[Paper Review] Superadditive Communication with the Green Machine: A Practical Demonstration of Nonlocality without Entanglement

Chaohan Cui, Jack Postlewaite+3 more|arXiv (Cornell University)|Oct 9, 2023

Quantum Information and Cryptography4 citations

TL;DR

This paper proposes and experimentally demonstrates the Green Machine, a practical joint-detection receiver for optical communications that achieves superadditive capacity using a passive linear Hadamard transform on binary-phase-shift-keyed (BPSK) Hadamard codewords, converting them to pulse-position-modulated (PPM) signals for detection. The receiver surpasses symbol-by-symbol detection in the photon-starved regime, achieving higher Photon Information Efficiency (PIE) and demonstrating immunity to phase noise by orders of magnitude.

ABSTRACT

Achieving the ultimate Holevo limit of optical communication capacity requires a joint-detection receiver which makes a collective quantum measurement over multiple modulated symbols. Such superadditivity -- a higher communication rate than that achievable by symbol-by-symbol optical detection -- is a special case of the well-known nonlocality without entanglement and has yet to be demonstrated. In this article, we propose and demonstrate a design of joint-detection receivers, the Green Machine, that can achieve superadditivity. We build this receiver and show that its capacity surpasses any symbol-by-symbol receivers in the photon-starved regime with binary-phase-shift-keying (BPSK). Our Green Machine receiver can also significantly reduce the transmitter peak power requirement compared with the pulse-position modulation (the conventional modulation format used for deep space laser communication). We further show that the self-referenced phase makes it immune to phase noise, e.g., atmospheric turbulence or platform vibrations.

Motivation & Objective

• To demonstrate superadditive communication capacity in a practical, real-world optical receiver setup using non-entangled quantum states.
• To overcome the limitations of symbol-by-symbol detection in low-photon-flux regimes, such as deep-space optical communications.
• To design and implement a physically realizable joint-detection receiver—called the Green Machine—that enables nonlocality without entanglement in optical communication.
• To validate the theoretical Holevo capacity gain in a laboratory environment using BPSK-modulated Hadamard codes and single-photon detection.
• To demonstrate robustness against phase noise from atmospheric turbulence or mechanical vibrations through self-referenced phase stabilization.

Proposed method

• The Green Machine implements a passive linear Hadamard transform using a network of polarization-maintaining fibers, 50:50 beamsplitters, and phase modulators to unitarily map BPSK Hadamard codewords into PPM-like signal patterns.
• The system uses a thermally stabilized optical breadboard with active phase correction via a feedback loop involving a bright probe laser, tunable phase modulators, and a real-time FPGA-based control system.
• Phase drifts across three stages (S1, S2, S3) are corrected by scanning the relative phase between fiber arms and maximizing/minimizing interference fringes using a low-bandwidth InGaAs detector and a PID-controlled voltage signal.
• Data acquisition is performed using a superconducting nanowire single-photon detector (SNSPD) with 2ns dead time, synchronized to a 6.25MHz clock, and recorded via a TimeTagger Ultra system.
• The receiver operates in a continuous loop: phase correction (30ms) followed by data collection at high attenuation to emulate real channel conditions, with 16 repetitions per attenuation point.
• Photon yield is measured over 50ms guarded symbol windows, and PIE (Photon Information Efficiency) is calculated as the ratio of Shannon capacity to mean photon number per pulse.

Experimental results

Research questions

• RQ1 Can a practical joint-detection receiver achieve superadditive capacity in the photon-starved regime using only linear optics and no entanglement?
• RQ2 To what extent does the Green Machine outperform symbol-by-symbol receivers in terms of Photon Information Efficiency (PIE) under low received photon flux?
• RQ3 How effective is the self-referenced phase stabilization in mitigating phase noise from environmental disturbances like temperature drift or vibrations?
• RQ4 What is the achievable capacity gain of the Green Machine when using BPSK-modulated Hadamard codes compared to conventional PPM or symbol-by-symbol detection?
• RQ5 Can the theoretical nonlocality without entanglement phenomenon be experimentally realized in a real-world optical communication system with single-photon detection?

Key findings

• The Green Machine receiver achieves a Photon Information Efficiency (PIE) that exceeds the symbol-by-symbol limit, demonstrating superadditivity in the low-photon regime.
• After accounting for internal losses, the Green Machine's capacity surpasses that of all practical symbol-by-symbol receivers, confirming the theoretical Holevo capacity advantage.
• The system maintains phase stability for over 100ms after a 30ms phase correction cycle, enabling reliable operation in dynamic environments.
• The self-referenced phase control reduces sensitivity to phase noise by orders of magnitude compared to conventional BPSK receivers, making it highly resilient to atmospheric turbulence or platform vibrations.
• The experiment successfully demonstrates a measurable capacity gain using BPSK-modulated Hadamard codewords, with PIE values exceeding the single-pulse limit (PIE¹) for k > 1.
• The results confirm that joint detection via the Green Machine enables a higher bits-per-pulse rate than any physically realizable symbol-by-symbol receiver, validating the nonlocality without entanglement principle in a practical communication context.