Manipulation of single-photon states encoded in transverse spatial modes: Possible and impossible tasks

2007/12/31 by Gabriel F. Calvo, Antonio Picón · 9 citations
Computer Science · Engineering · Mathematics · Physics and Astronomy · #Algorithm #Artificial intelligence #Computer science #Degrees of freedom (physics and chemistry) #Encoding (memory) #Engineering #Gaussian #Impossibility #Limit (mathematics) #Linear subspace #Mathematical analysis #Mathematics #Orbital Angular Momentum in Optics #Photon #Physics #Pure mathematics #Quantum #Quantum Information and Cryptography #Quantum mechanics #Quantum optics and atomic interactions #Quantum state #Set (abstract data type) #State (computer science) #Symplectic geometry #Transverse plane #physics.optics #quant-ph

paper · pdf · doi:10.1103/physreva.77.012302

published in Physical Review A 77(1) (American Physical Society) · Published in PRA

openalex publication_date 2008/01/03 · arxiv created 2008/02/11 · arxiv updated 2011/02/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

Controlled generation and manipulation of photon states encoded in their spatial degrees of freedom is a crucial ingredient in many quantum-information tasks exploiting higher-than-two dimensional encoding. Here, we prove the impossibility to arbitrarily modify d-level state superpositions (qudits) for d>2, encoded in the transverse modes of light, with optical components associated to the group of symplectic transforms (Gaussian operations). Surprisingly, we also provide an explicit construction of how non-Gaussian operations acting on mode subspaces do enable one to overcome the limit d=2. In addition, this set of operations realizes the full SU(3) algebra.

Citations

• Entanglement of the orbital angular momentum states of photons
• Entanglement of orbital angular momentum states between an ensemble of cold atoms and a photon
• Two-mode quantum systems: Invariant classification of squeezing transformations and squeezed states
• Security of Quantum Key Distribution Usingd-Level Systems
• Measuring two-photon orbital angular momentum entanglement
• Experimental quantum cryptography with qutrits
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• How to create and detect N-dimensional entangled photons with an active phase hologram
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• Determination of Continuous Variable Entanglement by Purity Measurements
• Optical Spin-to-Orbital Angular Momentum Conversion in Inhomogeneous Anisotropic Media
• Long-distance quantum communication with atomic ensembles and linear optics
• Spin-induced angular momentum switching
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• Peres-Horodecki Separability Criterion for Continuous Variable Systems
• Increasing Entanglement between Gaussian States by Coherent Photon Subtraction
• Reversible State Transfer between Light and a Single Trapped Atom

Cited by

• Measuring the Complete Transverse Spatial Mode Spectrum of a Wave Field