A Resource Framework for Quantum Shannon Theory

Quantum Shannon theory is loosely defined as a collection of coding theorems, such as classical and quantum source compression, noisy channel coding theorems, entanglement distillation, etc., which characterize asymptotic properties of quantum and classical channels and states. In this paper we advocate a unified approach to an important class of problems in quantum Shannon theory, consisting of those that are bipartite, unidirectional and memoryless. We formalize two principles that have long been tacitly understood. First, we describe how the Church of the larger Hilbert space allows us to move flexibly between states, channels, ensembles and their purifications. Second, we introduce finite and asymptotic (quantum) information processing resources as the basic objects of quantum Shannon theory and recast the protocols used in direct coding theorems as inequalities between resources. We develop the rules of a resource calculus which allows us to manipulate and combine resource inequalities. This framework simplifies many coding theorem proofs and provides structural insights into the logical dependencies among coding theorems. We review the above-mentioned basic coding results and show how a subset of them can be unified into a family of related resource inequalities. Finally, we use this family to find optimal trade-off curves for all protocols involving one noisy quantum resource and two noiseless ones.Comment: 60 page

A family of quantum protocols

We introduce two dual, purely quantum protocols: for entanglement distillation assisted by quantum communication (``mother'' protocol) and for entanglement assisted quantum communication (``father'' protocol). We show how a large class of ``children'' protocols (including many previously known ones) can be derived from the two by direct application of teleportation or super-dense coding. Furthermore, the parent may be recovered from most of the children protocols by making them ``coherent''. We also summarize the various resource trade-offs these protocols give rise to.Comment: 5 pages, 1 figur

Property testing of unitary operators

In this paper, we systematically study property testing of unitary operators. We first introduce a distance measure that reflects the average difference between unitary operators. Then we show that, with respect to this distance measure, the orthogonal group, quantum juntas (i.e. unitary operators that only nontrivially act on a few qubits of the system) and Clifford group can be all efficiently tested. In fact, their testing algorithms have query complexities independent of the system's size and have only one-sided error. Then we give an algorithm that tests any finite subset of the unitary group, and demonstrate an application of this algorithm to the permutation group. This algorithm also has one-sided error and polynomial query complexity, but it is unknown whether it can be efficiently implemented in general

Gate fidelity fluctuations and quantum process invariants

We characterize the quantum gate fidelity in a state-independent manner by giving an explicit expression for its variance. The method we provide can be extended to calculate all higher order moments of the gate fidelity. Using these results we obtain a simple expression for the variance of a single qubit system and deduce the asymptotic behavior for large-dimensional quantum systems. Applications of these results to quantum chaos and randomized benchmarking are discussed.Comment: 13 pages, no figures, published versio

Efficient Discrete Approximations of Quantum Gates

Quantum compiling addresses the problem of approximating an arbitrary quantum gate with a string of gates drawn from a particular finite set. It has been shown that this is possible for almost all choices of base sets and furthermore that the number of gates required for precision epsilon is only polynomial in log 1/epsilon. Here we prove that using certain sets of base gates quantum compiling requires a string length that is linear in log 1/epsilon, a result which matches the lower bound from counting volume up to constant factor.Comment: 7 pages, no figures, v3 revised to correct major error in previous version

Symmetric coupling of four spin-1/2 systems

We address the non-binary coupling of identical angular momenta based upon the representation theory for the symmetric group. A correspondence is pointed out between the complete set of commuting operators and the reference-frame-free subsystems. We provide a detailed analysis of the coupling of three and four spin-1/2 systems and discuss a symmetric coupling of four spin-1/2 systems.Comment: 20 pages, no figure

Outcomes following biosimilar TNF inhibitors use for inflammatory-mediated immune disorders in pregnancy

Background: Biosimilar tumour necrosis factor inhibitors (TNFi) are increasingly used to treat inflammatory immune-mediated disorders as they cost less than the originator biologic drug. More women are therefore becoming pregnant on biosimilar TNFi. This is the first paper to explore the safety and efficacy of biosimilar therapies in pregnancy. Methods: A retrospective review of clinical data reviewed pregnancy outcomes and inflammatory disease activity in 18 pregnancies where the mother was using a biosimilar TNFi at conception. Results: Biosimilar therapy was not associated with congenital abnormalities, preterm birth or other adverse pregnancy outcomes. Stopping biosimilar TNFi in pregnancy was associated with childbirth at an earlier gestation, as well as a flare of inflammatory disease in pregnancy or post-partum. Conclusions: Women and clinicians should feel confident in using biosimilar TNFi in early pregnancy, and continuing them through pregnancy to prevent flares in late pregnancy or the early post-partum

How to hide a secret direction

We present a procedure to share a secret spatial direction in the absence of a common reference frame using a multipartite quantum state. The procedure guarantees that the parties can determine the direction if they perform joint measurements on the state, but fail to do so if they restrict themselves to local operations and classical communication (LOCC). We calculate the fidelity for joint measurements, give bounds on the fidelity achievable by LOCC, and prove that there is a non-vanishing gap between the two of them, even in the limit of infinitely many copies. The robustness of the procedure under particle loss is also studied. As a by-product we find bounds on the probability of discriminating by LOCC between the invariant subspaces of total angular momentum N/2 and N/2-1 in a system of N elementary spins.Comment: 4 pages, 1 figur

Ontology mapping for the laboratory analytics domain

The Pistoia Alliance Ontologies Mapping Project has applied the Ontology Matching algorithm, Paxo to the laboratory analytics domain. Nine ontologies relevant to laboratory analytics were selected. Among all possible pair combinations, thirteen of Paxo’s computed mapping sets were selected for evaluation through comparison with a silver standard alignment generated from the consensus votes of a panel of systems participating in the OAEI campaign