Finally, here is a modern, self-contained text on quantum information theory suitable for graduate-level courses. Developing the subject 'from the ground up' it covers classical results as well as ...major advances of the past decade. Beginning with an extensive overview of classical information theory suitable for the non-expert, the author then turns his attention to quantum mechanics for quantum information theory, and the important protocols of teleportation, super-dense coding and entanglement distribution. He develops all of the tools necessary for understanding important results in quantum information theory, including capacity theorems for classical, entanglement-assisted, private and quantum communication. The book also covers important recent developments such as superadditivity of private, coherent and Holevo information, and the superactivation of quantum capacity. This book will be warmly welcomed by the upcoming generation of quantum information theorists and the already established community of classical information theorists.
The sudden death of a young, apparently fit and healthy person is amongst the most challenging scenarios in clinical medicine. Sudden cardiac death (SCD) is a devastating and tragic outcome of a ...number of underlying cardiovascular diseases. While coronary artery disease and acute myocardial infarction are the most common causes of SCD in older populations, genetic (inherited) cardiac disorders comprise a substantial proportion of SCD cases aged 40 years and less. This includes the primary arrhythmogenic disorders such as long QT syndromes and inherited cardiomyopathies, namely hypertrophic cardiomyopathy. In up to 30% of young SCD, no cause of death is identified at postmortem, so-called autopsy-negative or sudden arrhythmic death syndrome (SADS). Management of families following SCD begins with a concerted effort to identify the cause of death in the decedent, based on either premorbid clinical details or the pathological findings at postmortem. Where no cause of death is identified, genetic testing of deoxyribonucleic acid extracted from postmortem blood (the molecular autopsy) may identify a cause of death in up to 30% of SADS cases. Irrespective of the genetic testing considerations, all families in which a sudden unexplained death has occurred require targeted and standardized clinical testing in an attempt to identify relatives who may be at-risk of having the same inherited heart disease and therefore also predisposed to an increased risk of SCD. Optimal care of SCD families therefore requires dedicated and appropriately trained staff in the setting of a specialized multidisciplinary cardiac genetic clinic.
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we ...develop a resource theory for magic quantum channels to characterize and quantify the quantum 'magic' or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d, it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.
Magic-state distillation (or nonstabilizer state manipulation) is a crucial component in the leading approaches to realizing scalable, fault-tolerant, and universal quantum computation. Related to ...nonstabilizer state manipulation is the resource theory of nonstabilizer states, for which one of the goals is to characterize and quantify nonstabilizerness of a quantum state. In this Letter, we introduce the family of thauma measures to quantify the amount of nonstabilizerness in a quantum state, and we exploit this family of measures to address several open questions in the resource theory of nonstabilizer states. As a first application, we establish the hypothesis testing thauma as an efficiently computable benchmark for the one-shot distillable nonstabilizerness, which in turn leads to a variety of bounds on the rate at which nonstabilizerness can be distilled, as well as on the overhead of magic-state distillation. We then prove that the max-thauma can be used as an efficiently computable tool in benchmarking the efficiency of magic-state distillation, and that it can outperform previous approaches based on mana. Finally, we use the min-thauma to bound a quantity known in the literature as the "regularized relative entropy of magic." As a consequence of this bound, we find that two classes of states with maximal mana, a previously established nonstabilizerness measure, cannot be interconverted in the asymptotic regime at a rate equal to one. This result resolves a basic question in the resource theory of nonstabilizer states and reveals a difference between the resource theory of nonstabilizer states and other resource theories such as entanglement and coherence.
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the existence of codes that are capacity-achieving for the task of sending classical data over a channel with classical inputs and ...quantum outputs. Although they demonstrated the existence of such codes, their proof does not provide an explicit construction of codes for this task. The aim of this paper is to fill this gap by constructing near-explicit "polar" codes that are capacity-achieving. The codes exploit the channel polarization phenomenon observed by Arikan for the case of classical channels. Channel polarization is an effect in which one can synthesize a set of channels, by "channel combining" and "channel splitting," in which a fraction of the synthesized channels are perfect for data transmission, while the other channels are completely useless for data transmission, with the good fraction equal to the capacity of the channel. The channel polarization effect then leads to a simple scheme for data transmission: send the information bits through the perfect channels and "frozen" bits through the useless ones. The main technical contributions of this paper are threefold. First, we leverage several known results from the quantum information literature to demonstrate that the channel polarization effect occurs for channels with classical inputs and quantum outputs. We then construct linear polar codes based on this effect, and the encoding complexity is O ( N log N ), where N is the blocklength of the code. We also demonstrate that a quantum successive cancellation decoder works well, in the sense that the word error rate decays exponentially with the blocklength of the code. For this last result, we exploit Sen's recent "noncommutative union bound" that holds for a sequence of projectors applied to a quantum state.
There are few areas in cardiology in which the impact of genetics and genetic testing on clinical management has been as great as in cardiac channelopathies, arrhythmic disorders of genetic origin ...related to the ionic control of the cardiac action potential. Among the growing number of diseases identified as channelopathies, 3 are sufficiently prevalent to represent significant clinical and societal problems and to warrant adequate understanding by practicing cardiologists: long QT syndrome, catecholaminergic polymorphic ventricular tachycardia, and Brugada syndrome. This review will focus selectively on the impact of genetic discoveries on clinical management of these 3 diseases. For each disorder, we will discuss to what extent genetic knowledge and clinical genetic test results modify the way cardiologists should approach and manage affected patients. We will also address the optimal use of genetic testing, including its potential limitations and the potential medico-legal implications when such testing is not performed. We will highlight how important it is to understand the ways that genotype can affect clinical manifestations, risk stratification, and responses to the therapy. We will also illustrate the close bridge between molecular biology and clinical medicine, and will emphasize that consideration of the genetic basis for these heritable arrhythmia syndromes and the proper use and interpretation of clinical genetic testing should remain the standard of care.
In this paper, we introduce intrinsic non-locality and quantum intrinsic non-locality as quantifiers for Bell non-locality, and we prove that they satisfy certain desirable properties such as ...faithfulness, convexity, and monotonicity under local operations and shared randomness. We then prove that intrinsic non-locality is an upper bound on the secret-key-agreement capacity of any device-independent protocol conducted using a device characterized by a correlation p, while quantum intrinsic non-locality is an upper bound on the same capacity for a correlation arising from an underlying quantum model. We also prove that intrinsic steerability is faithful, and it is an upper bound on the secret-key-agreement capacity of any one-sided-device-independent protocol conducted using a device characterized by an assemblage ˆ . Finally, we prove that quantum intrinsic non-locality is bounded from above by intrinsic steerability.
Congenital long QT syndrome (LQTS) is characterised by heart rate corrected QT interval prolongation and life-threatening arrhythmias, leading to syncope and sudden death. Variations in genes ...encoding for cardiac ion channels, accessory ion channel subunits or proteins modulating the function of the ion channel have been identified as disease-causing mutations in up to 75% of all LQTS cases. Based on the underlying genetic defect, LQTS has been subdivided into different subtypes. Growing insights into the genetic background and pathophysiology of LQTS has led to the identification of genotype-phenotype relationships for the most common genetic subtypes, the recognition of genetic and non-genetic modifiers of phenotype, optimisation of risk stratification algorithms and the discovery of gene-specific therapies in LQTS. Nevertheless, despite these great advancements in the LQTS field, large gaps in knowledge still exist. For example, up to 25% of LQTS cases still remain genotype elusive, which hampers proper identification of family members at risk, and it is still largely unknown what determines the large variability in disease severity, where even within one family an identical mutation causes malignant arrhythmias in some carriers, while in other carriers, the disease is clinically silent. In this review, we summarise the current evidence available on the diagnosis, clinical management and therapeutic strategies in LQTS. We also discuss new scientific developments and areas of research, which are expected to increase our understanding of the complex genetic architecture in genotype-negative patients, lead to improved risk stratification in asymptomatic mutation carriers and more targeted (gene-specific and even mutation-specific) therapies.
The data processing inequality states that the quantum relative entropy between two states
ρ
and
σ
can never increase by applying the same quantum channel
N
to both states. This inequality can be ...strengthened with a remainder term in the form of a distance between
ρ
and the closest recovered state
(
R
∘
N
)
(
ρ
)
, where
R
is a recovery map with the property that
σ
=
(
R
∘
N
)
(
σ
)
. We show the existence of an
explicit
recovery map that is
universal
in the sense that it depends only on
σ
and the quantum channel
N
to be reversed. This result gives an alternate, information-theoretic characterization of the conditions for approximate quantum error correction.
Bipartite quantum interactions have applications in a number of different areas of quantum physics, reaching from fundamental areas such as quantum thermodynamics and the theory of quantum ...measurements to other applications such as quantum computers, quantum key distribution, and other information processing protocols. A particular aspect of the study of bipartite interactions is concerned with the entanglement that can be created from such interactions. In this Letter, we present our work on two basic building blocks of bipartite quantum protocols, namely, the generation of maximally entangled states and secret key via bipartite quantum interactions. In particular, we provide a nontrivial, efficiently computable upper bound on the positive-partial-transpose-assisted quantum capacity of a bipartite quantum interaction. In addition, we provide an upper bound on the secret-key-agreement capacity of a bipartite quantum interaction assisted by local operations and classical communication. As an application, we introduce a cryptographic protocol for the readout of a digital memory device that is secure against a passive eavesdropper.
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