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Complete experimental toolbox for alignment-free quantum communication
Vincenzo D'Ambrosio, Eleonora Nagali, Stephen P. Walborn, Leandro Aolita, Sergei Slussarenko, Lorenzo Marrucci, Fabio Sciarrino
TL;DR
Quantum communication ordinarily requires users to share a reference frame, creating overhead when they move or rotate relative to one another. This paper develops and experimentally tests single-photon rotationally invariant hybrid qubits, demonstrating alignment-free quantum-communication tasks and a compact, perturbation-resistant toolbox.
Problem
Quantum communication requires users to establish and maintain a shared reference frame, imposing communication-resource overhead when they move or rotate relative to one another.
Method
The paper encodes quantum information in rotationally invariant hybrid polarization-OAM states of single photons using a q-plate-based encoder and decoder.
Results
The experiments demonstrate a complete alignment-free toolbox, including feasible alignment-free key distribution, proof-of-principle entanglement distribution, and Bell-inequality violation.
Takeaways & Limitations
The scheme supports general misalignment-immune quantum-communication protocols and is suited to robust, compact implementations such as satellite-mounted systems.
Abstract
from arXiv · showhide
Quantum communication employs the counter-intuitive features of quantum physics to perform tasks that are im- possible in the classical world. It is crucial for testing the foundations of quantum theory and promises to rev- olutionize our information and communication technolo- gies. However, for two or more parties to execute even the simplest quantum transmission, they must establish, and maintain, a shared reference frame. This introduces a considerable overhead in communication resources, par- ticularly if the parties are in motion or rotating relative to each other. We experimentally demonstrate how to circumvent this problem with the efficient transmission of quantum information encoded in rotationally invariant states of single photons. By developing a complete toolbox for the efficient encoding and decoding of quantum infor- mation in such photonic qubits, we demonstrate the fea- sibility of alignment-free quantum key-distribution, and perform a proof-of-principle alignment-free entanglement distribution and violation of a Bell inequality. Our scheme should find applications in fundamental tests of quantum mechanics and satellite-based quantum communication.
Supplementary Information: Complete experimental toolbox for alignment-free
This supplementary information analyzes the spatial-perturbation resistance of rotationally invariant hybrid photonic qubits and compares the approach with prior alignment-free schemes.
- The supplement combines theoretical and experimental analyses of hybrid encoding under spatial-mode perturbations, including displacement, tilt, obstruction, apertures, and turbulence.
- The scheme’s decoding procedure filters components that would alter the qubit, while polarization remains largely unaffected by spatial perturbations.
- The supplement reviews previously proposed quantum-communication approaches without a shared reference frame and compares their main properties with this scheme.
I. RESISTANCE OF HYBRID QUBITS TO SPATIAL PERTURBATIONS: THEORY
The theory models spatial perturbations and decoding in radial and azimuthal spatial-mode bases, showing that a symmetry condition preserves qubit fidelity while potentially reducing transmission efficiency.
- Spatial modes are labeled by azimuthal number m, representing OAM, and radial number p; the treatment is not restricted to Laguerre-Gaussian radial modes.
- The q-plate converts a Gaussian polarization-encoded photon into a rotation-invariant hybrid state, which is then subjected to a generic spatial perturbation and decoded.
- Single-mode-fiber filtering passes only m = 0, p = 0 states before detection, eliminating other spatial modes.
- A perturbation preserves the qubit state up to a global amplitude and phase factor when the stated coefficient equality holds for all radial indices p and p′.
- Mirror-symmetric transformations, including displacement, tilt, elliptical deformation, circular apertures, and knife-edge masks, automatically satisfy the fidelity-preserving condition.
- Pure multiplicative transformations from thin inhomogeneous media also satisfy the condition because their coefficients depend symmetrically on OAM indices.
A. Parallel beam displacement
The displacement analysis represents translated Laguerre-Gaussian modes and shows that the relevant transformation coefficients are independent of the OAM-sign choice, preserving the required symmetry.
- A. Parallel beam displacement: The analysis generalizes translated Laguerre-Gaussian beams with initial p = 0 and m = ±1 in polar coordinates.
- A. Parallel beam displacement: The displacement vector is parameterized by polar coordinates δ and θ, with w0 denoting beam waist and Im modified Bessel functions.
- A. Parallel beam displacement: Projection onto modes with p′ = 0 and m′ = m = ±1 yields transformation coefficients independent of the sign of m = m′, satisfying Eq. (8).
B. Beam tilting
The beam-tilting analysis derives transformation coefficients for the relevant Laguerre-Gaussian modes and identifies the parameters governing the symmetry condition.
- B. Beam tilting: The analysis derives transformation coefficients for beam tilt using Laguerre-Gaussian modes with p = p′ = 0 and m = m′ = ±1.
- B. Beam tilting: The coefficient parameter is α = k sin γ, where k is the beam wavenumber and γ is the tilt angle; the tilt azimuth η is irrelevant, and Eq. (8) is satisfied.
C. Combination of beam tilt and displacement
The combined beam-tilt and displacement transformation preserves the required condition for rotational invariance when tilt and displacement share an azimuthal direction.
- C. Combination of beam tilt and displacement: The transformation coefficients satisfy Eq. (8) when tilt and displacement occur in the same or opposite azimuthal direction.This corresponds to θ = η or θ = η ± π.
- C. Combination of beam tilt and displacement: The condition is consistent with the mirror-symmetry analysis, which is broken when the tilt and displacement directions are neither aligned nor opposite.
II. RESISTANCE OF HYBRID QUBITS TO SPATIAL PERTURBATIONS: EXPERIMENTS
The experiments test whether the proposed alignment-free quantum communication scheme withstands spatial-mode perturbations and compare hybrid qubits with pure OAM encoding.
- II. RESISTANCE OF HYBRID QUBITS TO SPATIAL PERTURBATIONS: EXPERIMENTS: The experiments test resistance to spatial-mode perturbations against the theory under unavoidable imperfections of an experimental setup.
- II. RESISTANCE OF HYBRID QUBITS TO SPATIAL PERTURBATIONS: EXPERIMENTS: The study compares transmission fidelity for rotational-invariant hybrid qubits and pure OAM-encoded qubits in every tested case.
A. Experimental setup
The experimental setup combines photon-pair generation, q-plate conversion, spatial perturbation tests, and polarization analysis to study hybrid qubit transmission.
- A. Experimental setup: Photon pairs are generated by type-II spontaneous parametric fluorescence in a β-barium borate crystal and delivered through single-mode fibers.The source operates at 76 MHz with 795 nm photons and a 3 nm spectral bandwidth.
- A. Experimental setup: The setup tests circular apertures and movable half-plane obstructions while comparing hybrid and pure OAM qubits.
- A. Experimental setup: Q-plates with topological charge q = 1/2 convert polarization-entangled states into rotationally invariant hybrid states with mean efficiency (94 ± 2)%.
- A. Experimental setup: Q-plates provide more efficient and less alignment-complex encoding and decoding than standard polarization and OAM device arrangements.Standard spatial light modulators typically cannot exceed 40–45% efficiency when measuring an OAM-encoded qubit in a given basis.
- A. Experimental setup: The receiving units are separated by (60.0 ± 0.5) cm, and coincidence events are analyzed using a 3 ns gate.
B. Resistance of hybrid qubits to beam perturbations
Hybrid qubits retain high transmission fidelity under circular and half-plane spatial obstructions, including rotated measurement stages and displaced apertures, unlike pure OAM qubits in asymmetric conditions.
- B. Resistance of hybrid qubits to beam perturbations: The tests vary half-plane coverage and iris radius, measuring state fidelity with aligned and 45°-rotated measurement stages.Fidelities are averaged over six eigenstates from three mutually unbiased bases.
- B. Resistance of hybrid qubits to beam perturbations: The beam-displacement experiment uses a beam waist of w0 = (1.0 ± 0.1)mm.
- B. Resistance of hybrid qubits to beam perturbations: F = (98 ± 1)% is the average hybrid-qubit fidelity across circular-aperture data points, independent of transmittivity, rotation angle, and pinhole displacement.
- B. Resistance of hybrid qubits to beam perturbations: F = (97 ± 1)% is obtained for centered circular apertures with pure OAM qubits, whereas displaced apertures rapidly reduce their fidelity as transmittivity decreases.
- B. Resistance of hybrid qubits to beam perturbations: Half-plane obstructions spread the OAM spectrum and create cross-talk for pure OAM qubits, while polarization confines affected contributions outside the encoded hybrid subspace.
C. Resistance of hybrid qubits to beam displacement and misalignment
The hybrid-qubit system maintains communication fidelity under substantial beam misalignment and displacement, outperforming pure OAM encoding under displacement. Device imperfections constrain performance when the beam is displaced.
- 30°: communication fidelity remains above the security threshold for rotations up to this angle without fiber realignment.Beyond 30°, slight single-mode-fiber readjustment restores high fidelity.
- Hybrid-qubit fidelity decreases with beam displacement, but much more slowly than for pure OAM encoding.The comparison was made for two fixed measurement-stage angles.
- The observed displacement-related fidelity reduction is attributed to imperfections in the q-plate’s approximately 100 µm central defect.Beam displacement overlaps the defect with a brighter beam region, increasing its effect and reducing coupling through good regions.
III. DISCUSSION ON PREVIOUS CONTRIBUTIONS TOWARDS ALIGNMENT-FREE QUANTUM COMMUNICATION
Earlier alignment-free approaches addressed particular tasks or restricted misalignment conditions, while broader schemes incurred substantial resource or stability requirements. The present discussion highlights limitations involving arbitrary time variation, general qubit transmission, and efficient implementation.
- Prepare-and-measure QKD: Earlier prepare-and-measure QKD methods addressed unknown transverse-axis orientation but required tomographically complete sender–receiver correlations to bound eavesdropper knowledge.The discussion identifies this requirement as part of the LSRO10 scheme’s operation.
- Prepare-and-measure QKD: For secret-key fractions of r ≈5%, LSRO10 required about 10^7 signals while restricting consecutive rotation changes to 10^-10 or 10^-5 degrees.The limits correspond to constant-speed and random-walk rotation, respectively, under the stated realistic conditions.
- Non-locality tests: Recent non-locality approaches could extract non-local correlations with randomly chosen settings, but required the relative angle θ to remain fixed throughout data exchange.Their finite probability of observing non-locality did not remove this stability condition.
- Logical-qubit encoding: A prior misalignment-immune demonstration for a single logical qubit used four physical qubits encoded across polarization and time-bin degrees of an entangled-photon pair.The implementation required a parametric down-conversion setup.
IV. SUMMARY
The scheme combines rotationally invariant single-photon hybrid qubits with an intrinsic decoder-based error-correction mechanism. It is presented as broadly applicable across quantum communication tasks and resistant to diverse spatial perturbations.
- High transmission fidelity persists under a large class of spatial-mode perturbations and remains much higher than for pure OAM-encoded qubits.The scheme is reported to tolerate beam misalignment, wandering effects, and obstructions.
- The universal decoder’s intrinsic error-correction mechanism is identified as the key feature behind fidelity robustness.This mechanism supports resilience to the spatial perturbations examined theoretically and experimentally.
- The approach is applicable to any quantum communication task, valid for arbitrary misalignments on any time scale, and encodes logical qubits in single photons.These are presented as key differences from previous proposals and experiments.
- The hybrid encoding supports general misalignment-immune protocols including quantum teleportation, dense coding, and entanglement swapping.Entanglement swapping is identified as a basic component of quantum repeaters.