Nonquantum Entanglement Resolves a Basic Issue in Polarization Optics

Simon, B. Neethi; Simon, Sudhavathani; Gori, F.; Santarsiero, Massimo; Borghi, Riccardo; Mukunda, N.; Simon, R.

doi:10.1103/physrevlett.104.023901

Cited by 157 publications

(139 citation statements)

References 14 publications

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“…Intriguingly, also in classical optics there are field configurations which cannot be described as a tensor product of definite modes of each individual degree of freedom of the system [4]. These non-separable structures display a classical analogue of quantum entanglement [5][6][7][8]. One example are vector vortex beams, which are non-separable superpositions of transverse modes and polarization states of a laser beam [9][10][11].…”

Section: Pacs Numbersmentioning

confidence: 99%

Tripartite nonseparability in classical optics

et al. 2016

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It is possible to prepare classical optical beams which cannot be characterized by a tensor product of vectors describing each of their degrees of freedom. Here we report the experimental creation of such a non-separable, tripartite GHZ-like state of path, polarization and transverse modes of a classical laser beam. We use a Mach-Zehnder interferometer with an additional mirror and other optical elements to perform measurements that violate Mermin's inequality. This demonstration of a classical optical analogue of tripartite entanglement paves the path to novel optical applications inspired by multipartite quantum information protocols. PACS numbers:A composite quantum system is said to be entangled when it is not fully described by the state of its components [1]. Besides indicating a departure from classical physics, entangled states represent an important resource for a number of quantum information protocols [2]. In classical optics, the mode structure associated with different degrees of freedom of the wave field can also be described by complex vector spaces. As examples, an arbitrary polarization can be written as a complex superposition of circularly polarized beams, and the spatial configuration of a paraxial beam can be decomposed in terms of Laguerre-Gaussian beams. These degrees of freedom can be represented on two independent Poincaré spheres [3], in complete analogy with the Bloch sphere used to represent qubit states [2]. Intriguingly, also in classical optics there are field configurations which cannot be described as a tensor product of definite modes of each individual degree of freedom of the system [4]. These non-separable structures display a classical analogue of quantum entanglement [5][6][7][8]. One example are vector vortex beams, which are non-separable superpositions of transverse modes and polarization states of a laser beam [9][10][11]. This analogy was used to demonstrate the topological phase acquired by entangled states evolving under local unitary operations [12]. Recently, it has attracted a growing interest due both to the fundamental aspects involved, but also for potential applications to classical optical information processing [13][14][15][16][17][18][19][20]. Nonseparable structures have also proved their utility in the quantum optical domain [22][23][24][25][26][27][28][29][30][31][32][33]. Analogously to its quantum counterpart, classical entanglement has been characterized via the violation of Bell-like inequalities [34][35][36].Composite quantum systems may have more than two parts. For tripartite systems, Mermin [37] simplified an earlier argument by Greenberger, Horne and Zeilinger * Corresponding author.[38], to show that any local hidden-variable theory for tripartite systems must satisfy (1) where Z, Y, Z represent the Pauli operators. This inequality is violated by the so-called GHZ-Mermin state:for which ZZZ = +1 and ZXX = XZX = XXZ = −1, resulting in M = 4, the maximum algebraic violation of Mermin's inequality (1). In [39], Spreeuw proposed a scheme in which t...

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Section: Pacs Numbersmentioning

confidence: 99%

Tripartite nonseparability in classical optics

et al. 2016

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“…The CHSH inequality can also be violated when considering intrabeam correlations between different degrees of freedom of intense beams, coherent or not [21]. This, sometimes referred to as nonquantum entanglement, or inseparability of degrees of freedom, has been considered [22,23] as a tool to shed new light into certain characteristics of classical fields, by applying techniques usually restricted to a quantum scenario.…”

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confidence: 99%

Revealing Hidden Coherence in Partially Coherent Light

et al. 2015

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Coherence and correlations represent two related properties of a compound system. The system can be, for instance, the polarization of a photon, which forms part of a polarization-entangled two-photon state, or the spatial shape of a coherent beam, where each spatial mode bears different polarizations. Whereas a local unitary transformation of the system does not affect its coherence, global unitary transformations modifying both the system and its surroundings can enhance its coherence, transforming mutual correlations into coherence. The question naturally arises of what is the best measure that quantifies the correlations that can be turned into coherence, and how much coherence can be extracted. We answer both questions, and illustrate its application for some typical simple systems, with the aim at illuminating the general concept of enhancing coherence by modifying correlations. Introduction.-Coherence is one of the most important concepts needed to describe the characteristics of a stream of photons [1, 2], where it allows us to characterize the interference capability of interacting fields. However its use is far more general as it plays a striking role in a whole range of physical, chemical, and biological phenomena [3]. Measures of coherence can be implemented using classical and quantum ideas, which lead to the question of in which sense quantum coherence might deviate from classical coherence phenomena [4], and to the evaluation of measures of coherence [5][6][7].Commonly used coherence measures consider a physical system as a whole, omitting its structure. The knowledge of the internal distribution of coherence between subsystems and their correlations becomes necessary for predicting the evolution (migration) of coherence in the studied system. The evolution of a twin beam from the near field into the far field represents a typical example occurring in nature [8]. The creation of entangled states by merging the initially separable incoherent and coherent states serves as another example [7]. Or, in quantum computing the controlled-NOT gate entangles (disentangles) two-qubit states [9,10], at the expense (in favor) of coherence. Many quantum metrology and communication applications benefit from correlations of entangled photon pairs originating in spontaneous parametric down-conversion [11][12][13]. Even separable states of photon pairs, i.e. states with suppressed correlations, are very useful, e.g., in the heralded single photon sources [14,15]. For all of these, and many others, examples the understanding of common evolution of coherence and correlations is crucial.The Clauser-Horne-Shimony-Holt (CHSH) Bell's-like inequality [16][17][18] has been usually considered to quantify nonclassical correlations present between physically sepa-

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“…We highlight the applicability of one and the same formalism both to the classical and quantum optical realms, obtaining parallel and consistent results in both of them [18,[53][54][55][56].…”

Section: Discussionmentioning

confidence: 99%

Fisher information as a generalized measure of coherence in classical and quantum optics

Luis

2012

Opt. Express

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Abstract:We show that metrological resolution in the detection of small phase shifts provides a suitable generalization of the degrees of coherence and polarization. Resolution is estimated via Fisher information. Besides the standard two-beam Gaussian case, this approach provides also good results for multiple field components and nonGaussian statistics. This works equally well in quantum and classical optics. (Cambridge U. Press, 1995). 2. J. W. Goodman, Statistical Optics (John Wiley and Sons Inc., 1985). 3. B. Karczewski, "Degree of coherence of the electromagnetic field," Phys. Lett. 5, 191-192 (1963 3868-3880 (1987). 54. A. Luis, "Quantum mechanics as a geometric phase: phase-space interferometers," J. Phys. A 34, 7677-7684 (2001). References and links L. Mandel and E. Wolf, Optical Coherence and Quantum Optics

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Nonquantum Entanglement Resolves a Basic Issue in Polarization Optics

Cited by 157 publications

References 14 publications

Tripartite nonseparability in classical optics

Tripartite nonseparability in classical optics

Revealing Hidden Coherence in Partially Coherent Light

Fisher information as a generalized measure of coherence in classical and quantum optics

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