Twisted photons: new quantum perspectives in high dimensions

Erhard, Manuel; Fickler, Robert; Krenn, Mario; Zeilinger, Anton

doi:10.1038/lsa.2017.146

Cited by 532 publications

(383 citation statements)

References 148 publications

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“…For every nonzero l , the beams are vortices carrying

ℏ l

orbital angular momentum (OAM). These modes are particularly interesting due to their high capacity for quantum information, as well as their potential use for generating high‐dimensional entanglement . The SPDC process in transversely uniform nonlinear crystals has been shown to conserve OAM between the interacting fields, such that

l_{normalsignal} + l_{normalidler} = l_{normalpump}

.…”

Section: Spdc With Structured Beamsmentioning

confidence: 99%

Simulating Correlations of Structured Spontaneously Down‐Converted Photon Pairs

Trajtenberg‐Mills

Karnieli

Voloch‐Bloch

et al. 2020

Laser & Photonics Reviews

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Introducing structure into photon pair generation via spontaneous parametric down‐conversion (SPDC) is shown to be useful for controlling the output state and exploiting new degrees of freedom for quantum technologies. This paper presents a new method for simulating first‐ and second‐order correlations of the down‐converted photons in the presence of structured pump beams and shaped nonlinear photonic crystals. This method is nonperturbative, and thus accounts for high‐order effects, and can be made very efficient using parallel computing. Experimental results of photodetection and coincidence rates in complex spatial configurations are recovered quantitatively by this method. These include SPDC in 2D nonlinear photonic crystals, as well as with structured light beams such as Laguerre Gaussian and Hermite Gaussian beams. This simulation method reveals conservation rules for the down‐converted signal and idler beams that depend on the nonlinear crystal modulation pattern and the pump shape. This scheme can facilitate the design of nonlinear crystals and pumping conditions for generating non‐classical light with pre‐defined properties.

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“…For every nonzero l , the beams are vortices carrying

ℏ l

l_{normalsignal} + l_{normalidler} = l_{normalpump}

.…”

Section: Spdc With Structured Beamsmentioning

confidence: 99%

Simulating Correlations of Structured Spontaneously Down‐Converted Photon Pairs

Trajtenberg‐Mills

Karnieli

Voloch‐Bloch

et al. 2020

Laser & Photonics Reviews

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“…enables encoding qudits-as opposed to qubits-for investigating quantum communication with indefinite causal order in larger Hilbert space dimensions [5,8]. The benefits of using qudits for quantum information processing applications, such as improved security in quantum cryptography and higher information capacity in quantum communication, are well known [33,34]. Moreover, certain protocols demonstrating an advantage from indefinite causal order will require qudits for their implementation [5,8].…”

Section: -3mentioning

confidence: 99%

Indefinite Causal Order in a Quantum Switch

et al. 2018

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Quantum mechanics allows events to happen with no definite causal order: this can be verified by measuring a causal witness, in the same way that an entanglement witness verifies entanglement. Here, we realize a photonic quantum switch, where two operationsÂ andB act in a quantum superposition of their two possible orders. The operations are on the transverse spatial mode of the photons; polarization coherently controls their order. Our implementation ensures that the operations cannot be distinguished by spatial or temporal position-further it allows qudit encoding in the target. We confirm our quantum switch has no definite causal order by constructing a causal witness and measuring its value to be 18 standard deviations beyond the definite-order bound. DOI: 10.1103/PhysRevLett.121.090503 In daily experience, it is natural to think of events happening in a fixed causal order. Strikingly, it has been proposed that quantum physics allows for nonclassical causal structures where the order of events is indefinite [1,2]. It has been theoretically shown that such a possibility provides an advantage for computation [3], communication complexity [4,5], and other information processing tasks [6][7][8]. Furthermore, investigations of indefinite causal orders suggest a promising route towards a theory that combines general relativity and quantum mechanics [9,10].Indefinite causal orders can be studied using a framework that distinguishes whether some experimental situationcalled a "process"-is compatible with a fixed causal order of the events or not. An example of a process with indefinite causal order is the "quantum switch" [1]. In the quantum switch, the order in which two quantum operationÂ andBconsidered as "black box operations"-are performed on a target system is coherently controlled by a control quantum system (Fig. 1). This can also be seen as a particular case of "superposition of time evolution" [11]. The advantages provided by the quantum switch arise from the fact that it cannot be reproduced by an ordinary quantum circuit which uses the same number of black box operations [3][4][5][6][7].Here, we present an optical implementation of the quantum switch where the control system is the photon's polarization and the target is the transverse spatial mode. We verify indefinite causal order by introducing a causal witness [14,15], for which we obtain a value 18 standard deviations beyond the bound for definite ordering. One notable achievement of our experiment is that it opens the possibility of encoding more than two levels in the target system-transverse spatial mode can indeed be highdimensional and hence can act as a qudit.In previous implementations [12,13], the location of each black box-the spot where photons go through a set of wave plates-was different depending on the order, resulting in four distinct locations in space [ Fig. 1(c)]. Furthermore, the photons had a coherence length much shorter than the distance between the two sets of wave plates: in effect, the operations could also be distinct in...

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“…Moreover, the new formulation has special relevance for the propagation character, and potential informationconveying capacity, of structured light [6]. The motivations behind the study are to highlight the importance of a correct photon commutation relation, to explore a connection to beams endowed with orbital angular momentum (OAM) [7], Letter Vol. 43, No.…”

mentioning

confidence: 99%

Quantum features in the orthogonality of optical modes for structured and plane-wave light

Andrews

Forbes

2018

Opt. Lett.

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A fundamental photon creation-annihilation commutation relation underpins the familiar quantum formulation of optics. However, an internal inconsistency becomes apparent in the pursuit of structured light applications. This requires the relationship between operator commutation and mode orthogonality to be recast in a form ensuring full consistency with the precepts of quantum theory. A suitable reformulation, shown to register correctly an intrinsic quantum uncertainty in the associated interactions, has special relevance to optical vortex physics-particularly with regard to information content-through its connection to the degrees of freedom in the associated radiation modes. In the field of quantum optics, much of the basic theory is conventionally cast in terms that are primarily designed to apply to a single mode of radiation-a single wavelength, direction, and polarization. In the most obvious extension of these principles-allowing for more numerous modes of radiationthere are usually significant intervals between the accommodated frequencies, as, e.g., in the case of frequency combs [1], or else there are substantial differences in the directions of propagation. At the heart of most of the quantum formalism, there is a simple and widely familiar boson commutation relation between photon creation and annihilation operators [2]. One physical interpretation is that a photon propagating in a given radiation mode in vacuum cannot spontaneously divert into another mode.In the sphere of optics, the creation-annihilation commutation relation is often presented in a mathematically concise form, neglecting polarization features that ought also, for generality, to be accommodated. Although these features are not commonly given attention, they supplement the wave vector information in uniquely defining each radiation mode. The commutation relation is specifically cast in terms of a binary basis, for although polarization measurements can be made at a spatially localized location with high fidelity, it is well understood that two linear polarization states whose electric vectors differ by only a few degrees cannot be regarded as orthogonal. However, for the directions of propagation associated with the wave vector, the assumption of an orthonormal basis is not so straightforward. Moreover the wave vector of light does not commonly engage with detection apparatusunless weak quadrupole attributes are engaged, which is rarely the case.The difficulties of assuming an infinitely sharp distinction between modes of similar wave vectors are thrown into sharp relief in the case of structured radiation [3], in which there can be local variation of wave vector direction within the confines of a single well-defined beam. An optical vortex, or "twisted light," constitutes a prime example, where the wave vector represents the normal to a wavefront of helicoidal form. Significantly, it has been shown that the twisted character extends down to the level of individual photons [4,5], such that any given photon in a structured beam may ...

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Twisted photons: new quantum perspectives in high dimensions

Cited by 532 publications

References 148 publications

Simulating Correlations of Structured Spontaneously Down‐Converted Photon Pairs

Simulating Correlations of Structured Spontaneously Down‐Converted Photon Pairs

Indefinite Causal Order in a Quantum Switch

Quantum features in the orthogonality of optical modes for structured and plane-wave light

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