On quantum non-signalling boxes

A classical non-signalling (or causal) box is an operation on classical bipartite input with classical bipartite output such that no signal can be sent from a party to the other through the use of the box. The quantum counterpart of such boxes, i.e. completely positive trace-preserving maps on bipartite states, though studied in literature, have been investigated less intensively than classical boxes. We present here some results and remarks about such maps. In particular, we analyze: the relations among properties as causality, non-locality and entanglement; the connection between causal and entanglement breaking maps; the characterization of causal maps in terms of the classification of states with fixed reductions. We also provide new proofs of the fact that every non-product unitary transformation is not causal, as well as for the equivalence of the so-called semicausality and semilocalizability properties.Comment: 18 pages, 7 figures, revtex

A truncated lipoglycan from mycobacteria with altered immunological properties

Maintenance of cell-wall integrity in Mycobacterium tuberculosis is essential and is the target of several antitubercular drugs. For example, ethambutol targets arabinogalactan and lipoarabinomannan (LAM) biosynthesis through the inhibition of several arabinofuranosyltransferases. Apart from their role in cell-wall integrity, mycobacterial LAMs also exhibit important immunomodulatory activities. Here we report the isolation and detailed structural characterization of a unique LAM molecule derived from Mycobacterium smegmatis deficient in the arabinofuranosyltransferase AftC (AftC-LAM). This mutant LAM expresses a severely truncated arabinan domain completely devoid of 3,5-Araf–branching residues, revealing an intrinsic involvement of AftC in the biosynthesis of LAM. Furthermore, we found that ethambutol efficiently inhibits biosynthesis of the AftC-LAM arabinan core, unambiguously demonstrating the involvement of the arabinofuranosyltransferase EmbC in early stages of LAM-arabinan biosynthesis. Finally, we demonstrate that AftC-LAM exhibits an enhanced proinflammatory activity, which is due to its ability to activate Toll-like receptor 2 (TLR2). Overall, our efforts further describe the mechanism of action of an important antitubercular drug, ethambutol, and demonstrate a role for specific arabinofuranosyltransferases in LAM biosynthesis. In addition, the availability of sufficient amounts of chemically defined wild-type and isogenic truncated LAMs paves the way for further investigations of the structure–function relationship of TLR2 activation by mycobacterial lipoglycans

Semicausal operations are semilocalizable

We prove a conjecture by DiVincenzo, which in the terminology of Preskill et al. [quant-ph/0102043] states that ``semicausal operations are semilocalizable''. That is, we show that any operation on the combined system of Alice and Bob, which does not allow Bob to send messages to Alice, can be represented as an operation by Alice, transmitting a quantum particle to Bob, and a local operation by Bob. The proof is based on the uniqueness of the Stinespring representation for a completely positive map. We sketch some of the problems in transferring these concepts to the context of relativistic quantum field theory.Comment: 4 pages, 1 figure, revte

Identification and structural characterisation of a partially arabinosylated lipoarabinomannan variant isolated from a Corynebacterium glutamicum ubiAmutant

Arabinan polysaccharide side-chains are present in both Mycobacterium tuberculosis and Corynebacterium glutamicum in the heteropolysaccharide arabinogalactan (AG), and in M. tuberculosis in the lipoglycan, lipoarabinomannan (LAM). Herein, we show by quantitative sugar and glycosyl linkage analysis that C. glutamicum possesses a much smaller LAM version, Cg-LAM, characterised by single t-Araf residues linked to th

Biosynthesis of mycobacterial arabinogalactan: identification of a novel (13)arabinofuranosyltransferase

The cell wall mycolyl-arabinogalactan-peptidoglycan complex is essential in mycobacterial species, such as Mycobacterium tuberculosis and is the target of several anti-tubercular drugs. For instance, ethambutol targets arabinogalactan biosynthesis through inhibition of the arabinofuranosyltransferases Mt-EmbA and Mt-EmbB. A bioinformatics approach identified putative integral membrane proteins, MSMEG2785 in Mycobacterium smegmatis, Rv2673 in Mycobacterium tuberculosis and NCgl1822 in Corynebacterium glutamicum, with 10 predicted transmembrane domains and a glycosyltransferase motif (DDX), features that are common to the GT-C superfamily of glycosyltransferases. Deletion of M. smegmatis MSMEG2785 resulted in altered growth and glycosyl linkage analysis revealed the absence of AG (13)-linked arabinofuranosyl (Araf) residues. Complementation of the M. smegmatis deletion mutant was fully restored to a wild type phenotype by MSMEG2785 and Rv2673, and as a result, we have now termed this previously uncharacterized open reading frame, arabinofuranosyltransferase C (aftC). Enzyme assays using the sugar donor -D-arabinofuranosyl-1-monophosphoryldecaprenol (DPA) and a newly synthesized linear (15)-linked Ara5 neoglycolipid acceptor together with chemical identification of products formed, clearly identified AftC as a branching (13) arabinofuranosyltransferase. This newly discovered glycosyltransferase sheds further light on the complexities of Mycobacterium cell wall biosynthesis, such as in M. tuberculosis and related species and represents a potential new drug target

Transforming quantum operations: quantum supermaps

We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.Comment: 6 pages, 1 figure, published versio

Classification of mixed three-qubit states

We introduce a classification of mixed three-qubit states, in which we define the classes of separable, biseparable, W- and GHZ-states. These classes are successively embedded into each other. We show that contrary to pure W-type states, the mixed W-class is not of measure zero. We construct witness operators that detect the class of a mixed state. We discuss the conjecture that all entangled states with positive partial transpose (PPTES) belong to the W-class. Finally, we present a new family of PPTES "edge" states with maximal ranks.Comment: 4 pages, 1 figur

Canonical Decompositions of n-qubit Quantum Computations and Concurrence

The two-qubit canonical decomposition SU(4) = [SU(2) \otimes SU(2)] Delta [SU(2) \otimes SU(2)] writes any two-qubit quantum computation as a composition of a local unitary, a relative phasing of Bell states, and a second local unitary. Using Lie theory, we generalize this to an n-qubit decomposition, the concurrence canonical decomposition (C.C.D.) SU(2^n)=KAK. The group K fixes a bilinear form related to the concurrence, and in particular any computation in K preserves the tangle ||^2 for n even. Thus, the C.C.D. shows that any n-qubit quantum computation is a composition of a computation preserving this n-tangle, a computation in A which applies relative phases to a set of GHZ states, and a second computation which preserves it. As an application, we study the extent to which a large, random unitary may change concurrence. The result states that for a randomly chosen a in A within SU(2^{2p}), the probability that a carries a state of tangle 0 to a state of maximum tangle approaches 1 as the even number of qubits approaches infinity. Any v=k_1 a k_2 for such an a \in A has the same property. Finally, although ||^2 vanishes identically when the number of qubits is odd, we show that a more complicated C.C.D. still exists in which K is a symplectic group.Comment: v2 corrects odd qubit CCD misstatements, reference chapter for KAK v3 notation change to coincide with sequel, typos. 20 pages, 0 figure

A reversible theory of entanglement and its relation to the second law

We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. As announced in [Brandao and Plenio, Nature Physics 4, 8 (2008)], and in stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a regularized and smoothed version of the logarithmic robustness of entanglement. Here we give a rigorous proof of this result, which is fundamentally based on a certain recent extension of quantum Stein's Lemma proved in [Brandao and Plenio, Commun. Math. 295, 791 (2010)], giving the best measurement strategy for discriminating several copies of an entangled state from an arbitrary sequence of non-entangled states, with an optimal distinguishability rate equal to the regularized relative entropy of entanglement. We moreover analyse the connection of our approach to axiomatic formulations of the second law of thermodynamics.Comment: 21 pages. revised versio

Faithful Squashed Entanglement

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, strictly positive if and only if the state is entangled. We derive the bound on squashed entanglement from a bound on quantum conditional mutual information, which is used to define squashed entanglement and corresponds to the amount by which strong subadditivity of von Neumann entropy fails to be saturated. Our result therefore sheds light on the structure of states that almost satisfy strong subadditivity with equality. The proof is based on two recent results from quantum information theory: the operational interpretation of the quantum mutual information as the optimal rate for state redistribution and the interpretation of the regularised relative entropy of entanglement as an error exponent in hypothesis testing. The distance to the set of separable states is measured by the one-way LOCC norm, an operationally-motivated norm giving the optimal probability of distinguishing two bipartite quantum states, each shared by two parties, using any protocol formed by local quantum operations and one-directional classical communication between the parties. A similar result for the Frobenius or Euclidean norm follows immediately. The result has two applications in complexity theory. The first is a quasipolynomial-time algorithm solving the weak membership problem for the set of separable states in one-way LOCC or Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show that multiple provers are not more powerful than a single prover when the verifier is restricted to one-way LOCC operations thereby providing a new characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published version, claims have been weakened from the LOCC norm to the one-way LOCC nor