The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory

The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel's entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channel

One-Shot Decoupling

If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. Decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production.Comment: v2: improved converse theorem, v3: published versio

One-Shot Decoupling

If a quantum system A, which is initially correlated to another system, E, undergoes an evolution separated from E, then the correlation to E generally decreases. Here, we study the conditions under which the correlation disappears (almost) completely, resulting in a decoupling of A from E. We give a criterion for decoupling in terms of two smooth entropies, one quantifying the amount of initial correlation between A and E, and the other characterizing the mapping that describes the evolution of A. The criterion applies to arbitrary such mappings in the general one-shot setting. Furthermore, the criterion is tight for mappings that satisfy certain natural conditions. One-shot decoupling has a number of applications both in physics and information theory, e.g., as a building block for quantum information processing protocols. As an example, we give a one-shot state merging protocol and show that it is essentially optimal in terms of its entanglement consumption/production

Catalytic Decoupling of Quantum Information

The decoupling technique is a fundamental tool in quantum information theory with applications ranging from thermodynamics to many-body physics and black hole radiation whereby a quantum system is decoupled from another one by discarding an appropriately chosen part of it. Here, we introduce catalytic decoupling, i.e., decoupling with the help of an independent system. Thereby, we remove a restriction on the standard decoupling notion and present a tight characterization in terms of the max-mutual information. The novel notion unifies various tasks and leads to a resource theory of decoupling

Decoupling with unitary approximate two-designs

Consider a bipartite system, of which one subsystem, A, undergoes a physical evolution separated from the other subsystem, R. One may ask under which conditions this evolution destroys all initial correlations between the subsystems A and R, i.e. decouples the subsystems. A quantitative answer to this question is provided by decoupling theorems, which have been developed recently in the area of quantum information theory. This paper builds on preceding work, which shows that decoupling is achieved if the evolution on A consists of a typical unitary, chosen with respect to the Haar measure, followed by a process that adds sufficient decoherence. Here, we prove a generalized decoupling theorem for the case where the unitary is chosen from an approximate two-design. A main implication of this result is that decoupling is physical, in the sense that it occurs already for short sequences of random two-body interactions, which can be modeled as efficient circuits. Our decoupling result is independent of the dimension of the R system, which shows that approximate 2-designs are appropriate for decoupling even if the dimension of this system is large.Comment: Published versio

The Quantum Reverse Shannon Theorem based on One-Shot Information Theory

The Quantum Reverse Shannon Theorem states that any quantum channel can be simulated by an unlimited amount of shared entanglement and an amount of classical communication equal to the channel's entanglement assisted classical capacity. In this paper, we provide a new proof of this theorem, which has previously been proved by Bennett, Devetak, Harrow, Shor, and Winter. Our proof has a clear structure being based on two recent information-theoretic results: one-shot Quantum State Merging and the Post-Selection Technique for quantum channels.Comment: 30 pages, 4 figures, published versio

The thermodynamic meaning of negative entropy

Landauer's erasure principle exposes an intrinsic relation between thermodynamics and information theory: the erasure of information stored in a system, S, requires an amount of work proportional to the entropy of that system. This entropy, H(S|O), depends on the information that a given observer, O, has about S, and the work necessary to erase a system may therefore vary for different observers. Here, we consider a general setting where the information held by the observer may be quantum-mechanical, and show that an amount of work proportional to H(S|O) is still sufficient to erase S. Since the entropy H(S|O) can now become negative, erasing a system can result in a net gain of work (and a corresponding cooling of the environment).Comment: Added clarification on non-cyclic erasure and reversible computation (Appendix E). For a new version of all technical proofs see the Supplementary Information of the journal version (free access

The Uncertainty Principle in the Presence of Quantum Memory

The uncertainty principle, originally formulated by Heisenberg, dramatically illustrates the difference between classical and quantum mechanics. The principle bounds the uncertainties about the outcomes of two incompatible measurements, such as position and momentum, on a particle. It implies that one cannot predict the outcomes for both possible choices of measurement to arbitrary precision, even if information about the preparation of the particle is available in a classical memory. However, if the particle is prepared entangled with a quantum memory, a device which is likely to soon be available, it is possible to predict the outcomes for both measurement choices precisely. In this work we strengthen the uncertainty principle to incorporate this case, providing a lower bound on the uncertainties which depends on the amount of entanglement between the particle and the quantum memory. We detail the application of our result to witnessing entanglement and to quantum key distribution.Comment: 5 pages plus 12 of supplementary information. Updated to match the journal versio

Long-term home ventilation of children in Italy: A national survey.

BACKGROUND: Improved technology, as well as professional and parental awareness, enable many ventilator-dependent children to live at home. However, the profile of this growing population, the quality and adequacy of home care, and patients' needs still require thorough assessment. OBJECTIVES: To define the characteristics of Italian children receiving long-term home mechanical ventilation (HMV) in Italy. METHODS: A detailed questionnaire was sent to 302 National Health Service hospitals potentially involved in the care of HVM in children (aged <17 years). Information was collected on patient characteristics, type of ventilation, and home respiratory care. RESULTS: A total of 362 HMV children was identified. The prevalence was 4.2 per 100,000 (95% CI: 3.8-4.6), median age was 8 years (interquartile range 4-14), median age at starting mechanical ventilation was 4 years (1-11), and 56% were male. The most frequent diagnostic categories were neuromuscular disorders (49%), lung and upper respiratory tract diseases (18%), hypoxic (ischemic) encephalopathy (13%), and abnormal ventilation control (12%). Medical professionals with nurses (for 62% of children) and physiotherapists (20%) participated in the patients' discharge from hospital, though parents were the primary care giver, and in 47% of cases, the sole care giver. Invasive ventilation was used in 41% and was significantly related to young age, southern regional residence, longer time spent under mechanical ventilation, neuromuscular disorders, or hypoxic (ischemic) encephalopathy. CONCLUSIONS: Care and technical assistance of long-term HMV children need assessment, planning, and resources. A wide variability in pattern of HMV was found throughout Italy. An Italian national ventilation program, as well as a national registry, could be useful in improving the care of these often critically ill children

Notulae to the Italian flora of algae, bryophytes, fungi and lichens: 11

In this contribution, new data concerning bryophytes, fungi, and lichens of the Italian flora are presented. It includes new records and confirmations for the bryophyte genera Aneura, Aulacomnium, Dumortiera, Fossombronia, Hennediella, Hygrohypnella, Pohlia, Porella, Riccardia, Tortella, and Tortula, the fungal genera Cortinarius, Mycena, Naucoria, Trichoglossum, and Tubaria and the lichen genera Agonimia, Blastenia, Chaenotheca, Cladonia, Endocarpon, Gyalecta, Lecanographa, Parmeliella, Porpidia, Stenhammarella, and Thelidium