scholarly journals Rigorous Derivation of the Phase Shift Formula for the Hilbert Space Scattering Operator of a Single Particle

1960 ◽  
Vol 1 (2) ◽  
pp. 139-148 ◽  
Author(s):  
T. A. Green ◽  
O. E. Lanford
Keyword(s):  
Hilbert Space ◽  
Phase Shift ◽  
Single Particle ◽  
Scattering Operator ◽  
Rigorous Derivation

Quantum secret sharing protocol based on four-dimensional three-particle entangled states

2016 ◽  
Vol 30 (02) ◽  
pp. 1550267 ◽  
Author(s):  
Yi Xiang ◽  
Zhi Wen Mo
Keyword(s):  
Hilbert Space ◽  
Secret Sharing ◽  
Single Particle ◽  
High Efficiency ◽  
Quantum Secret Sharing ◽  
Entangled States ◽  
Secret Key ◽  
Particle Measurements ◽  
Eavesdropping Attack ◽  
Dimensional Hilbert Space

In this paper, we proposed a three-party quantum secret sharing (QSS) scheme using four-dimensional three-particle entangled states. In this QSS scheme, each agent can obtain a shadow of the secret key by performing single-particle measurements. Compared with the existing QSS protocol, this scheme has high efficiency and can resist the eavesdropping attack and entangle-measuring attack, which using three-particle entangled states are based on four-dimensional Hilbert space.

scholarly journals A Guide to Rotations in Quantum Mechanics

1987 ◽  
Vol 40 (4) ◽  
pp. 465 ◽  
Author(s):  
Michael A Morrison ◽  
Gregory A Parker
Keyword(s):  
Hilbert Space ◽  
Quantum Mechanics ◽  
Spherical Harmonics ◽  
Single Particle ◽  
Careful Attention ◽  
Euclidean Three Space ◽  
Three Space

To lay a foundation for the study and use of rotation operators in graduate quantum mechanics and in research, a thorough discussion is presented of rotations in Euclidean three space (R3 ) and of their effect on kets in the Hilbert space of a single particle. The Wigner D-matrices are obtained and used to rotate spherical harmonics. An extensive ready-reference appendix of the properties of these matrices, expressed in a consistent notation, is provided. Careful attention is paid throughout to various conventions (e.g. active versus passive viewpoints) that are used in the literature.

SINGLE-PARTICLE RESONANCES IN Ca ISOTOPES

2010 ◽  
Vol 25 (09) ◽  
pp. 727-735 ◽  
Author(s):  
ZI-ZHEN ZHANG ◽  
HAI LIN ◽  
YIN-MEI MI
Keyword(s):  
Phase Shift ◽  
Single Particle ◽  
Mean Field ◽  
Coordinate Space ◽  
Shift Method ◽  
Relativistic Mean Field ◽  
Scattering States ◽  
Resonant States ◽  
Scattering Phase ◽  
Phase Shift Method

Single-particle resonant states in Ca isotopes are studied systematically by real stabilization method (RSM) in coordinate space within the framework of the self-consistent relativistic mean field (RMF) theory. Phase shifts are obtained by scattering phase shift method. The resonant parameters (the energies, widths) are extracted by fitting energy and phase shift. Wave functions of resonances are obtained by matching conditions of bound and scattering states. Taking 60 Ca as an example, results are compared with corresponding results obtained from the analytic continuation in the coupling constant approach and the scattering phase shift method. Satisfied agreements are found. The rules of resonant parameters changing in Ca isotopes are also analyzed.

scholarly journals Hamiltonian extensions in quantum metrology

2017 ◽  
Vol 4 (1) ◽  
Author(s):  
Julien Mathieu Elias Fraïsse ◽  
Daniel Braun
Keyword(s):  
Hilbert Space ◽  
Phase Shift ◽  
General Framework ◽  
Open Quantum Systems ◽  
Arbitrary Dimension ◽  
Quantum Fisher Information ◽  
Original System ◽  
Quantum Systems ◽  
Quantum Metrology ◽  
Shift Measurement

AbstractWe study very generally towhat extent the uncertainty with which a phase shift can be estimated in quantum metrology can be reduced by extending the Hamiltonian that generates the phase shift to an ancilla system with a Hilbert space of arbitrary dimension, and allowing arbitrary interactions between the original system and the ancilla. Such Hamiltonian extensions provide a general framework for open quantum systems, as well as for “non-linear metrology schemes” that have been investigated over the last few years. We prove that such Hamiltonian extensions cannot improve the sensitivity of the phase shift measurement when considering the quantum Fisher information optimized over input states.

Brueckner Self-Consistent Study of 16O and 40Ca Using Phase-Shift Determined Potentials

1973 ◽  
Vol 51 (2) ◽  
pp. 115-120 ◽  
Author(s):  
R. J. W. Hodgson ◽  
Tran Duc Hoang
Keyword(s):  
Binding Energy ◽  
Phase Shift ◽  
Harmonic Oscillator ◽  
Single Particle ◽  
Effective Interaction ◽  
Scattering Data ◽  
Matrix Elements ◽  
High Energies ◽  
Self Consistent

A self-consistent Brueckner calculation of the binding energy and single-particle energies of 16O and 40Ca is carried out employing an effective interaction which is determined directly from the two-body scattering data. The interaction is described by its harmonic-oscillator matrix elements. It is found that the results are quite sensitive to the form of the phase shift at high energies.

scholarly journals Universal quantum computing using single-particle discrete-time quantum walk

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shivani Singh ◽  
Prateek Chawla ◽  
Anupam Sarkar ◽  
C. M. Chandrashekar
Keyword(s):  
Hilbert Space ◽  
Discrete Time ◽  
Single Particle ◽  
Quantum Walk ◽  
Quantum Gates ◽  
Position Space ◽  
Single Qubit ◽  
Time Quantum ◽  
Universal Quantum ◽  
Qubit States

AbstractQuantum walk has been regarded as a primitive to universal quantum computation. In this paper, we demonstrate the realization of the universal set of quantum gates on two- and three-qubit systems by using the operations required to describe the single particle discrete-time quantum walk on a position space. The idea is to utilize the effective Hilbert space of the single qubit and the position space on which it evolves in order to realize multi-qubit states and universal set of quantum gates on them. Realization of many non-trivial gates and engineering arbitrary states is simpler in the proposed quantum walk model when compared to the circuit based model of computation. We will also discuss the scalability of the model and some propositions for using lesser number of qubits in realizing larger qubit systems.

scholarly journals Single Particle States Of The Mass-4 Nucle

1966 ◽  
Vol 19 (5) ◽  
pp. 705 ◽  
Keyword(s):  
Elastic Scattering ◽  
Phase Shift ◽  
Single Particle ◽  
P Wave

Recently, Tombrello (1965, 1966) has established that 4Li and 4H have a spectrum of broad P-wave resonances from phase shift analyses of the 3He(p, p) and 3H(n, n) elastic scattering reactions respectively. The reduced widths of these resonances are large

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