Quantum Analog-Digital Conversion

Many quantum algorithms, such as Harrow-Hassidim-Lloyd (HHL) algorithm, depend on oracles that efficiently encode classical data into a quantum state. The encoding of the data can be categorized into two types; analog-encoding where the data are stored as amplitudes of a state, and digital-encoding where they are stored as qubit-strings. The former has been utilized to process classical data in an exponentially large space of a quantum system, where as the latter is required to perform arithmetics on a quantum computer. Quantum algorithms like HHL achieve quantum speedups with a sophisticated use of these two encodings. In this work, we present algorithms that converts these two encodings to one another. While quantum digital-to-analog conversions have implicitly been used in existing quantum algorithms, we reformulate it and give a generalized protocol that works probabilistically. On the other hand, we propose an deterministic algorithm that performs a quantum analog-to-digital conversion. These algorithms can be utilized to realize high-level quantum algorithms such as a nonlinear transformation of amplitude of a quantum state. As an example, we construct a "quantum amplitude perceptron", a quantum version of neural network, and hence has a possible application in the area of quantum machine learning.Comment: 7 page

Effective squeezing enhancement via measurement-induced non-Gaussian operation and its application to dense coding scheme

We study the measurement-induced non-Gaussian operation on the single- and two-mode \textit{Gaussian} squeezed vacuum states with beam splitters and on-off type photon detectors, with which \textit{mixed non-Gaussian} states are generally obtained in the conditional process. It is known that the entanglement can be enhanced via this non-Gaussian operation on the two-mode squeezed vacuum state. We show that, in the range of practical squeezing parameters, the conditional outputs are still close to Gaussian states, but their second order variances of quantum fluctuations and correlations are effectively suppressed and enhanced, respectively. To investigate an operational meaning of these states, especially entangled states, we also evaluate the quantum dense coding scheme from the viewpoint of the mutual information, and we show that non-Gaussian entangled state can be advantageous compared with the original two-mode squeezed state.Comment: REVTeX4, 14 pages with 21 figure

Measurement-free topological protection using dissipative feedback

Protecting quantum information from decoherence due to environmental noise is vital for fault-tolerant quantum computation. To this end, standard quantum error correction employs parallel projective measurements of individual particles, which makes the system extremely complicated. Here we propose measurement-free topological protection in two dimension without any selective addressing of individual particles. We make use of engineered dissipative dynamics and feedback operations to reduce the entropy generated by decoherence in such a way that quantum information is topologically protected. We calculate an error threshold, below which quantum information is protected, without assuming selective addressing, projective measurements, nor instantaneous classical processing. All physical operations are local and translationally invariant, and no parallel projective measurement is required, which implies high scalability. Furthermore, since the engineered dissipative dynamics we utilized has been well studied in quantum simulation, the proposed scheme can be a promising route progressing from quantum simulation to fault-tolerant quantum information processing.Comment: 17pages, 6 figure

Electron Identification and Energy Measurement with Emulsion Cloud Chamber

AbstractCharged particles undergo the Multiple Coulomb Scattering (MCS) when passing through a material. Their momentum can be estimated from the distribution of the scattering angle directly. Angle of electrons (or positrons) largely changes because of the energy loss in bremsstrahlung, and they are distinguished from other charged particles by making use of its feature. Electron energy is generally measured by counting of electromagnetic shower (e.m. shower) tracks in Emulsion Cloud Chamber (ECC), so enough absorber material is needed to develop the shower. In the range from sub-GeV to a few GeV, electrons don’t develop noticeable showers. In order to estimate the energy of electrons in this range with a limited material, we established the new method which is based on the scattering angle considering the energy loss in bremsstrahlung. From the Monte Carlo simulation (MC) data, which is generated by electron beam (0.5GeV, 1GeV, 2GeV) exposure to ECC, we derived the correlation between energy and scattering angle in each emulsion layer. We fixed the function and some parameters which 1GeV MC sample would return 1GeV as the center value, and then applied to 0.5GeV and 2GeV sample and confirmed the energy resolution about 50% within two radiation length

Unambiguous discrimination among oracle operators

We address the problem of unambiguous discrimination among oracle operators. The general theory of unambiguous discrimination among unitary operators is extended with this application in mind. We prove that entanglement with an ancilla cannot assist any discrimination strategy for commuting unitary operators. We also obtain a simple, practical test for the unambiguous distinguishability of an arbitrary set of unitary operators on a given system. Using this result, we prove that the unambiguous distinguishability criterion is the same for both standard and minimal oracle operators. We then show that, except in certain trivial cases, unambiguous discrimination among all standard oracle operators corresponding to integer functions with fixed domain and range is impossible. However, we find that it is possible to unambiguously discriminate among the Grover oracle operators corresponding to an arbitrarily large unsorted database. The unambiguous distinguishability of standard oracle operators corresponding to totally indistinguishable functions, which possess a strong form of classical indistinguishability, is analysed. We prove that these operators are not unambiguously distinguishable for any finite set of totally indistinguishable functions on a Boolean domain and with arbitrary fixed range. Sets of such functions on a larger domain can have unambiguously distinguishable standard oracle operators and we provide a complete analysis of the simplest case, that of four functions. We also examine the possibility of unambiguous oracle operator discrimination with multiple parallel calls and investigate an intriguing unitary superoperator transformation between standard and entanglement-assisted minimal oracle operators.Comment: 35 pages. Final version. To appear in J. Phys. A: Math. & Theo

Spatially Inhomogeneous Superconducting State near Hc2H_{\rm c2} in UPd2_2Al3_3

We have performed $^{27}$Al-NMR measurements on single-crystalline UPd$_2$Al$_3$ with the field parallel to the $c$ axis to investigate the superconducting (SC) properties near the upper critical field of superconductivity $H_{\rm c2}$. The broadening of the NMR linewidth below 14~K indicates the appearance of the internal field at the Al site, which originates from the antiferromagnetically ordered moments of U 5$f$ electrons. In the SC state well below $\mu_0H_{\rm c2}$ = 3.4~T, the broadening of the NMR linewidth due to the SC diamagnetism and a decrease in the Knight shift are observed, which are well-understood by the framework of spin-singlet superconductivity. In contrast, the Knight shift does not change below $T_{\rm c}(H)$, and the NMR spectrum is broadened symmetrically in the SC state in the field range of 3~T $< \mu_0 H < \mu_0 H_{\rm c2}$. The unusual NMR spectrum near $H_{\rm c2}$ suggests that a spatially inhomogeneous SC state such as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state would be realized.Comment: 5 pages, 5 figure