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Search Results: 1 - 10 of 463487 matches for " A. Sasaki "
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Geometrical Conditions for CPTP Maps and their Application to a Quantum Repeater and a State-dependent Quantum Cloning Machine
A. Carlini,M. Sasaki
Physics , 2003, DOI: 10.1103/PhysRevA.68.042327
Abstract: We address the problem of finding optimal CPTP (completely positive, trace preserving) maps between a set of binary pure states and another set of binary generic mixed state in a two dimensional space. The necessary and sufficient conditions for the existence of such CPTP maps can be discussed within a simple geometrical picture. We exploit this analysis to show the existence of an optimal quantum repeater which is superior to the known repeating strategies for a set of coherent states sent through a lossy quantum channel. We also show that the geometrical formulation of the CPTP mapping conditions can be a simpler method to derive a state-dependent quantum (anti) cloning machine than the study so far based on the explicit solution of several constraints imposed by unitarity in an extended Hilbert space.
The Quantumness of a Set of Quantum States
Christopher A. Fuchs,Masahide Sasaki
Physics , 2003,
Abstract: This article is an introduction to quant-ph/0302092. We propose to quantify how "quantum" a set of quantum states is. The quantumness of a set is the worst-case difficulty of transmitting the states through a classical communication channel. Potential applications of this measure arise in quantum cryptography, where one might like to use an alphabet of states most sensitive to quantum eavesdropping, and in lab demonstrations of quantum teleportation, where it is necessary to check that entanglement has indeed been used.
Squeezing Quantum Information through a Classical Channel: Measuring the "Quantumness" of a Set of Quantum States
Christopher A. Fuchs,Masahide Sasaki
Physics , 2003,
Abstract: In this paper we propose a general method to quantify how "quantum" a set of quantum states is. The idea is to gauge the quantumness of the set by the worst-case difficulty of transmitting the states through a purely classical communication channel. Potential applications of this notion arise in quantum cryptography, where one might like to use an alphabet of states that promises to be the most sensitive to quantum eavesdropping, and in laboratory demonstrations of quantum teleportation, where it is necessary to check that quantum entanglement has actually been used in the protocol.
Calogero-Moser Models III: Elliptic Potentials and Twisting
A. J. Bordner,R. Sasaki
Physics , 1998, DOI: 10.1143/PTP.101.799
Abstract: Universal Lax pairs of the root type with spectral parameter and independent coupling constants for twisted non-simply laced Calogero-Moser models are constructed. Together with the Lax pairs for the simply laced models and untwisted non-simply laced models presented in two previous papers, this completes the derivation of universal Lax pairs for all of the Calogero-Moser models based on root systems. As for the twisted models based on B_n, C_n and BC_nroot systems, a new type of potential term with independent coupling constants can be added without destroying integrability. They are called extended twisted models. All of the Lax pairs for the twisted models presented here are new, except for the one for the F_4 model based on the short roots. The Lax pairs for the twisted G_2 model have some novel features. Derivation of various functions, twisted and untwisted, appearing in the Lax pairs for elliptic potentials with the spectral parameter is provided. The origin of the spectral parameter is also naturally explained. The Lax pairs with spectral parameter, twisted and untwisted, for the hyperbolic, the trigonometric and the rational potential models are obtained as degenerate limits of those for the elliptic potential models.
Proposal on Tunneling Effect between Quantum Hall States  [PDF]
Shosuke Sasaki
Journal of Modern Physics (JMP) , 2013, DOI: 10.4236/jmp.2013.49A001
Abstract:

In the integer and fractional quantum Hall effects, the electric current flows through a thin layer under the strong magnetic field. The diagonal resistance becomes very small at integer and specific fractional filling factors where the electron scatterings are very few. Accordingly the coherent length is large and therefore a tunneling effect of electrons may be observed. We consider a new type of a quantum Hall device which has a narrow potential barrier in the thin layer. Then the electrons flow with tunneling effect through the potential barrier. When the oscillating magnetic field is applied in addition to the constant field, the voltage steps may appear in the curve of voltage V versus electric current I. If the voltage steps are found in the experiment, it is confirmed that the 2D electron system yields the same phenomenon as that of the ac-Josephson effect in a superconducting system. Furthermore the step V is related to the transfer charge Q as V = (hf)/Q where f is the frequency of the oscillating field and h is the Planck constant. Then the detection of the step V determines the transfer charge Q. The ratio Q/e (e is the elementary charge) clarifies the

Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5)*  [PDF]
Yoshikatsu Sasaki
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.48055
Abstract:

In this article, we study the string equation of type (2,5), which is derived from 2D gravity theory or the string theory. We consider the equation as a 4th order analogue of the first Painlevé equation, take the autonomous limit, and solve it concretely by use of the Weierstrass’ elliptic function.

Erratum to “Weierstrass’ Elliptic Function Solution to the Autonomous Limit of the String Equation of Type (2,5)” [Advances in Pure Mathematics 4 (2014), 494-497]  [PDF]
Yoshikatsu Sasaki
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.412077
Abstract: In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.
Degeneration of the Superintegrable System with Potentials Described by the Sixth Painlevé Transcendents  [PDF]
Yoshikatsu Sasaki
Journal of Applied Mathematics and Physics (JAMP) , 2014, DOI: 10.4236/jamp.2014.211113
Abstract:

This article concerns the quantum superintegrable system obtained by Tremblay and Winternitz, which allows the separation of variables in polar coordinates and possesses three conserved quantities with the potential described by the sixth Painlevé equation. The degeneration procedure from the sixth Painlvé equation to the fifth one yields another new superintegrable system; however, the Hermitian nature is broken.

Spin Polarization of Fractional Quantum Hall States with ν < 2  [PDF]
Shosuke Sasaki
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.66085
Abstract: The spin polarization of a fractional quantum Hall state shows very interesting properties. The curve of polarization versus magnetic field has wide plateaus. The fractional quantum Hall effect is caused by the Coulomb interaction because the 2D electron system without the Coulomb interaction yields no energy gap at the fractional filling factor. Therefore, the wide plateau in the polarization curve is also caused by the Coulomb interaction. When the magnetic field is weak, some electrons have up-spins and the others down-spins. Therein the spin-exchange transition occurs between two electrons with up and down spins via the Coulomb interaction. Then the charge distribution before the transition is the same as one after the transition. So these two states have the same classical Coulomb energy. Accordingly, the partial Hamiltonian composed of the spin exchange interaction should be treated exactly. We have succeeded in diagonalizing the spin exchange interaction for the first and second nearest electron pairs. The theoretical results reproduce the wide plateaus very well. If the interval modulations between Landau orbitals are taken into the Hamiltonian, the total energy has the Peierls instability. We can diagonalize the Hamiltonian with the interval modulation. The results reproduce wide plateaus and small shoulders which are in good agreement with the experimental data.
Relation between FQHE Plateau Width and Valley Energy  [PDF]
Shosuke Sasaki
Journal of Modern Physics (JMP) , 2015, DOI: 10.4236/jmp.2015.67100
Abstract: We have investigated the Fractional Quantum Hall Effect (FQHE) on the fundamental Hamiltonian with the Coulomb interactions between normal electrons without any quasi particle. The electron pairs placed in the Landau orbitals can transfer to many empty orbitals. The number of the quantum transitions decreases discontinuously when the filling factor v deviates from the specific fractional number of v0. The discontinuous decreasing produces the energy valley at the specific filling factors v0 = 2/3, 4/5, 3/5, 4/7, 3/7, 2/5, 1/3 and so on. The diagonal elements of the total Hamiltonian and the number of the quantum transitions give the total energy of the FQH states. The energy per electron has the discontinuous spectrum depending on the filling factor v. We obtain the function form of the energy per electron in the quantum Hall system. Then the theoretical Hall resistance curve is calculated near several filling factors. Therein the quantum Hall plateaus are derived from the energy valleys. The depths of the energy valleys are compared with the widths of the quantum Hall plateaus appearing in the experimental data of the Hall resistance. Our theoretical results are in good agreement with the experimental results.
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