Two quantum analogues of Fisher information from a large deviation viewpoint of quantum estimation

We discuss two quantum analogues of Fisher information, symmetric logarithmic derivative (SLD) Fisher information and Kubo-Mori-Bogoljubov (KMB) Fisher information from a large deviation viewpoint of quantum estimation and prove that the former gives the true bound and the latter gives the bound of consistent superefficient estimators. In another comparison, it is shown that the difference between them is characterized by the change of the order of limits.Comment: LaTeX with iopart.cls, iopart12.clo, iopams.st

Spin-3/2 Fermions in Twistor Formalism

Consistency conditions for the local existence of massless spin 3/2 fields has been explored that the field equations for massless helicity 3/2 are consistent iff the space-time is Ricci-flat and that in Minkowski space-time the space of conserved charges for the fields is its twistor space itself. After considering the twistorial methods to study such massless helicity 3/2 fields, we derive in flat space-time that the charges of spin-3/2 fields defined topologically by the first Chern number of their spin-lowered self-dual Maxwell fields, are given by their twistor space, and in curved space-time that the (anti-)self-duality of the space-time is the necessary condition. Since in N=1 supergravity torsions are the essential ingredients, we generalize our space-time to that with torsion (Einstein-Cartan theory) and have investigated the consistency of existence of spin 3/2 fields in it. A simple solution is found that the space-time has to be conformally (anti-)self-dual, left-(or right-)torsion-free. The integrability condition on $\alpha$-surface shows that the (anti-)self-dual Weyl spinor can be described only by the covariant derivative of the right-(left-)handed-torsion.Comment: 13 pages, Latex2e. The derivations and the conclusions are improve

General Scheme for Perfect Quantum Network Coding with Free Classical Communication

This paper considers the problem of efficiently transmitting quantum states through a network. It has been known for some time that without additional assumptions it is impossible to achieve this task perfectly in general -- indeed, it is impossible even for the simple butterfly network. As additional resource we allow free classical communication between any pair of network nodes. It is shown that perfect quantum network coding is achievable in this model whenever classical network coding is possible over the same network when replacing all quantum capacities by classical capacities. More precisely, it is proved that perfect quantum network coding using free classical communication is possible over a network with $k$ source-target pairs if there exists a classical linear (or even vector linear) coding scheme over a finite ring. Our proof is constructive in that we give explicit quantum coding operations for each network node. This paper also gives an upper bound on the number of classical communication required in terms of $k$, the maximal fan-in of any network node, and the size of the network.Comment: 12 pages, 2 figures, generalizes some of the results in arXiv:0902.1299 to the k-pair problem and codes over rings. Appeared in the Proceedings of the 36th International Colloquium on Automata, Languages and Programming (ICALP'09), LNCS 5555, pp. 622-633, 200

Exponents of quantum fixed-length pure state source coding

We derive the optimal exponent of the error probability of the quantum fixed-length pure state source coding in both cases of blind coding and visible coding. The optimal exponent is universally attained by Jozsa et al. (PRL, 81, 1714 (1998))'s universal code. In the direct part, a group representation theoretical type method is essential. In the converse part, Nielsen and Kempe (PRL, 86, 5184 (2001))'s lemma is essential.Comment: LaTeX2e and revetx4 with aps,twocolumn,superscriptaddress,showpacs,pra,amssymb,amsmath. The previous version has a mistak

CIRCULAR DICHROISM OF LIGHT-HARVESTING COMPLEXES FROM PURPLE PHOTOSYNTHETIC BACTERIA

The CD spectra of a range of antenna complexes from several different species of purple photosynthetic bacteria were recorded in the wavelength range of 190 to 930 nm. Analysis of the far UV CD (190 to 250 nm) showed that in each case except for the B800-850 from Chr. vinosum the secondary structure of the light-harvesting complexes contains a large amount of α-helix (50%) and very little 0-pleated sheet. This confirms the predictions of the group of Zuber of a high a-helical content based upon consideration of the primary structures of several antenna apoproteins. The CD spectra from the carotenoids and the bacteriochlorophylls show considerable variations depending upon the type of antenna complex. The different amplitude ratios in the CD spectrum for the bacteriochlorophyll Qy, Qx and Soret bands indicate not only different degrees of exciton coupling, but also a strong and variable hyperchromism (Scherz and Parson, 1984a, b)

Universal approximation of multi-copy states and universal quantum lossless data compression

We have proven that there exists a quantum state approximating any multi-copy state universally when we measure the error by means of the normalized relative entropy. While the qubit case was proven by Krattenthaler and Slater (IEEE Trans. IT, 46, 801-819 (2000); quant-ph/9612043), the general case has been open for more than ten years. For a deeper analysis, we have solved the mini-max problem concerning `approximation error' up to the second order. Furthermore, we have applied this result to quantum lossless data compression, and have constructed a universal quantum lossless data compression

Quantum hypothesis testing with group symmetry

The asymptotic discrimination problem of two quantum states is studied in the setting where measurements are required to be invariant under some symmetry group of the system. We consider various asymptotic error exponents in connection with the problems of the Chernoff bound, the Hoeffding bound and Stein's lemma, and derive bounds on these quantities in terms of their corresponding statistical distance measures. A special emphasis is put on the comparison of the performances of group-invariant and unrestricted measurements.Comment: 33 page

Box Graphs and Singular Fibers

We determine the higher codimension fibers of elliptically fibered Calabi-Yau fourfolds with section by studying the three-dimensional N=2 supersymmetric gauge theory with matter which describes the low energy effective theory of M-theory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as `flopping' of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi-)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic Calabi-Yau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, non-Kodaira, fiber types for E_6, E_7 and E_8.Comment: 107 pages, 44 figures, v2: added case of E7 monodromy-reduced fiber

Universal entanglement concentration

We propose a new protocol of \textit{universal} entanglement concentration, which converts many copies of an \textit{unknown} pure state to an \textit{% exact} maximally entangled state. The yield of the protocol, which is outputted as a classical information, is probabilistic, and achives the entropy rate with high probability, just as non-universal entanglement concentration protocols do. Our protocol is optimal among all similar protocols in terms of wide varieties of measures either up to higher orders or non-asymptotically, depending on the choice of the measure. The key of the proof of optimality is the following fact, which is a consequence of the symmetry-based construction of the protocol: For any invariant measures, optimal protocols are found out in modifications of the protocol only in its classical output, or the claim on the product. We also observe that the classical part of the output of the protocol gives a natural estimate of the entropy of entanglement, and prove that that estimate achieves the better asymptotic performance than any other (potentially global) measurements.Comment: Revised a lot, especially proofs, though no change in theorems, lemmas itself. Very long, but essential part is from Sec.I to Sec IV-C. Some of the appendces are almost independent of the main bod