[Paper Review] Detection of gravitational waves with quantum encryption technology

Fabrizio Tamburini, Bruce A. Bassett+1 more|ArXiv.org|Jun 29, 2000

Chaos-based Image/Signal Encryption1 references3 citations

TL;DR

This paper proposes a novel method to detect gravitational waves using quantum encryption technology based on entangled photon pairs and Bell’s inequalities. By treating gravitational waves as 'shadow eavesdroppers' that reduce quantum non-locality, the method detects distortions in the statistical properties of quantum keys, enabling the identification of both deterministic and stochastic gravitational wave sources through deviations from white noise in correlation statistics.

ABSTRACT

We propose a new technique for detecting gravitational waves using Quantum Entangled STate (QUEST) technology. Gravitational waves reduce the non-locality of correlated quanta controlled by Bell's inequalities, distorting quantum encryption key statistics away from a pure white noise. Gravitational waves therefore act as shadow eavesdroppers. The resulting colour distortions can, at least in principle, be separated from noise and can differentiate both deterministic and stochastic sources.

Motivation & Objective

• To develop a new detection method for gravitational waves using quantum entanglement and quantum cryptography principles.
• To exploit the fact that gravitational waves disrupt quantum non-locality, thereby distorting quantum key statistics in a detectable way.
• To demonstrate that gravitational waves can be identified as 'shadow eavesdroppers' by measuring deviations from ideal white noise in quantum key correlations.
• To propose a complementary detection technique to existing interferometric detectors like LIGO and LISA, operating via quantum state non-locality.
• To explore the feasibility of detecting low-frequency gravitational waves using quantum-entangled photon pairs, particularly when the gravitational wavelength is shorter than the baseline between detectors.

Proposed method

• Utilizes the Ekert quantum key distribution protocol with entangled photon pairs in a singlet state to generate correlated binary keys at two distant detectors.
• Employs random polarizer swapping at Alice and Bob’s stations to generate binary strings K_A and K_B, which are then cross-correlated after discarding non-coincident measurement settings.
• Analyzes the cross-correlation matrix of the keys to detect off-diagonal power, indicating non-white noise due to gravitational wave-induced path length and timing distortions.
• Defines the fluctuation function ξ(t) = |N₁ - N₀| to quantify detection imbalance, modeled via a stochastic differential equation involving the gravitational wave strain h(t) and intrinsic noise w(t).
• Applies Bell’s inequality via the S-operator S ≡ |E(δ′_A,δ′′_B) + E(δ′_A,δ′′_B) + E(δ′′_A,δ′_B) - E(δ′′_A,δ′′_B)| to quantify entanglement degradation caused by gravitational waves.
• Estimates the intrinsic noise spectral density S_N ≈ 2×10⁻⁴³ Hz⁻¹, with a characteristic noise amplitude h_rms ≈ 6.3×10⁻²² (f/1 Hz)¹/² for 20-minute data subsets, comparable to LIGO's sensitivity at 200 Hz.

Experimental results

Research questions

• RQ1 Can gravitational waves be detected by observing their effect on the statistical properties of quantum keys generated via entanglement?
• RQ2 To what extent do gravitational waves mimic the effects of eavesdropping in quantum cryptography by reducing quantum non-locality?
• RQ3 Can the deviation from white noise in quantum key statistics be used to distinguish gravitational wave signals from background noise?
• RQ4 What is the sensitivity of a quantum-entangled detector to low-frequency gravitational waves, especially when λ_GW < 2d_AB?
• RQ5 How does the performance of a QUEST-based detector compare to traditional interferometric detectors like LIGO in terms of noise and signal detection?

Key findings

• Gravitational waves distort the statistics of quantum keys by introducing non-white noise, causing K_A ≠ K_B and breaking the ideal white noise distribution of detection events.
• The fluctuation function ξ(t) evolves according to dξ/dt = (Γ_ph/2)(w(t) + h(t)), where h(t) is the gravitational wave strain and w(t) is intrinsic detector noise with zero mean and delta-correlated power.
• The intrinsic noise spectral density is estimated as S_N ≈ 2×10⁻⁴³ Hz⁻¹, with a characteristic noise amplitude h_rms ≈ 6.3×10⁻²² (f/1 Hz)¹/² for 20-minute data segments.
• The method is most sensitive at low frequencies, with a low-frequency cutoff around f ~ c/(2d_AB), where d_AB is the baseline between detectors.
• Gravitational waves reduce the Bell inequality violation parameter S, mimicking the effect of an eavesdropper, thus enabling detection via S < 2√2.
• The proposed QUEST detector is complementary to LIGO and LISA, operating via quantum non-locality rather than interferometric phase shifts, and is insensitive to shot noise but sensitive to other environmental noise sources.