Showing papers on "Coherent information published in 2015"
TL;DR: A computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems is introduced, which reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states.
Abstract: Einstein-Podolsky-Rosen steering incarnates a useful nonclassical correlation which sits between entanglement and Bell nonlocality. While a number of qualitative steering criteria exist, very little has been achieved for what concerns quantifying steerability. We introduce a computable measure of steering for arbitrary bipartite Gaussian states of continuous variable systems. For two-mode Gaussian states, the measure reduces to a form of coherent information, which is proven never to exceed entanglement, and to reduce to it on pure states. We provide an operational connection between our measure and the key rate in one-sided device-independent quantum key distribution. We further prove that Peres' conjecture holds in its stronger form within the fully Gaussian regime: namely, steering bound entangled Gaussian states by Gaussian measurements is impossible.
254 citations
Book•
14 Oct 2015
TL;DR: This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices, and introduces the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states.
Abstract: This book provides the reader with the mathematical framework required to fully explore the potential of small quantum information processing devices. As decoherence will continue to limit their size, it is essential to master the conceptual tools which make such investigations possible. A strong emphasis is given to information measures that are essential for the study of devices of finite size, including Rnyi entropies and smooth entropies. The presentation is self-contained and includes rigorous and concise proofs of the most important properties of these measures. The first chapters will introduce the formalism of quantum mechanics, with particular emphasis on norms and metrics for quantum states. This is necessary to explore quantum generalizations of Rnyi divergence and conditional entropy, information measures that lie at the core of information theory. The smooth entropy framework is discussed next and provides a natural means to lift many arguments from information theory to the quantum setting. Finally selected applications of the theory to statistics and cryptography are discussed. The book is aimed at graduate students in Physics and Information Theory. Mathematical fluency is necessary, but no prior knowledge of quantum theory is required.
254 citations
TL;DR: It is shown that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one and harnessing non- Markovianity may improve the efficiency of quantum information processing and communication.
Abstract: Quantum technologies rely on the ability to coherently transfer information encoded in quantum states along quantum channels. Decoherence induced by the environment sets limits on the efficiency of any quantum-enhanced protocol. Generally, the longer a quantum channel is the worse its capacity is. We show that for non-Markovian quantum channels this is not always true: surprisingly the capacity of a longer channel can be greater than of a shorter one. We introduce a general theoretical framework linking non-Markovianity to the capacities of quantum channels and demonstrate how harnessing non-Markovianity may improve the efficiency of quantum information processing and communication.
245 citations
TL;DR: This review serves to strengthen the link between results in quantum state discrimination and quantum information applications, by showing the ways in which the fundamental results are exploited in applications and vice versa.
Abstract: Quantum state discrimination underlies various applications in quantum information processing tasks. It essentially describes the distinguishability of quantum systems in different states, and the general process of extracting classical information from quantum systems. It is also useful in quantum information applications, such as the characterization of mutual information in cryptographic protocols, or as a technique for deriving fundamental theorems on quantum foundations. It has deep connections to physical principles such as relativistic causality. Quantum state discrimination traces a long history of several decades, starting with the early attempts to formalize information processing of physical systems such as optical communication with photons. Nevertheless, in most cases, the problems of finding optimal strategies of quantum state discrimination remain unsolved, and related applications are valid in some limited cases only. The present review aims to provide an overview on quantum state discrimination, covering some recent progress, and addressing applications in some selected areas. This review serves to strengthen the link between results in quantum state discrimination and quantum information applications, by showing the ways in which the fundamental results are exploited in applications and vice versa.
192 citations
Posted Content•
TL;DR: In this paper, the authors introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics, and keep the writing in a self-consistent way, requiring minimum background in quantum information sciences.
Abstract: This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.
184 citations
TL;DR: This work rederive the proof of the c-theorem for d = 3 in terms of mutual information, and check the arguments with holographic entanglement entropy, a free scalar field, and an extensive mutual information model.
Abstract: Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription for the monotonous quantity in the c-theorem for d = 3. This is in principle computable using any regularization for the entropy, and in particular is a definition suitable for lattice models. We rederive the proof of the c-theorem for d = 3 in terms of mutual information, and check our arguments with holographic entanglement entropy, a free scalar field, and an extensive mutual information model.
175 citations
TL;DR: It is proved that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system.
Abstract: Quantum Darwinism posits that only specific information about a quantum system that is redundantly proliferated to many parts of its environment becomes accessible and objective, leading to the emergence of classical reality. However, it is not clear under what conditions this mechanism holds true. Here we prove that the emergence of classical features along the lines of quantum Darwinism is a general feature of any quantum dynamics: observers who acquire information indirectly through the environment have effective access at most to classical information about one and the same measurement of the quantum system. Our analysis does not rely on a strict conceptual splitting between a system-of-interest and its environment, and allows one to interpret any system as part of the environment of any other system. Finally, our approach leads to a full operational characterization of quantum discord in terms of local redistribution of correlations.
116 citations
TL;DR: It is shown that for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity, and that only a finite number of channel uses is always sufficient.
Abstract: Transmitting data reliably over noisy communication channels is one of the most important applications of information theory, and is well understood for channels modelled by classical physics. However, when quantum effects are involved, we do not know how to compute channel capacities. This is because the formula for the quantum capacity involves maximizing the coherent information over an unbounded number of channel uses. In fact, entanglement across channel uses can even increase the coherent information from zero to non-zero. Here we study the number of channel uses necessary to detect positive coherent information. In all previous known examples, two channel uses already sufficed. It might be that only a finite number of channel uses is always sufficient. We show that this is not the case: for any number of uses, there are channels for which the coherent information is zero, but which nonetheless have capacity
110 citations
TL;DR: It is shown that the conditional mutual information is an upper bound on the regularized relative entropy distance between the quantum state and its reconstructed version and it is also an upper Bound for the measured relative entropydistance of the state to its reconstructed versions.
Abstract: We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite reductions. Namely, we show that the conditional mutual information is an upper bound on the regularized relative entropy distance between the quantum state and its reconstructed version. It is also an upper bound for the measured relative entropy distance of the state to its reconstructed version. The main ingredient of the proof is the fact that the conditional mutual information is the optimal quantum communication rate in the task of state redistribution.
98 citations
TL;DR: In this article, a connection between non-Markovian memory effects and thermodynamical quantities such as work is established, and it is shown how memory effects can be interpreted as revivals of work that can be extracted from a quantum system.
Abstract: We establish a connection between non-Markovian memory effects and thermodynamical quantities such as work. We show how memory effects can be interpreted as revivals of work that can be extracted from a quantum system. We prove that non-Markovianity may allow an increase in the extractable work even when the entropy of the system is increasing. Our results have important implications both in quantum thermodynamics and in quantum information theory. In the former context they pave the way to the understanding of concepts like work in a non-Markovian open system scenario. In the latter context they lead to interesting consequences for quantum state merging protocols in presence of noise.
73 citations
TL;DR: An alternative representation of quantum Fisher information for unitary parametrization processes, which can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative is discussed.
Abstract: Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. In this representation, all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator . Utilizing this representation, quantum Fisher information is only determined by and the initial state. Furthermore, can be expressed in an expanded form. The highlights of this form is that it can bring great convenience during the calculation for the Hamiltonians owning recursive commutations with their partial derivative. We apply this representation in a collective spin system and show the specific expression of . For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Moreover, for an exponential form initial state, an analytical expression of quantum Fisher information by operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation.
TL;DR: This work considers a prepare-and-measure scenario with classical or quantum communication, and develops two different methods for placing lower bounds on the communication entropy, given observable data, based on the framework of causal inference networks.
Abstract: We show that the entropy of a message can be tested in a device-independent way. Specifically, we consider a prepare-and-measure scenario with classical or quantum communication, and develop two different methods for placing lower bounds on the communication entropy, given observable data. The first method is based on the framework of causal inference networks. The second technique, based on convex optimization, shows that quantum communication provides an advantage over classical communication, in the sense of requiring a lower entropy to reproduce given data. These ideas may serve as a basis for novel applications in device-independent quantum information processing.
Posted Content•
TL;DR: In this paper, the authors established a resource theory describing the DQC1 protocol and explored relations to the theory of coherence, entanglement and information processing for coherent control of quantum systems.
Abstract: Control at the interface between the classical and the quantum world is fundamental in quantum physics. In particular, how classical control is enhanced by coherence effects is an important question both from a theoretical as well as from a technological point of view. In this work, we establish a resource theory describing this setting and explore relations to the theory of coherence, entanglement and information processing. Specifically, for the coherent control of quantum systems the relevant resources of entanglement and coherence are found to be equivalent and closely related to a measure of discord. The results are then applied to the DQC1 protocol and the precision of the final measurement is expressed in terms of the available resources.
TL;DR: It is proved that the conditional mutual information I(A:C|B) of a tripartite quantum state ρABC can be bounded from below by its distance to the closest recovered state RB→BC(ρAB), where the C-part is reconstructed from the B-part only and the recovery map RB→ BC merely depends on ρBC.
Abstract: A central question in quantum information theory is to determine how well lost information can be reconstructed. Crucially, the corresponding recovery operation should perform well without knowing the information to be reconstructed. In this work, we show that the quantum conditional mutual information measures the performance of such recovery operations. More precisely, we prove that the conditional mutual information $I(A:C|B)$ of a tripartite quantum state $\rho_{ABC}$ can be bounded from below by its distance to the closest recovered state $\mathcal{R}_{B \to BC}(\rho_{AB})$, where the $C$-part is reconstructed from the $B$-part only and the recovery map $\mathcal{R}_{B \to BC}$ merely depends on $\rho_{BC}$. One particular application of this result implies the equivalence between two different approaches to define topological order in quantum systems.
TL;DR: The quantum version of the fundamental entropic data processing inequality is presented in this paper, which establishes a lower bound for the entropy that can be generated in the output channels of a scattering process, which involves a collection of independent input bosonic modes.
Abstract: The quantum version of a fundamental entropic data-processing inequality is presented. It establishes a lower bound for the entropy that can be generated in the output channels of a scattering process, which involves a collection of independent input bosonic modes (e.g., the modes of the electromagnetic field). The impact of this inequality in quantum information theory is potentially large and some relevant implications are considered in this work.
TL;DR: In this article, a new scheme of quantum information processing based on spin coherent states of two component Bose-Einstein condensates was proposed, which goes beyond the continuous variable regime such that the full space of the Bloch sphere is used.
TL;DR: A family of channels is constructed for which the private and coherent information can remain strictly superadditive for unbounded number of uses, thus demonstrating that the regularization is necessary.
Abstract: The quantum capacity of a quantum channel is always smaller than the capacity of the channel for private communication Both quantities are given by the infinite regularization of the coherent and the private information, respectively, which makes their evaluation very difficult Here, we construct a family of channels for which the private and coherent information can remain strictly superadditive for unbounded number of uses, thus demonstrating that the regularization is necessary We prove this by showing that the coherent information is strictly larger than the private information of a smaller number of uses of the channel This implies that even though the quantum capacity is upper bounded by the private capacity, the nonregularized quantities can be interleaved
TL;DR: A general framework for optimizing the average information entropy for driven quantum systems is constructed, using this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.
Abstract: The design of efficient quantum information processing will rely on optimal nonequilibrium transitions of driven quantum systems. Building on a recently developed geometric framework for computing optimal protocols for classical systems driven in finite time, we construct a general framework for optimizing the average information entropy for driven quantum systems. Geodesics on the parameter manifold endowed with a positive semidefinite metric correspond to protocols that minimize the average information entropy production in finite time. We use this framework to explicitly compute the optimal entropy production for a simple two-state quantum system coupled to a heat bath of bosonic oscillators, which has applications to quantum annealing.
TL;DR: A review is presented of the relation between information and entropy, focusing on two main issues: the similarity of the formal definitions of physical entropy and of information, according to statistical mechanics and information theory; and the possible subjectivity of entropy considered as missing information.
Abstract: A review is presented of the relation between information and entropy, focusing on two main issues: the similarity of the formal definitions of physical entropy, according to statistical mechanics, and of information, according to information theory; and the possible subjectivity of entropy considered as missing information. The paper updates the 1983 analysis of Shaw and Davis. The difference in the interpretations of information given respectively by Shannon and by Wiener, significant for the information sciences, receives particular consideration.
A nalysis of a range of material, from literary theory to thermodynamics, is used to draw out the issues. Emphasis is placed on recourse to the original sources, and on direct quotation, to attempt to overcome some of the misunderstandings and over‐simplifications which have occurred with these topics.
While it is strongly related to entropy, information is neither identical with it, nor its opposite. Information is related to order and pattern, but also to disor der and randomness. The relations between information and the ‘interesting complexity’, which embodies both pattern and randomness, are worthy of attention.
TL;DR: It is conjecture that the proposed Renyi conditional quantum mutual informations are monotone increasing in the Renyi parameter, and proof of this conjecture for some special cases is proved.
Abstract: Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the Renyi entropies is expected to enhance their scope in applications. We prescribe Renyi generalizations for any quantum information measure which consists of a linear combination of von Neumann entropies with coefficients chosen from the set {−1,0,1} . As examples, we describe Renyi generalizations of the conditional quantum mutual information, some quantum multipartite information measures, and the topological entanglement entropy. Among these, we discuss the various properties of the Renyi conditional quantum mutual information and sketch some potential applications. We conjecture that the proposed Renyi conditional quantum mutual informations are monotone increasing in the Renyi parameter, and we have proof of this conjecture for some special cases.
TL;DR: A pilot-aided feedforward data recovery scheme which enables reliable coherent detection using a "locally" generated LO and the variance of the phase noise introduced by the proposed scheme is measured to be 0.04, which is small enough to enable secure key distribution.
Abstract: Continuous-variable quantum key distribution (CV-QKD) protocols based on coherent detection have been studied extensively in both theory and experiment. In all the existing implementations of CV-QKD, both the quantum signal and the local oscillator (LO) are generated from the same laser and propagate through the insecure quantum channel. This arrangement may open security loopholes and also limit the potential applications of CV-QKD. In this paper, we propose and demonstrate a pilot-aided feedforward data recovery scheme which enables reliable coherent detection using a "locally" generated LO. Using two independent commercial laser sources and a spool of 25 km optical fiber, we construct a coherent communication system. The variance of the phase noise introduced by the proposed scheme is measured to be 0.04 (rad^2), which is small enough to enable secure key distribution. This technology also opens the door for other quantum communication protocols, such as the recently proposed measurement-device-independent (MDI) CV-QKD where independent light sources are employed by different users.
TL;DR: It is shown that Kaniadakis entropy reduces the mutual information, which is always smaller than its usual von Neumann counterpart, and the degree of entanglement is determined.
Abstract: A first use of Kaniadakis entropy in the context of quantum information is presented. First we show that (as all smooth and concave trace-form entropies) it exhibits some properties allowing it to be a possible candidate for a generalized quantum information theory. We then use it to determine the degree of entanglement. The influence of the parameter κ, that underpins Kaniadakis entropy, on the mutual information measure is then highlighted. It is shown that Kaniadakis entropy reduces the mutual information, which is always smaller than its usual von Neumann counterpart. Our results may contribute to the ongoing investigation involving generalized entropies in the context of quantum information.
TL;DR: A lower bound on the maximum number of qubits, Qn, e(N), which can be transmitted over n uses of a quantum channel N, for a given non-zero error threshold e is obtained.
Abstract: We obtain a lower bound on the maximum number of qubits, $Q^{n, \varepsilon}({\mathcal{N}})$, which can be transmitted over $n$ uses of a quantum channel $\mathcal{N}$, for a given non-zero error threshold $\varepsilon$. To obtain our result, we first derive a bound on the one-shot entanglement transmission capacity of the channel, and then compute its asymptotic expansion up to the second order. In our method to prove this achievability bound, the decoding map, used by the receiver on the output of the channel, is chosen to be the {\em{Petz recovery map}} (also known as the {\em{transpose channel}}). Our result, in particular, shows that this choice of the decoder can be used to establish the coherent information as an achievable rate for quantum information transmission. Applying our achievability bound to the 50-50 erasure channel (which has zero quantum capacity), we find that there is a sharp error threshold above which $Q^{n, \varepsilon}({\mathcal{N}})$ scales as $\sqrt{n}$.
TL;DR: In this paper, a quantum learning scheme for binary discrimination of coherent states of light was developed for the reading of information stored in a digital memory, where a coherent light source is used to illuminate a memory cell and retrieve its encoded bit by determining the quantum state of the reflected signal.
Abstract: We develop a quantum learning scheme for binary discrimination of coherent states of light. This is a problem of technological relevance for the reading of information stored in a digital memory. In our setting, a coherent light source is used to illuminate a memory cell and retrieve its encoded bit by determining the quantum state of the reflected signal. We consider a situation where the amplitude of the states produced by the source is not fully known, but instead this information is encoded in a large training set comprising many copies of the same coherent state. We show that an optimal global measurement, performed jointly over the signal and the training set, provides higher successful identification rates than any learning strategy based on first estimating the unknown amplitude by means of Gaussian measurements on the training set, followed by an adaptive discrimination procedure on the signal. By considering a simplified variant of the problem, we argue that this is the case even for non-Gaussian estimation measurements. Our results show that, even in absence of entanglement, collective quantum measurements yield an enhancement in the readout of classical information, which is particularly relevant in the operating regime of low-energy signals.
TL;DR: A notion of state spectrum is generalized, allowing for a majorization relation and a new family of generalized entropic measures in a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting.
Abstract: In this article, we discuss the formal structure of a generalized information theory based on the extension of the probability calculus of Kolmogorov to a (possibly) non-commutative setting. By studying this framework, we argue that quantum information can be considered as a particular case of a huge family of non-commutative extensions of its classical counterpart. In any conceivable information theory, the possibility of dealing with different kinds of information measures plays a key role. Here, we generalize a notion of state spectrum, allowing us to introduce a majorization relation and a new family of generalized entropic measures.
TL;DR: An explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit the quantum information over a noisy quantum channel and which can be used for secret key distillation as well as private channel coding is constructed.
Abstract: We construct an explicit quantum coding scheme which achieves a communication rate not less than the coherent information when used to transmit the quantum information over a noisy quantum channel. For Pauli and erasure channels, we also present efficient encoding and decoding algorithms for this communication scheme based on polar codes (essentially linear in the blocklength), but which do not require the sender and receiver to share any entanglement before the protocol begins. Due to the existence of degeneracies in the involved error-correcting codes, it is indeed possible that the rate of the scheme exceeds the coherent information. We provide a simple criterion which indicates such performance. Finally, we discuss how the scheme can be used for secret key distillation as well as private channel coding.
17 Feb 2015
TL;DR: This work provides an entropic derivation of Hamiltonian dynamics and using concepts from information geometry derive the standard quantum field theory in the Schrodinger representation on the quantum theory of scalar fields.
Abstract: Entropic Dynamics is an information-based framework that seeks to derive the laws of physics as an application of the methods of entropic inference. The dynamics is derived by maximizing an entropy subject to constraints that represent the physically relevant information that the motion is continuous and non-dissipative. Here we focus on the quantum theory of scalar fields. We provide an entropic derivation of Hamiltonian dynamics and using concepts from information geometry derive the standard quantum field theory in the Schrodinger representation.
TL;DR: In this article, the authors explore the possibility to securely store information on a memory for later retrieval using quantum reading, which exploits quantumentanglement to efficiently read data from a memory whereas classical strategies (e.g., based on coherent states or their mixtures) cannot retrieve any information.
Abstract: Besides achieving secure communication between two spatially-separated parties,another important issue in modern cryptography is related to secure communication intime, i.e., the possibility to confidentially store information on a memory for later retrieval.Here we explore this possibility in the setting of quantum reading, which exploits quantumentanglement to efficiently read data from a memory whereas classical strategies (e.g., basedon coherent states or their mixtures) cannot retrieve any information. From this point ofview, the technique of quantum reading can provide a new form of technological security fordata storage.
TL;DR: In this article, the authors studied the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state.
Abstract: We study the entropy increase of quantum systems evolving under primitive, doubly stochastic Markovian noise and thus converging to the maximally mixed state. This entropy increase can be quantified by a logarithmic-Sobolev constant of the Liouvillian generating the noise. We prove a universal lower bound on this constant that stays invariant under taking tensor-powers. Our methods involve a new comparison method to relate logarithmic-Sobolev constants of different Liouvillians and a technique to compute logarithmic-Sobolev inequalities of Liouvillians with eigenvectors forming a projective representation of a finite abelian group. Our bounds improve upon similar results established before and as an application we prove an upper bound on continuous-time quantum capacities. In the last part of this work we study entropy production estimates of discrete-time doubly-stochastic quantum channels by extending the framework of discrete-time logarithmic-Sobolev inequalities to the quantum case.
TL;DR: In this article, a recent approach to the foundations of quantum mechanics inspired by quantum information theory is presented, based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features.
Abstract: We review a recent approach to the foundations of quantum mechanics inspired by quantum information theory [1, 2]. The approach is based on a general framework, which allows one to address a large class of physical theories which share basic information-theoretic features. We first illustrate two very primitive features, expressed by the axioms of causality and purity-preservation, which are satisfied by both classical and quantum theory. We then discuss the axiom of purification, which expresses a strong version of the Conservation of Information and captures the core of a vast number of protocols in quantum information. Purification is a highly non-classical feature and leads directly to the emergence of entanglement at the purely conceptual level, without any reference to the superposition principle. Supplemented by a few additional requirements, satisfied by classical and quantum theory, it provides a complete axiomatic characterization of quantum theory for finite dimensional systems.