In a word, it has the phase sifted probability amplitude of -1/[N.

This gate does the operation that returns the probability amplitude in each state to the mean of the probability amplitude of all the qubits.

When a certain quantum register |b > is the state of |20 >, |b > is sifted by operation, and it has the probability amplitude of -1/8.

3] of a complex probability amplitude is related to random events in the cylinder space [R.

It is known that any non-vanishing variation of the phase action has a vanishing amplitude of the transitional probability and, on the contrary, that the vanishing variation corresponds to a non-vanishing probability amplitude [23-25].

We will based our derivation of the fine structure constant based on Feynman's physical interpretation of the electron's charge as the probability amplitude that an electron emits (or absorbs) a photon.

2], the square of the probability amplitude (in natural units of h = c = 1) and physically represents the electron's emission of a virtual photon (off-shell, [k.

Masses of the fundamental particles were derived in [3] based on the definitions that mass is the probability amplitude for a particle to change direction.

Yet, recent work shows that

probability amplitudes in quantum gauge field theories, such as those describing the Standard Model and its extensions, take surprisingly simple forms.

He discussed the existence and significance of

probability amplitudes.

In 1936, Birkhoff and von Neumann extended conventional quantum mechanics by using quaternions (in place of complex numbers) to represent the wave-functions and probability amplitudes.

If the probability amplitudes are assumed to be complexified quaternions, one cannot give a satisfactory probability interpretation.