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arXiv:quant-ph/0404095 · Physical Review A

Classical simulation of quantum entanglement using optical transverse modes in multimode waveguides

Jian Bo Fu, Zhijian Si, Shaofang Tang, Jian Qiu Deng

Published Oct 21, 2004• 28 citations
arXivHTMLPDF

Abstract

We discuss ``mode-entangled states'' based on the optical transverse modes of the optical field propagating in multimode waveguides, which are classical simulation of the quantum entangled states. The simulation is discussed in detail, including the violation of the Bell inequality and the correlation properties of optical pulses' group delays. The research on this simulation may be important, for it not only provides useful insights into fundamental features of quantum entanglement, but also yields interesting insights into quantum computation and quantum communication.

DOI
10.1103/physreva.70.042313

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We numerically demonstrate that "mode-entangled states" based on the transverse modes of classical optical fields in multimode waveguides violate Bell's inequality. Numerically simulating the correlation measurement scheme of Bell's inequality, we obtain the normalized correlation functions of the intensity fluctuations for the two entangled classical fields. By using the correlation functions, the maximum violations of Bell's inequality are obtained. This implies that the two classical fields in the mode-entangled states, although spatially separated, present a nonlocal correlation.
We propose a novel interferometer by using optical transverse modes in multimode waveguide that can beat the standard quantum limit. In the scheme, the classical simulation of NNN-partical quantum entangled states is generated by using NNN independent classical fields and linear optical elements. Similar to the quantum-enhanced measurements, the classical simulation can also achieve N\sqrt{N}N​ enhancement over the precision of the measurement NNN times for independent fields. Due to only using classical fields and linear optical elements, the scheme can be realized much more easily.
We demonstrate that a tensor product structure and optical analogy of quantum entanglement can be obtained by introducing pseudorandom phase sequences into classical fields with two orthogonal modes. Using the classical analogy, 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.
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