[Paper Review] Process tomography of quantum channels using classical light

Bienvenu Ndagano, Benjamin Perez-García+8 more|arXiv (Cornell University)|May 17, 2016

Quantum Mechanics and Applications2 references3 citations

TL;DR

This paper presents a method to perform quantum process tomography of optical channels using classical light, leveraging the equivalence between classical entanglement in vector beams and quantum entanglement in photon pairs. By exploiting the one-to-one correspondence in state evolution under single-degree-of-freedom channel operations, the authors demonstrate real-time characterization of turbulence-induced channel distortions in free-space and fiber links, enabling precise quantum error correction without requiring a functional quantum link upfront.

ABSTRACT

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links which cannot be repaired without a tomography of the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterising quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled pho- tons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories and thus enables precise quantum error-correction in short and long haul optical communication, in both free-space and fibre.

Motivation & Objective

• To overcome the paradox of needing a working quantum link to characterize it by using classical light for channel tomography.
• To establish a physical equivalence between classical entanglement in vector beams and quantum entanglement in photon pairs under single-degree-of-freedom channel operations.
• To enable real-time characterization of stochastic channel dynamics in turbulent free-space and fiber links for robust quantum communication.
• To develop a practical, non-quantum-based method for quantum error-correction in high-dimensional spatial-mode quantum channels.
• To validate the approach experimentally using vector beams and compare their evolution to that of entangled photon pairs under identical turbulent conditions.

Proposed method

• Utilizes classically entangled vector beams—generated via spatial mode superposition with orthogonal polarization states—as a proxy for quantum entangled photon pairs.
• Demonstrates that the state evolution of two classically entangled degrees of freedom (OAM and polarization) matches that of two quantum-entangled degrees of freedom when the channel acts on only one degree of freedom.
• Employs a phase screen model to simulate atmospheric turbulence, with the Strehl ratio derived from the quadratic structure function approximation to quantify beam quality degradation.
• Applies the Kraus operator formalism to model the channel as a rank-two filter, enabling the derivation of a conjugate filter for error correction.
• Uses concurrence as a measure of entanglement, computing its evolution for both classical and quantum states under identical channel conditions.
• Validates the correspondence by comparing the concurrence decay of classical vector beams and quantum Bell states under identical turbulence parameters, showing identical functional dependence on the Strehl ratio.

Experimental results

Research questions

• RQ1 Can classical light be used to reliably characterize quantum channels without requiring a functional quantum link?
• RQ2 Is there a one-to-one correspondence between the evolution of classically entangled vector beams and quantum-entangled photon pairs under single-degree-of-freedom channel operations?
• RQ3 To what extent does the concurrence of classical and quantum entangled states evolve identically under turbulent atmospheric conditions?
• RQ4 Can the channel's stochastic dynamics be reconstructed from classical light measurements to enable real-time quantum error correction?
• RQ5 How does OAM mode separation and turbulence strength affect entanglement decay in both classical and quantum systems?

Key findings

• The concurrence of a Bell state under a single-phase-screen turbulence channel evolves as $ \mathcal{C} = \frac{\text{SR}}{\text{SR}^2 - \text{SR} + 1} $, where SR is the Strehl ratio, showing identical functional dependence to classical vector beam evolution.
• Classical vector beams with OAM and polarization entanglement exhibit identical entanglement dynamics to quantum-entangled photon pairs when the channel acts on only one degree of freedom.
• The concurrence of the output state is given by $ \mathcal{C}_{\text{out}} = |1 - \exp(-\ell^2 / \Delta^2)| \cdot \mathcal{C}_{\text{in}} $, demonstrating that increased OAM mode separation reduces crosstalk and preserves entanglement.
• When $ \Delta = 0 $, indicating no turbulence, the output concurrence equals the input concurrence, confirming no degradation.
• For $ \ell \to \infty $, the output concurrence approaches the input concurrence, indicating that widely separated OAM modes are robust against crosstalk.
• The conjugate filter $ \tilde{M} = (\lambda_1|0\rangle\langle 0| + \lambda_0|1\rangle\langle 1|)U^\dagger $ can be used to invert the channel action, enabling effective error correction via post-processing.