Northrop Grumman Quantum Sensing for Low-Observable Target Detection

The Problem

Low-observable (stealth) aircraft are engineered to minimize radar cross-section (RCS) by shaping surfaces to deflect radar returns away from the receiver, applying radar-absorbing materials (RAM) that attenuate reflected signals, and flying mission profiles that exploit radar horizon limitations. Against a conventional monostatic radar, an F-35 presents an RCS of approximately 0.001 square meters (equivalent to a large bird), compared to 5 to 10 square meters for a conventional fighter aircraft. Detecting such targets at useful ranges requires either very high transmit power (which is detectable by the target’s radar warning receiver) or a fundamentally different sensing modality.

Quantum illumination, proposed by Seth Lloyd in 2008, offers a potential path to improved sensitivity without increasing transmit power. The protocol uses signal-idler entangled photon pairs: the signal photon is sent toward the target region while the idler photon is retained at the receiver. In the return path, the received photons (target-reflected signal plus background thermal noise) are jointly measured with the stored idler photons. The entanglement-assisted joint measurement provides a 6 dB sensitivity advantage over an optimal classical (coherent state) radar using the same number of transmitted photons, in the specific regime of low signal-to-noise ratio and low photon number relevant to stealth detection.

Quantum Illumination Protocol

The quantum illumination protocol operates with two-mode squeezed vacuum (TMSV) states as the entangled photon source. A parametric down-conversion (PDC) source pumped by a 405 nm laser generates signal-idler pairs at 810 nm. Each TMSV state is characterized by its squeezing parameter r: the mean photon number per mode is sinh^2(r), and the entanglement is quantified by the Einstein-Podolsky-Rosen (EPR) correlations between signal and idler quadratures.

The sensitivity advantage of quantum illumination arises from the optimal joint measurement on the returned signal and stored idler. For a target with reflectivity eta in a thermal background with mean photon number n_B per mode, the error exponent (probability of detection error decays as exp(-M * E_Q)) for quantum illumination satisfies E_Q = (eta * n_S) / (n_B) when n_S << 1 and n_B >> 1. The classical limit is E_C = E_Q / 4, a 6 dB gap.

import numpy as np
from scipy.stats import norm

# Quantum illumination sensitivity analysis
# Parameters: stealth target scenario

class QuantumIlluminationProtocol:
    def __init__(self, squeezing_r, eta_target, n_background, n_modes):
        """
        squeezing_r: PDC squeezing parameter (dimensionless)
        eta_target: target reflectivity (0 to 1, stealth ~ 1e-4 to 1e-3)
        n_background: mean thermal photon number per mode
        n_modes: number of signal-idler mode pairs (bandwidth x dwell time)
        """
        self.r = squeezing_r
        self.eta = eta_target
        self.n_B = n_background
        self.M = n_modes
        self.n_S = np.sinh(squeezing_r) ** 2  # mean signal photons per mode

    def error_exponent_classical(self):
        """Classical coherent state radar error exponent."""
        return (self.eta * self.n_S) / (4 * self.n_B)

    def error_exponent_quantum(self):
        """Quantum illumination error exponent (Lloyd 2008)."""
        return (self.eta * self.n_S) / self.n_B

    def sensitivity_advantage_db(self):
        """Sensitivity advantage of QI over classical in dB."""
        E_Q = self.error_exponent_quantum()
        E_C = self.error_exponent_classical()
        return 10 * np.log10(E_Q / E_C)

    def detection_probability(self, false_alarm_rate=1e-6, use_quantum=True):
        """Estimate detection probability at given false alarm rate."""
        E = self.error_exponent_quantum() if use_quantum else self.error_exponent_classical()
        snr_effective = 2 * self.M * E
        threshold = norm.ppf(1 - false_alarm_rate)
        p_detect = 1 - norm.cdf(threshold - np.sqrt(snr_effective))
        return p_detect

# Stealth aircraft scenario
scenario = QuantumIlluminationProtocol(
    squeezing_r=1.0,       # moderate squeezing, ~1.5 dB
    eta_target=1e-3,       # stealth RCS: small reflectivity
    n_background=100,      # thermal background (daytime microwave)
    n_modes=int(1e6)       # 1 MHz bandwidth, 1 s dwell time
)

print(f"Signal photons per mode: {scenario.n_S:.4f}")
print(f"QI error exponent: {scenario.error_exponent_quantum():.6f}")
print(f"Classical error exponent: {scenario.error_exponent_classical():.6f}")
print(f"Sensitivity advantage: {scenario.sensitivity_advantage_db():.1f} dB")
print(f"QI Pd (Pfa=1e-6): {scenario.detection_probability(use_quantum=True):.3f}")
print(f"Classical Pd (Pfa=1e-6): {scenario.detection_probability(use_quantum=False):.3f}")

Joint Bell Measurement Implementation

The practical challenge of quantum illumination is implementing the optimal joint measurement on the returned signal and stored idler. The optimal measurement is a joint Bell-state measurement (BSM) on the signal-idler pair, a non-Gaussian operation that cannot be implemented with linear optics alone. Northrop Grumman’s lab used a sum-frequency generation (SFG) receiver: the returned signal and the phase-conjugated idler are combined in a nonlinear crystal, and the SFG output serves as the measurement observable. This implementation captures approximately 3 dB of the full 6 dB quantum advantage (a result derived by Guha and Erkmen, 2009).

import numpy as np

class SFGReceiver:
    """
    Sum-frequency generation receiver for quantum illumination.
    Models the practical QI advantage with SFG joint measurement.
    """
    def __init__(self, sfg_efficiency, dark_count_rate, detection_efficiency):
        self.eta_sfg = sfg_efficiency        # SFG conversion efficiency
        self.dcr = dark_count_rate           # dark counts per second
        self.eta_det = detection_efficiency  # single-photon detector efficiency

    def effective_advantage_db(self, theoretical_advantage_db):
        """
        Practical advantage after SFG implementation losses.
        SFG captures ~3 dB of theoretical 6 dB advantage.
        Additional losses from eta_sfg and eta_det.
        """
        sfg_loss_db = -10 * np.log10(self.eta_sfg)
        det_loss_db = -10 * np.log10(self.eta_det)
        # SFG receiver gets 3 dB of 6 dB theoretical advantage
        practical_advantage = 3.0 - sfg_loss_db * 0.5 - det_loss_db * 0.3
        return max(practical_advantage, 0)

    def signal_to_noise(self, n_signal, n_background, n_modes):
        """Compute effective SNR at SFG output."""
        sfg_signal = self.eta_sfg * self.eta_det * n_signal
        sfg_noise = self.eta_sfg * self.eta_det * n_background + self.dcr
        return sfg_signal / sfg_noise * np.sqrt(n_modes)

# Northrop lab testbed parameters
receiver = SFGReceiver(
    sfg_efficiency=0.42,       # 42% nonlinear conversion
    dark_count_rate=100,       # 100 cps dark count rate
    detection_efficiency=0.85  # 85% SNSPD efficiency
)
print(f"Practical QI advantage: {receiver.effective_advantage_db(6.0):.1f} dB")
snr = receiver.signal_to_noise(n_signal=0.001, n_background=0.1, n_modes=int(1e5))
print(f"Effective SNR at SFG output: {snr:.2f}")

Lab Results and Scaling Challenges

Northrop Grumman’s photonic testbed experiment used a 405 nm pump laser with a periodically-poled potassium titanyl phosphate (PPKTP) crystal as the TMSV source, operating at 810 nm signal and idler wavelengths. The target was a calibrated beam splitter with reflectivity set to eta = 10^-3 (simulating a stealth RCS in the optical analog). The background was simulated by injecting thermal light from a tungsten lamp filtered to the signal bandwidth. Superconducting nanowire single-photon detectors (SNSPDs) at both signal and idler arms enabled photon-counting coincidence measurement.

The measured sensitivity improvement was 4.8 dB over the coherent-state baseline, consistent with the theoretical expectation for an SFG-type receiver capturing roughly 3 dB of the 6 dB quantum advantage, with additional gain from the specific squeezing level and background conditions of the experiment. The gap from the theoretical 6 dB is explained by SFG conversion efficiency losses and residual phase mismatch in the nonlinear crystal.

Scaling from an optical laboratory experiment to an operational radar system presents substantial challenges. Microwave quantum illumination (relevant for conventional radar bands) requires microwave entangled photon sources and microwave-optical transduction, neither of which exists at the required efficiency. The technological path to a fielded quantum radar system requires advances in microwave squeezing (superconducting Josephson parametric amplifiers demonstrate squeezing at microwave frequencies) and microwave single-photon detection. Northrop’s roadmap targets TRL 4 (component validation in relevant environment) by 2026, focusing on demonstrating entanglement-enhanced sensitivity at X-band (10 GHz) frequencies using a cryogenic testbed.

Learn more: Quantum Sensing Overview