An entanglement measure for n-qubits

Recently, Coffman, Kundu, and Wootters introduced the residual entanglement for three qubits to quantify the three-qubit entanglement in Phys. Rev. A 61, 052306 (2000). In Phys. Rev. A 65, 032304 (2007), we defined the residual entanglement for $n$ qubits, whose values are between 0 and 1. In this paper, we want to show that the residual entanglement for $n$ qubits is a natural measure of entanglement by demonstrating the following properties. (1). It is SL-invariant, especially LU-invariant. (2). It is an entanglement monotone. (3). It is invariant under permutations of the qubits. (4). It vanishes or is multiplicative for product states.Comment: 16 pages, no figure

SLOCC invariant and semi-invariants for SLOCC classification of four-qubits

We show there are at least 28 distinct true SLOCC entanglement classes for four-qubits by means of SLOCC invariant and semi-invariants and derive the number of the degenerated SLOCC classes for n-qubits.Comment: 22 pages, no figures, 9 tables, submit the paper to a journa

A More General Quantum Searching Algorithm And the Precise Formula of the Amplitude and the Non-symmetric Effects of Different Rotating Angles

This paper presented two general quantum search algorithms. We derived the iterated formulas and the simpler approximate formulas and the precise formula for the amplitude in the desired state. A mathematical proof of Grover's algorithm being optimal among the algorithms with arbitrary phase rotations was given in this paper. This first reported the non-symmetric effects of different rotating angles, and gave the first-order approximate phase condition when rotating angles are different.Comment: 13 pages, misusing tex formatting commands in title, shorted the titles, corrected typos, added the justifications to the section

The Simple Criteria of SLOCC Equivalence Classes

We put forward an alternative approach to the SLOCC classification of entanglement states of three-qubit and four-qubit systems. By directly solving matrix equations, we obtain the relations satisfied by the amplitudes of states. The relations are readily tested since in them only addition, subtraction and multiplication occur.Comment: The original version was submitted to PRA in Feb. 2005, the paper No. is AA10020. 14 pages for the present version. No figure

An sTGC Prototype Readout System for ATLAS New-Small-Wheel Upgrade

This paper presents a readout system designed for testing the prototype of Small-Strip Thin Gap Chamber (sTGC), which is one of the main detector technologies used for ATLAS New-Small-Wheel Upgrade. This readout system aims at testing one full-size sTGC quadruplet with cosmic muon triggers

Fixed-point Quantum Search for Different Phase Shifts

Grover recently presented the fixed-point search algorithm. In this letter, we study the fixed-point search algorithm obtained by replacing equal phase shifts of $\pi /3$ by different phase shifts.Comment: 8 page