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Journal of the Optical Society of America B

Classical optics analogy of quantum teleportation

Diego Francisco, Silvia Adriana Ledesma

Published Feb 28, 2008• 22 citations
Publisher

Abstract

A classical optics setup to simulate the quantum teleportation process is presented. The analogy is based on the possibility of encoding a quantum state of a system with a 2N-dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a basis is associated with the complex amplitude of the electromagnetic field in a given region of the laser wavefront. Temporal evolutions are represented as changes of the complex amplitude of the field when the wavefront is modified by different optical elements. The classical optics representation of quantum state as images and of universal quantum gates as optical processors is shown. The design and operation of an optical module that is used to simulate the quantum teleportation process are discussed. Experimental results where the teleportation of a one qbit state is simulated are shown.

DOI
10.1364/josab.25.000383

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A classical optics setup to simulate the quantum teleportation process is presented. The analogy is based on the possibility of encoding a quantum state of a system with a 2N-dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a basis is associated with the complex amplitude of the electromagnetic field in a given region of the laser wavefront. Temporal evolutions are represented as changes of the complex amplitude of the field when the wavefront is modified by different optical elements. The classical optics representation of quantum state as images and of universal quantum gates as optical processors is shown. The design and operation of an optical module that is used to simulate the quantum teleportation process are discussed. Experimental results where the teleportation of a one qbit state is simulated are shown.
Recently, classical optics based systems to emulate quantum information processing have been proposed. The analogy is based on the possibility of encoding a quantum state of a system with a 2N‐dimensional Hilbert space as an image in the input of an optical system. The probability amplitude of each state of a certain basis is associated with the complex amplitude of the electromagnetic field in a given slice of the laser wavefront. Temporal evolution is represented as the change of the complex amplitude of the field when the wavefront pass through a certain optical arrangement. Different modules that represent universal gates for quantum computation have been implemented. For instance, unitary operations acting on the qbits space (or U(2) gates) are represented by means of two phase plates, two spherical lenses and a phase grating in a typical image processing set up. In this work, we present CNOT gates which are emulated by means of a cube prism that splits a pair of adjacent rays incoming from the input image. As an example of application, we present an optical module that can be used to simulate the quantum teleportation process. We also show experimental results that illustrate the validity of the analogy. Although the experimental results obtained are promising and show the capability of the system for simulate the real quantum process, we must take into account that any classical simulation of quantum phenomena, has as fundamental limitation the impossibility of representing non local entanglement. In this classical context, quantum teleportation has only an illustrative interpretation.
We present an optical module to simulate one step of a quantum walk algorithm. The quantum state of a system with a 2N2N2N-dimensional Hilbert space is encoded in the spatial distribution of the amplitude of the electromagnetic field in a plane. In such spatial encoding, the probability amplitude of each state of a basis is associated with the complex electromagnetic amplitude in a given slice of the laser wave front. We discuss the design and operation of an optical module that is used to implement one step of a quantum walk algorithm. Using this module, composed by standard optical elements, the evolution of the quantum state corresponds to the application of a Hadamard gate on a single qubit (representing the two-dimensional quantum coin) followed by a displacement of the NNN-dimensional quantum walker conditioned on the state of the coin. We show the actual implementation of the method and discuss its characteristics and limitations.
Summary form only given. The concept of quantum teleportation of continuous variables was suggested by Vaidman [see Phys. Rev. A, vol. 49, p. 1473, 1994]. The protocol for this kind of teleportation was elaborated and demonstrated experimentally by Kimble with collaborators [see Science, vol. 282, p. 706, 1998]. In this scheme the state being teleported is that of a single transverse mode of the electromagnetic field with finite frequency bandwidth. We describe the quantum teleportation scheme that allows one to teleport the quantum state of the wavefront of an electromagnetic wave. In other words we propose teleportation of the quantum state of a spatially multimode electromagnetic field.
Abstract Quantum computing has attracted much attention in recent decades, since it is believed to solve certain problems substantially faster than traditional computing methods. Theoretically, such an advance can be obtained by networks of the quantum operators in universal gate sets, one famous example of which is formed by quantum Control‐not gate and single qubit gates. However, realizing a device that performs practical quantum computing is tricky. This is because it requires a scalable qubit system with long coherence time and good controls, which is harsh for most current platforms. Here, it is demonstrated that the information process based on a relatively stable system—classical optical system, can be considered as an analogy of universal quantum computing. By encoding the information via the polarization state of classical beams, the optical computing elements that correspond to the universal gate set are presented and their combination for a general information process is theoretically illustrated. Taking the analogy of two‐qubit processor as an example, it is experimentally verified that the proposal works well. Considering the potential of optical system for reliable and low‐energy‐consuming computation, the results open a new way toward advanced information processing with high quality and efficiency.
Quantum–classical analogy reveals the shared mathematical framework and dynamical physical behaviors between quantum and classical systems. This work reviews structured light as a versatile platform for realizing such analogies. Theoretical mappings between quantum states and optical modes are summarized, followed by representative cases including entanglement state, cat state, coherent state, and squeezed state, where quantum features are emulated through tailored amplitude, phase, and polarization structures. Applications in quantum-inspired communication, teleportation, random walks, and billiard are further discussed. This work provides a systematic overview of the connections between quantum phenomena and classical optics and offers methodological guidance for future photonic implementations.