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Physical Review Letters

Experimental Simulation of Two-Particle Quantum Entanglement using Classical Fields

K. F. Lee, John E. Thomas

Published Feb 12, 2002• 69 citations
Publisher

Abstract

We experimentally demonstrate simulation of two entangled quantum bits using classical fields of two frequencies and two polarizations. Multiplication of optical heterodyne beat signals from two spatially separated regions simulates coincidence detection of two particles. The product signal so obtained contains several frequency components, one of which can be selected by bandpass frequency filtering. The bandpassed signal contains two indistinguishable, interfering contributions, permitting simulation of four polarization-entangled Bell-like states. These classical field methods may be useful in small scale simulations of quantum logic operations that require multiparticle entanglement without collapse.

DOI
10.1103/physrevlett.88.097902

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We experimentally demonstrate simulation of two entangled quantum bits using classical fields of two frequencies and two polarizations. Multiplication of optical heterodyne beat signals from two spatially separated regions simulates coincidence detection of two particles. The product signal so obtained contains several frequency components, one of which can be selected by bandpass frequency filtering. The bandpassed signal contains two indistinguishable, interfering contributions, permitting simulation of four polarization-entangled Bell-like states. These classical field methods may be useful in small scale simulations of quantum logic operations that require multiparticle entanglement without collapse.
We experimentally demonstrate a simple classical-field optical heterodyne method which employs postselection to reproduce the polarization correlations of a four-particle entangled state. We give a heuristic argument relating this method to the measurement of multiple quantum fields by correlated homodyne detection. We suggest that using multiple classical fields and postselection, one can reproduce the polarization correlations obtained in quantum experiments which employ multiple single-photon sources and linear optics to prepare multiparticle entangled states. Our experimental scheme produces four spatially separated beams which are separately detected by mixing with four independent optical local oscillators (LO) of variable polarization. Analog multiplication of the four beat signals enables projection onto a four-particle polarization-state basis. Appropriate band pass filtering is used to produce a signal proportional to the projections of the maximally entangled four-field polarization state, $\ensuremath{\mid}{H}_{1})\ensuremath{\mid}{H}_{2})\ensuremath{\mid}{H}_{3})\ensuremath{\mid}{H}_{4})+\ensuremath{\mid}{V}_{1})\ensuremath{\mid}{V}_{2})\ensuremath{\mid}{V}_{3})\ensuremath{\mid}{V}_{4})$, onto the product of the four LO polarizations. Since the data from multiple observers is combined prior to postselection, this method does not constitute a test of nonlocality. However, we reproduce the polarization correlations of the 32 elements in the truth table from the quantum mechanical Greenberger-Horne-Zeilinger experiments on the violation of local realism. We also demonstrate a form of classical entanglement swapping in a four-particle basis.
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We explore the concepts of coherence and entanglement as they apply to both the classical and quantum natures of light. In the classical domain, we take inspiration from the tools and concepts developed in foundational quantum mechanics and quantum information science to gain a better understanding of classical coherence theory of light with multiple degrees of freedom (DoFs). First, we use polarization and spatial parity DoFs to demonstrate the notion of classical entanglement, and show that Bell's measure can serve as a useful tool in distinguishing between classical optical coherence theory. Second, we establish a methodical yet versatile approach called 'optical coherency matrix tomography' for reconstructing the coherency matrix of an electromagnetic beam with multiple DoFs. This technique exploits the analogy between this problem in classical optics and that of tomographically reconstructing the density matrix associated with multipartite quantum states in quantum information science. Third, we report the first experimental measurements of the 4 x 4 coherency matrix associated with an electromagnetic beam in which polarization and a spatial DoF are relevant, ranging from the traditional two-point Young's double slit to spatial parity and orbital angular momentum modes. In the quantum domain, we use the modal structure of classical fields to develop qubits and structure Hilbert spaces for use in quantum information processing. Advancing to three-qubit logic gates is an important step towards the success of optical schemes for quantum computing. We experimentally implement a variety of two- and three- qubit, linear and deterministic, single-photon, controlled, quantum logic gates using polarization and spatial parity qubits. Lastly, we demonstrate the implementation of two-qubit single-photon logic using polarization and orbital angular momentum qubits.
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Abstract We report experiments in which the Bell parameter S that enters the Clauser–Horne–Shimony–Holt inequality: ∣ S ∣ ≤ 2 , attains values ∣ S ∣ > 2 . In our experiments, we used two spatially separated optical beams, the electric fields of which were correlated to one another. The amount of correlation was quantified by the spectral degree of coherence η ( α , β ) . This quantity measures the correlation between fields that exist at two distant locations and whose respective polarizations are given in terms of angles α and β , which can be set independently from one another. Such a correlation qualifies for the construction of the Bell parameter S . By changing the amount of field correlation, we could cover a range that goes from ∣ S ∣ < 2 to ∣ S ∣ > 2 . Our experimental findings should provide useful material for the ongoing, theoretical discussions about the quantum–classical border.
In classical macroscopic ultrafast optical four-wave mixing signals, phase matching selects three classes of light–matter interaction pathways: double quantum coherence; non-rephasing; and photon-echo. Multiple pathways contribute to each of these signals. We show that a coincidence-double-heterodyne detection scheme that employs two classical and two vacuum fields can isolate a single pathway contribution to each of these signals. We further demonstrate the advantage of the proposed technique by comparing it with the classical photon-echo signal for a model Frenkel-exciton dimer.