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arXiv:1604.07652

Pseudorandom Phase Ensemble and Nonlocal

Jian Bo Fu

Published Apr 25, 2016• 0 citations
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Abstract

In this paper, we introduce a new conception of 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. By using the ensemble conception, we demonstrate non-locality properties for classical fields similar to quantum entanglement.

DOI
10.48550/arxiv.1604.07652

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In this paper, we introduce a new conception of 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. By using the ensemble conception, we demonstrate non-locality properties for classical fields similar to quantum entanglement.
Abstract An effective simulation of quantum entanglement is presented using classical fields modulated with n pseudorandom phase sequences that constitute a n2 n -dimensional Hilbert space with a tensor product structure. Applications to classical fields are examplied by effective simulation of both Bell and GHZ states, and a correlation analysis was performed to characterize the simulation. Results that strictly comply with criteria of quantum entanglement were obtained and the approach was also shown to be applicable to a system consisting of n quantum particles.
We propose an optical parallel computation similar to quantum computation that can be realized by introducing pseudorandom phase sequences into classical optical fields with two orthogonal modes. Based on the pseudorandom phase sequences, we first propose a theoretical framework of "phase ensemble model" referring from the concept of quantum ensemble. Using the ensemble model, we further demonstrate the inseparability of the fields similar to quantum entanglement. It is interesting that a N2^N dimensional Hilbert space spanned by N optical fields is larger than that spanned by N quantum particles. This leads a problem for our scheme that is not the lack of resources but the redundancy of resources. In order to reduce the redundancy, we propose a special sequence permutation mechanism to efficiently imitate certain quantum states, including the product state, Bell states, GHZ state and W state. For better fault tolerance, we further devise each orthogonal mode of optical fields is measured to assign discrete values. Finally, we propose a generalized gate array model to imitate some quantum algorithms, such as Shor's algorithm, Grover's algorithm and quantum Fourier algorithm. The research on the optical parallel computation might be important, for it not only has the potential beyond quantum computation, but also provides useful insights into fundamental concepts of quantum mechanics.
We demonstrate that a tensor product structure and classical entanglement can be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using the classical entanglement, we discuss efficient simulation of several typical quantum states, including product state, Bell states, GHZ state, and W state. By performing quadrature demodulation scheme, we propose a sequence permutation mechanism to simulate certain quantum states and a generalized gate array model to simulate quantum algorithm, such as Shor’s algorithm and Grover’s algorithm. The research on classical simulation of quantum states is important, for it not only enables potential beyond quantum computation, but also provides useful insights into fundamental concepts of quantum mechanics. ∗Electronic address: jianfu@zju.edu.cn 1 ar X iv :1 50 5. 00 55 5v 3 [ qu an tph ] 6 M ay 2 01 6
Abstract Quantum entanglement and quantum nonlocality are examined in the context of the fundamental relationship between spacetime symmetry and conservation laws. It is established that quantum nonlocality arises from the very structure of spacetime. Arguments are presented in favor of the secondary nature of the spacetime continuum relative to more fundamental principles and concepts of the microworld. An example is given of a closed quantum entangled system, which demonstrates that such a system behaves as an indivisible whole: its particles are inseparably linked through the conservation of momentum. Physically, this manifests as strict correlations in measurements—correlations that must be nonlocal in nature. This supports the idea that there exist deep mechanisms of coordination, such as the principle of reciprocity between coordinate and momentum representations, and binary relations permeating the fabric of nonlocal spacetime. To understand the coherent behavior of such systems, it is necessary to move beyond local reductionism and accept the objective reality of global connections that bind the elements of the system into a unified ensemble.
We demonstrate that a single-photon field modulated with n different pseudorandom phase sequences (PPSs) can constitute a 2^n-dimensional Hilbert space that contains tensor product structure. By using the single photon field modulated with PPSs, we discuss effective simulation of Bell states and GHZ state, and apply both correlation analysis and von Neumann entropy to characterize the simulation. We obtain similar results with the cases in quantum mechanics and find that the conclusions can be easily generalized to n quantum particles. The research on simulation of quantum entanglement may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields new insights into quantum computation.