous quantum information-theoretic ideas. We avoid going into deep technical detail in this chapter, leaving such details for later chapters where we formally prove both classical and quantum Shannon-theoretic coding theorems. We do use some mathematics from probability Theory, namely, the law of large numbers. We will be delving into the technical details of this chapter's material in later chapters (specifically, Chapters 10, 12, and 13). Once you have reached later chapters that develop some more technical details, it might be helpful to turn back to this chapter to get an overall flavor for the motivation of the development. Data Compression We first discuss the problem of data compression. Those who are familiar with the Internet have used several popular data formats such as JPEG, MPEG, ZIP, GIF, etc. All of these file formats have corresponding algorithms for compressing the output of an information source.
-
The quantum dynamic capacity formula of a quantum channel
Quantum Information Processing, 2012Co-Authors: Mark M. Wilde, Min-hsiu HsiehAbstract:The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon Theory literature. In this work, we prove the theorem with an “ab initio” approach, using only the most basic tools in the quantum information theorist’s toolkit: the Alicki-Fannes’ inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon Theory literature. We also demonstrate that the “quantum dynamic capacity formula” characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula reduces the computation of the trade-off surface to a tractable, textbook problem in Pareto trade-off analysis, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.
-
from classical to quantum Shannon Theory
arXiv: Quantum Physics, 2011Co-Authors: Mark M. WildeAbstract:The aim of this book is to develop "from the ground up" many of the major, exciting, pre- and post-millenium developments in the general area of study known as quantum Shannon Theory. As such, we spend a significant amount of time on quantum mechanics for quantum information Theory (Part II), we give a careful study of the important unit protocols of teleportation, super-dense coding, and entanglement distribution (Part III), and we develop many of the tools necessary for understanding information transmission or compression (Part IV). Parts V and VI are the culmination of this book, where all of the tools developed come into play for understanding many of the important results in quantum Shannon Theory.
Min-hsiu Hsieh - One of the best experts on this subject based on the ideXlab platform.
-
The quantum dynamic capacity formula of a quantum channel
Quantum Information Processing, 2012Co-Authors: Mark M. Wilde, Min-hsiu HsiehAbstract:The dynamic capacity theorem characterizes the reliable communication rates of a quantum channel when combined with the noiseless resources of classical communication, quantum communication, and entanglement. In prior work, we proved the converse part of this theorem by making contact with many previous results in the quantum Shannon Theory literature. In this work, we prove the theorem with an “ab initio” approach, using only the most basic tools in the quantum information theorist’s toolkit: the Alicki-Fannes’ inequality, the chain rule for quantum mutual information, elementary properties of quantum entropy, and the quantum data processing inequality. The result is a simplified proof of the theorem that should be more accessible to those unfamiliar with the quantum Shannon Theory literature. We also demonstrate that the “quantum dynamic capacity formula” characterizes the Pareto optimal trade-off surface for the full dynamic capacity region. Additivity of this formula reduces the computation of the trade-off surface to a tractable, textbook problem in Pareto trade-off analysis, and we prove that its additivity holds for the quantum Hadamard channels and the quantum erasure channel. We then determine exact expressions for and plot the dynamic capacity region of the quantum dephasing channel, an example from the Hadamard class, and the quantum erasure channel.
-
Entanglement generation with a quantum channel and a shared state
2010 IEEE International Symposium on Information Theory, 2010Co-Authors: Mark M. Wilde, Min-hsiu HsiehAbstract:We introduce a new protocol, the channel-state coding protocol, to quantum Shannon Theory. This protocol generates entanglement between a sender and receiver by coding for a noisy quantum channel with the aid of a noisy shared state. The mother and father protocols arise as special cases of the channel-state coding protocol, where the channel is noiseless or the state is a noiseless maximally entangled state, respectively. The channel-state coding protocol paves the way for formulating entanglement-assisted quantum error-correcting codes that are robust to noise in shared entanglement. Finally, the channel-state coding protocol leads to a Smith-Yard superactivation, where we can generate entanglement using a zero-capacity erasure channel and a non-distillable bound entangled state.
-
Trading classical communication, quantum communication, and entanglement in quantum Shannon Theory
IEEE Transactions on Information Theory, 2010Co-Authors: Min-hsiu Hsieh, Mark M. WildeAbstract:In this paper, we give tradeoffs between classical communication, quantum communication, and entanglement for processing information in the Shannon-theoretic setting. We first prove a “unit-resource” capacity theorem that applies to the scenario where only the above three noiseless resources are available for consumption or generation. The optimal strategy mixes the three fundamental protocols of teleportation, superdense coding, and entanglement distribution. We then provide an achievable rate region and a matching multiletter converse for the “direct-static” capacity theorem. This theorem applies to the scenario where a large number of copies of a noisy bipartite state are available (in addition to consumption or generation of the above three noiseless resources). Our coding strategy involves a protocol that we name the classically assisted state redistribution protocol and the three fundamental protocols. We finally provide an achievable rate region and a matching multiletter converse for the “direct-dynamic” capacity theorem. This theorem applies to the scenario where a large number of uses of a noisy quantum channel are available in addition to the consumption or generation of the three noiseless resources. Our coding strategy combines the classically enhanced father protocol with the three fundamental unit protocols.
-
Catalytic quantum error correction
arXiv:quant-ph 0608027, 2006Co-Authors: Todd Brun, Igor Devetak, Min-hsiu HsiehAbstract:We develop the Theory of entanglement-assisted quantum error correcting (EAQEC) codes, a generalization of the stabilizer formalism to the setting in which the sender and receiver have access to pre-shared entanglement. Conventional stabilizer codes are equivalent to dual-containing symplectic codes. In contrast, EAQEC codes do not require the dual-containing condition, which greatly simplifies their construction. We show how any quaternary classical code can be made into a EAQEC code. In particular, efficient modern codes, like LDPC codes, which attain the Shannon capacity, can be made into EAQEC codes attaining the hashing bound. In a quantum computation setting, EAQEC codes give rise to catalytic quantum codes which maintain a region of inherited noiseless qubits. We also give an alternative construction of EAQEC codes by making classical entanglement assisted codes coherent. Information Theory and the Theory of error-correcting codes (coding Theory) are intimately connected. Both address the problem of sending information over noisy channels. The sender Alice encodes her message as a codeword, sends it through the channel, and the receiver Bob tries to infer the intended message based on the channel output. Information Theory (or rather the subfield of Shannon Theory) deals with the asymptotic setting of increasingly long codes, with asymptotically vanishing error probability. The noisy channel is typically assumed to act independently on the codeword bits. The fundamental quantity of interest is the capacity of the channel: the optimal rate (in bits per channel use) of information transfer. Claude Shannon [30] gave a remarkable characterization of the channel capacity in terms of mutual information. Unfortunately, the capacity is achieved by random coding, which means highly inefficient encoding and decoding algorithms. Coding Theory deals with the practical finite setting, characterized by a fixed code length, num-ber of encoded bits and correctable error set. The most popular codes have simple mathematical properties, such as linearity (a linear combination of codewords is another codeword), which al-lows for efficient encoding. The performance of these codes is then measured against the optimal performance set by Shannon Theory. This relationship carries over to quantum information processing. The basic communication task is sending quantum information over noisy quantum channels. This setting is also relevant for fault tolerant quantum computation, because decoherence can be regarded as a quantum channel
Upamanyu Madhow - One of the best experts on this subject based on the ideXlab platform.
-
On the Theory of multiGigabit transceiver implementations
2010 International Conference on Signal Processing and Communications (SPCOM), 2010Co-Authors: Upamanyu MadhowAbstract:The analog-to-digital converter (ADC) is the fundamental bottleneck to scaling mostly digital communication transceiver architectures to multiGigabit speeds: high-precision, high-speed ADCs are too costly, too power-hungry, or simply not available. One possible approach to this problem is to use drastically lower ADC precision in the receiver. However, the insertion of a severe nonlinearity in the transceiver chain implies that we must comprehensively rethink signal processing for communication, which is largely based on linear models. After reviewing what Shannon Theory tells us, we discuss recent results on demodulation, automatic gain control, and transmit precoding.
-
coded noncoherent communication with amplitude phase modulation from Shannon Theory to practical architectures
IEEE Transactions on Communications, 2008Co-Authors: Noah Jacobsen, Upamanyu MadhowAbstract:We develop bandwidth efficient radio transceivers, using amplitude/phase modulations, for frequency non-selective channels whose time variations are typical of outdoor mobile wireless systems. The transceiver is noncoherent, neither requiring pilots for channel estimation and tracking nor assuming prior channel knowledge on the part of the receiver. Serial concatenation of a binary outer channel code with an inner differential modulation code provides a turbo structure that, along with the channel memory, is exploited for joint iterative channel and data estimation. While prior work on noncoherent communication mainly focuses on PSK alphabets, we consider a moderate to high SNR regime in which amplitude/phase constellations are more efficient. First, the complexity of block noncoherent demodulation is reduced to a level that is comparable to coherent receivers. Then, a tool for choosing the constellation and bit-to-symbol mapping is developed by adapting extrinsic information transfer (EXIT) charts for noncoherent demodulation. The recommended constellations differ significantly from standard coherent channel constellations, and from prior recommendations for uncoded noncoherent systems. The analysis shows that standard convolutional codes are nearly optimal when paired with differential amplitude/phase modulation.
-
Coded noncoherent communication with amplitude/phase modulation: from Shannon Theory to practical architectures
IEEE Transactions on Communications, 2008Co-Authors: Noah Jacobsen, Upamanyu MadhowAbstract:We develop bandwidth efficient radio transceivers, using amplitude/phase modulations, for frequency non-selective channels whose time variations are typical of outdoor mobile wireless systems. The transceiver is noncoherent, neither requiring pilots for channel estimation and tracking nor assuming prior channel knowledge on the part of the receiver. Serial concatenation of a binary outer channel code with an inner differential modulation code provides a turbo structure that, along with the channel memory, is exploited for joint iterative channel and data estimation. While prior work on noncoherent communication mainly focuses on PSK alphabets, we consider a moderate to high SNR regime in which amplitude/phase constellations are more efficient. First, the complexity of block noncoherent demodulation is reduced to a level that is comparable to coherent receivers. Then, a tool for choosing the constellation and bit-to-symbol mapping is developed by adapting extrinsic information transfer (EXIT) charts for noncoherent demodulation. The recommended constellations differ significantly from standard coherent channel constellations, and from prior recommendations for uncoded noncoherent systems. The analysis shows that standard convolutional codes are nearly optimal when paired with differential amplitude/phase modulation.
Ciara Morgan - One of the best experts on this subject based on the ideXlab platform.
-
TQC - Implementing unitary 2-designs using random diagonal-unitary matrices
2020Co-Authors: Yoshifumi Nakata, Christoph Hirche, Ciara Morgan, Andreas WinterAbstract:Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon Theory. Here we prove that unitary 2-designs can be implemented approximately using random diagonal-unitaries.
-
Implementing unitary 2-designs using random diagonal-unitary matrices
arXiv: Quantum Physics, 2015Co-Authors: Yoshifumi Nakata, Christoph Hirche, Ciara Morgan, Andreas WinterAbstract:Unitary 2-designs are random unitary matrices which, in contrast to their Haar-distributed counterparts, have been shown to be efficiently realized by quantum circuits. Most notably, unitary 2-designs are known to achieve decoupling, a fundamental primitive of paramount importance in quantum Shannon Theory. Here we prove that unitary 2-designs can be implemented approximately using random diagonal-unitaries.
-
Efficient achievability for quantum protocols using decoupling theorems
2014 IEEE International Symposium on Information Theory, 2014Co-Authors: Christoph Hirche, Ciara MorganAbstract:Proving achievability of protocols in quantum Shannon Theory usually does not consider the efficiency at which the goal of the protocol can be achieved. Nevertheless it is known that protocols such as coherent state merging are efficiently achievable at optimal rate.We aim to investigate this fact further in a general one-shot setting, by considering certain classes of decoupling theorems and give exact rates for these classes. Moreover we compare results of general decoupling theorems using Haar distributed unitaries with those using smaller sets of operators, in particular ε-approximate 2-designs. We also observe the behavior of our rates in special cases such as ε approaching zero and the asymptotic limit.
Giulio Chiribella - One of the best experts on this subject based on the ideXlab platform.
-
quantum Shannon Theory with superpositions of trajectories
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2019Co-Authors: Giulio Chiribella, Hler KristjanssonAbstract:Shannon's Theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon Theory, explores the new possibilities ari...
-
quantum Shannon Theory with superpositions of trajectories
arXiv: Quantum Physics, 2019Co-Authors: Giulio Chiribella, Hler KristjanssonAbstract:Shannon's Theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon Theory, explores the new possibilities arising when the information carriers are quantum systems. Traditionally, quantum Shannon Theory has focussed on scenarios where the internal state of the information carriers is quantum, while their trajectory is classical. Here we propose a second level of quantisation where both the information and its propagation in spacetime is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the counterintuitive phenomena taking place when information travels simultaneously through multiple transmission lines.
-
a second quantised Shannon Theory
arXiv: Quantum Physics, 2018Co-Authors: Giulio Chiribella, Hler KristjanssonAbstract:Shannon's Theory of information was built on the assumption that the information carriers were classical systems. Its quantum counterpart, quantum Shannon Theory, explores the new possibilities that arise when the information carriers are quantum particles. Traditionally,quantum Shannon Theory has focussed on scenarios where the internal state of the particles is quantum, while their trajectory in spacetime is classical. Here we propose a second level of quantisation where both the information and its propagation in spacetime is treated quantum mechanically. The framework is illustrated with a number of examples, showcasing some of the couterintuitive phenomena taking place when information travels in a superposition of paths.
-
Enhanced Communication with the Assistance of Indefinite Causal Order.
Physical Review Letters, 2018Co-Authors: Daniel Ebler, Sina Salek, Giulio ChiribellaAbstract:: In quantum Shannon Theory, the way information is encoded and decoded takes advantage of the laws of quantum mechanics, while the way communication channels are interlinked is assumed to be classical. In this Letter, we relax the assumption that quantum channels are combined classically, showing that a quantum communication network where quantum channels are combined in a superposition of different orders can achieve tasks that are impossible in conventional quantum Shannon Theory. In particular, we show that two identical copies of a completely depolarizing channel become able to transmit information when they are combined in a quantum superposition of two alternative orders. This finding runs counter to the intuition that if two communication channels are identical, using them in different orders should not make any difference. The failure of such intuition stems from the fact that a single noisy channel can be a random mixture of elementary, noncommuting processes, whose order (or lack thereof) can affect the ability to transmit information.
-
Compression for quantum population coding
2017 IEEE International Symposium on Information Theory (ISIT), 2017Co-Authors: Yuxiang Yang, Giulio Chiribella, Masahito HayashiAbstract:We study the compression of arbitrary parametric families of n identically prepared finite-dimensional quantum states, in a setting that can be regarded as a quantum analogue of population coding. For a family with f free parameters, we propose an asymptotically faithful protocol that requires a memory of overall size (f/2) log n. Our construction uses a quantum version of local asymptotic normality and, as an intermediate step, solves the problem of the optimal compression of n identically prepared displaced thermal states. Our protocol achieves the ultimate bound predicted by quantum Shannon Theory. In addition, we explore the minimum requirement for quantum memory: On the one hand, the amount of quantum memory used by our protocol can be made arbitrarily small compared to the overall memory cost; on the other hand, any protocol using only classical memory cannot be faithful.