Pseudorandom Phase Ensemble and Nonlocal

Abstract

In this paper, we introduce a new concept of a pseudorandom phase ensemble to simulate a quantum ensemble. A pseudorandom sequence is inseparability and integral that are demonstrated only for a whole sequence, not for a single phase unit, which is similar to that of quantum ensembles and a quantum particle. Using the ensemble concept, we demonstrate non-locality properties for classical fields similar to quantum entanglement.

Optical analogy to quantum Fourier transform based on pseudorandom phase ensemble

“…In quantum Fourier transform, after the Hadamard gate and controlled-phase gate, we can obtain the final state |j = |j n−1 j n−2 • • • j 0 of quantum Fourier transform: In Ref. [5][6][7], a way to simulation of quantum states was introduced, which utilize the properties of pseudorandom sequence to modulate classical optical fields into different quantum states with different pseudorandom sequences. The formal product states for these fields can be a simulation to arbitrary quantum states in the pseudorandom phase ensemble model [7].…”

“…[5][6][7], a way to simulation of quantum states was introduced, which utilize the properties of pseudorandom sequence to modulate classical optical fields into different quantum states with different pseudorandom sequences. The formal product states for these fields can be a simulation to arbitrary quantum states in the pseudorandom phase ensemble model [7]. To further illustrate this method, the following is a brief introduction.…”

“…Ref. [7] further proposed the ensemble-averaged reduced states in ensemble model, which utilize the closure and balance property of pseudorandom phase sequence to remove some terms in the formal product states after ensemble averaging, whereby the required arbitrary quantum states can be obtained, including quantum entanglement states.…”

“…However, the result we obtain is with certainty but not with probability like the case in quantum Fourier transform. In pseudorandom phase ensemble, we utilize the characteristic of pseudorandom phase sequence to define the ensemble-averaged reduced state [7]. The balance property of pseudorandom phase sequences [5]: with the exception of λ (0) , any sequence of the set Ω satisfies…”

“…At the same time, Ref. [7] also introduced a new concept, pseudorandom phase ensemble, to simulate a quantum ensemble. However, it is necessary to implement similar quantum Fourier transform algorithm to implement some current quantum algorithms.…”