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

Group theoretical study of LOCC-detection of maximally entangled state using hypothesis testing

In the asymptotic setting, the optimal test for hypotheses testing of the maximally entangled state is derived under several locality conditions for measurements. The optimal test is obtained in several cases with the asymptotic framework as well as the finite-sample framework. In addition, the experimental scheme for the optimal test is presented

Adaptive experimental design for one-qubit state estimation with finite data based on a statistical update criterion

We consider 1-qubit mixed quantum state estimation by adaptively updating measurements according to previously obtained outcomes and measurement settings. Updates are determined by the average-variance-optimality (A-optimality) criterion, known in the classical theory of experimental design and applied here to quantum state estimation. In general, A-optimization is a nonlinear minimization problem; however, we find an analytic solution for 1-qubit state estimation using projective measurements, reducing computational effort. We compare numerically two adaptive and two nonadaptive schemes for finite data sets and show that the A-optimality criterion gives more precise estimates than standard quantum tomography.Comment: 15 pages, 7 figure

Density-matrix renormalization group study of pairing when electron-electron and electron-phonon interactions coexist: effect of the electronic band structure

Density-matrix renormalization group is used to study the pairing when both of electron-electron and electron-phonon interactions are strong in the Holstein-Hubbard model at half-filling in a region intermediate between the adiabatic (Migdal's) and antiadiabatic limits. We have found: (i) the pairing correlation obtained for a one-dimensional system is nearly degenerate with the CDW correlation in a region where the phonon-induced attraction is comparable with the electron-electron repulsion, but (ii) pairing becomes dominant when we destroy the electron-hole symmetry in a trestle lattice. This provides an instance in which pairing can arise, in a lattice-structure dependent manner, from coexisting electron-electron and electron-phonon interactions.Comment: 4 pages, 3 figures; to appear in Phys. Rev. Let

Asymptotic estimation theory for a finite dimensional pure state model

The optimization of measurement for n samples of pure sates are studied. The error of the optimal measurement for n samples is asymptotically compared with the one of the maximum likelihood estimators from n data given by the optimal measurement for one sample.Comment: LaTeX, 23 pages, Doctoral Thesi

Mineralogy of Y-981971 LL Chondrite and Brecciation Processes of the LL Parent Body

第3回極域科学シンポジウム/第35回南極隕石シンポジウム 11月30日（金） 国立国語研究所 2階講

Phase estimation via quantum interferometry for noisy detectors

The sensitivity in optical interferometry is strongly affected by losses during the signal propagation or at the detection stage. The optimal quantum states of the probing signals in the presence of loss were recently found. However, in many cases of practical interest, their associated accuracy is worse than the one obtainable without employing quantum resources (e.g. entanglement and squeezing) but neglecting the detector's loss. Here we detail an experiment that can reach the latter even in the presence of imperfect detectors: it employs a phase-sensitive amplification of the signals after the phase sensing, before the detection. We experimentally demonstrated the feasibility of a phase estimation experiment able to reach its optimal working regime. Since our method uses coherent states as input signals, it is a practical technique that can be used for high-sensitivity interferometry and, in contrast to the optimal strategies, does not require one to have an exact characterization of the loss beforehand.Comment: 4 pages + supplementary information (10 pages), 3 + 4 figure

Uncertainty Relation Revisited from Quantum Estimation Theory

By invoking quantum estimation theory we formulate bounds of errors in quantum measurement for arbitrary quantum states and observables in a finite-dimensional Hilbert space. We prove that the measurement errors of two observables satisfy Heisenberg's uncertainty relation, find the attainable bound, and provide a strategy to achieve it.Comment: manuscript including 4 pages and 2 figure

Single-component quasicrystalline nanocrystal superlattices through flexible polygon tiling rule

Quasicrystalline superlattices (QC-SLs) generated from single-component colloidal building blocks have been predicted by computer simulations but are challenging to reproduce experimentally. We discovered that 10-fold QC-SLs could self-organize from truncated tetrahedral quantum dots with anisotropic patchiness. Transmission electron microscopy and tomography measurements allow structural reconstruction of the QC-SL from the nanoscale packing to the atomic-scale orientation alignments. The unique QC order leads to a tiling concept, the “flexible polygon tiling rule,” that replicates the experimental observations. The keys for the single-component QC-SL formation were identified to be the anisotropic shape and patchiness of the building blocks and the assembly microscopic environment. Our discovery may spur the creation of various superstructures using anisotropic objects through an enthalpy-driven route