Space-Based Quantum Sensing forLow-Power Detection of Small Targets

Marco Lanzagortaa and Jeffrey Uhlmannb

aNaval Research Laboratory, Washington DC, USA;bDepartment of Computer Science, University of Missouri-Columbia

ABSTRACT

Correlations between entangled quantum states can be exploited to dramatically improve detection sensitivityunder certain conditions. In this paper we argue that space-based surveillance ideally satisfies these conditionsand represents a practical application of quantum sensing for the detection of near-earth objects which threatenspacecraft or terrestrial life.

Keywords: Quantum Radar, Quantum Sensing, Quantum Sensors, Quantum Information, Earth Defense,Missile Defense, Space Debris.

1. INTRODUCTION

In this paper we propose a quantum-based approach for wide-area, low-power detection of small objects which canthreaten spacecraft and satellites. The proposed system consists of a set of spaceborne multispectrum quantumsensors operating in the optical and/or X bands to achieve super-resolution (beyond the Rayleigh diffractionlimit) and super-sensitivity (beyond the shot noise limit) to provide a quadratic increase in detection sensitivitycompared to classical alternatives.

The paper is organized as follows: We begin with a discussion of the challenges posed by applications requiringwide-area surveillance. We then discuss how these challenges relate to the detection and mitigation of threatsposed by objects from space. We then discuss the particular challenges of detecting small spaceborne objectswhich have the potential to damage satellites and cause disruptions to critical infrastructure that depends onthem. This motivates consideration of a space-based quantum sensing system. We conclude with a discussion ofthe advantages and limitations of such a system and directions for future research.

2. BACKGROUND ON WIDE-AREA SURVEILLANCE

Wide-Area Surveillance (WAS) involves the continuous monitoring of an extended region of the surface of theearth, or a volume of space above or beyond the earth, typically to identify elements of a discrete set of specifictargets or events. Example WAS applications from the Strategic Defense Initiative (SDI) era include the BoostSurveillance and Tracking System (BSTS) and the Space Surveillance and Tracking System (SSTS).1

The principal goal of BSTS was to use satellite-based wide field-of-view (WFOV) infrared sensors to detectlaunch plumes at ICBM sites in the Soviet Union. A positive detection would be followed by transmission ofthe full sensor report for assessment and subsequent tasking of secondary assets to confirm and track the missilewith intent to intercept and destroy.

Although the set of missile sites to be monitored spanned a very large geographic area, the set of possible detectionevents was limited to a single very distinctive IR signature originating at one of fewer than 100 precisely-knownlocations. Despite what appears to be a highly manageable problem formulation, development of BSTS wasabandoned because there was no practical way to deploy enough satellites to maintain continuous dwell on thetarget sites to ensure reliable launch detection.

Final version published in Proceedings of the SPIE Conference on Radar Sensor Technology XIX, Paper 9461-41,Baltimore, MD, April 20-22, 2015.

Figure 1: SDI-era tracking system.2

To appreciate the significance of the failure of BSTS,consider what the challenge would have been if theproblem formulation required detection of mobile mis-sile platforms so that the entire land mass of the SovietUnion had to be monitored rather than only a fewdozen specific locations. Further consider the chal-lenge if plume signatures resembled various types ofnatural background phenomena.

Overall the most challenging constraint imposed bythe BSTS problem formulation was the need to de-tect single short-duration launch events, which wouldinherently demand uninterrupted dwell-continuity foreach launch site. SSTS and other subsequently-proposed ground and space-based WAS missile detec-tion systems relaxed the detection constraint to permitfirst-detects to occur during late boost or even early mid-course. Unfortunately, an expanded temporal detectionwindow incurs the challenge of a less distinctive detection signature and a vastly larger surveillance volume.

The critical upside to an indefinite detection window is that it allows the system’s measure of effectiveness tobe defined and optimized probabilistically. More specifically, whereas a missed BSTS detection equated to no-intercept (and thus its catastrophic consequences) the relaxed problem formulation provides for estimation ofa nonzero probability of intercept conditioned on the time of detection. Beyond merely casting the worst-casefailure potential in a softer light, the probabilistic model provides a flexible means for determining how best toallocate current and emerging detection and intercept technologies to optimize the quantified performance of theoverall system.

3. THREATS FROM SPACE

Current missile defense systems are reasonably effective only when either the launch region or the target regionis relatively small. Space-based threats such as comets and asteroids present challenges that dwarf anythingever considered in the context of missile defense. For example, a dense iron-type asteroid comparable in size to(within an order of magnitude) a ballistic missile has destructive potential comparable to a small nuclear bomb.Unlike an ICBM, however, an asteroid may emerge from any direction in space, at any point during the earth’sorbit around the sun, and strike anywhere on the earth.

Figure 2: Asteroid6 (TOP) DarkComet7 (BOTTOM).

To counter every type of space-based collision threat, a Detect-And-Deflect/ Detect-And-Destroy (DAD) system must be able to detect all objectswithin a volume of space encompassing most of the solar system that areof size sufficient to devastate a large city. After each detection, the DADsystem must then track the object for enough time to determine whetherits trajectory represents a threat. Critically, of course, all of this must beaccomplished early enough to allow for subsequent mitigation, i.e., to deflector destroy.

3.1 The Detection Problem

Virtually all effective wide-area surveillance systems rely on highly sensor-specific models for what represents “a target” for purposes of detection. Inthe case of BSTS the model took the form of a particular IR flash-and-decayenvelope observed at one of a pre-specified set of geographic locations. Inthe case of a mid-course ballistic missile, the detection model may be aspecific radar cross-section observed in a pre-specified trajectory corridor.

The specificity of the assumed detection model is critical for the design of reliable sensing systems that provideshigh sensitivity (i.e., high probability of detection) with means for effectively discriminating targets from non-targets. This is why high-fidelity tracking systems are almost always specifically tailored to track a particulartype of target, e.g., one system is designed to detect and track submarines and another is designed to detect andtrack attack aircraft.

The collision threat from space-based targets is daunting because it involves Variable Size / Signature Targets(VSTs). Objects can be of widely varying absolute and apparant size, e.g., a small benign object near the earthmay have the same optical profile as a large object further away, and can have vastly different material properties,e.g., one object may be highly visible at some wavelengths while another object of the same size may be nearlyinvisible in that spectrum. In fact, the spectral signature of a single object may vary significantly depending onits position relative to the sun.

3.2 The Discrimination Problem

Even if a position estimate for every object in the solar system larger than some pre-defined threshold could beinstantaneously obtained, this would provide almost no information sufficient to distinguish benign objects fromtheats. Two additional pieces of information are required for each object:

1. The composition of the object must be determined to distinguish between a low-density dustball that posesminimal threat (because it cannot penetrate the earth’s atmosphere intact) versus a high-density object ofthe same size that could cause localized devastation with long-term global effects on crops and climate.

2. The kinematics of the object must be determined to assess whether its trajectory will intersect the earthat any point during a pre-defined window of time, e.g., thirty years. This may require several detectionsbefore it is possible to confidently conclude that it is not a threat.

Obtaining the above information will almost certainly require the use of a suite of specialized sensor assetsdifferent from WAS assets used for initial detection.

3.3 The Mitigation Problem

Threat mitigation is not directly relevant to the focus of this paper, but it does have indirect implications.Specifically, the sensor and tracking capabilities necessary to distinguish whether or not an object is a threatmust be sufficient to determine the object’s trajectory with the accuracy necessary to, e.g., apply a laser forcontrolled ablative deflection.

4. WIDE-AREA DETECTION OF SMALL TARGETS

At present there is no feasible way to deploy a system capable of identifying and defending against all possiblespace-based collision threats. Consequently, attention has been focused on detection of relatively large Near-EarthObjects (NEOs). The Spacewatch,4 Near-Earth Tracking (NEAT),5 and Lincoln Near-Earth Asteroid Research(LINEAR)8 programs of the 1980s and 1990s were among the first systematic wide-area surveys undertakenwith high-sensitivity CCD arrays. Although these were not specifically DAD systems, they provided criticalinformation for quantifying the threat posed by NEOs.

Past wide-array surveys of NEOs, as well as the more recent Pan-STARRS,9,10 are designed to detect objectswith an apparent visual magnitude above a predefined threshold. This threshold is determined in part by sensorcalibration and in part by limits imposed by atmospheric attenuation. This threshold may be suitable for thedetection of NEOs with potential to pose catastrophic threats to the earth, but it does not address the threatposed by smaller objects to spacecraft and satellites.

The increasing reliance of critical infrastructure on the availability of satellites (e.g., GPS) creates a critical needfor sensing capabilities to detect threats posed by natural and man-made debris orbiting the earth as well assmall objects (e.g., micro-meteoroids) originating from beyond the earth. The challenge posed by this problemfor classical sensor technologies motivates consideration of non-classical quantum-based sensors.

5. QUANTUM RADAR

In recent years there has been a major scientific thrust to harness quantum phenomena to increase the per-formance of a wide variety of classical devices ranging from computation to sensing, and considerable progresshas occurred in the analysis and design of photonic-based quantum sensors (e.g. quantum radar and quantumlidar).11 These quantum sensors exploit the non-classical correlations embedded in entangled quantum states toimprove the extraction of target information in low signal-to-noise ratio environments.18

In general, there are two types of standoff quantum sensors:

• Quantum Illumination: These sensors use two-photon entangled state such as:

|Φ〉 =1√d

d∑k=1

|k〉S |k〉A (1)

where S represents the signal photon, A represents an idler photon, d is the number of modes, and |k〉 isa momentum state.11,14,15 These states are obtained, for instance, from Spontaneous Parametric Down-conversion using non-linear crystals. In general, sensors inspired by quantum illumination perform betterin the presence of noise and attenuation.18

• NOON-State Quantum Interferometry: As shown in Figure 3, these sensors are basically made of twomirrors and two 50/50 beam splitters. A far away target can be considered as a large arm in the interfer-ometer.11,16,17 The states injected into the two input arms of the interferometer are given by:

|Ψ〉 =|N〉1 ⊗ |0〉2 + |0〉1 ⊗ |N〉2√

N(2)

Notice that these states are superpositions of N photon states going through arm 1 and N vacuum statesgoing through arm 2, along with N photon states going through arm 2 and N vacuum states going througharm 1.

Figure 3: NOON state interferometermade of two mirrors and two 50/50 beamsplitters. The NOON entangled state is in-jected into the system through the ports 1and 2. A far away target can be consideredas a large arm in the interferometer.

It is well known that both types of standoff quantum sensors of-fer a unique set of advantages and disadvantages.11 For instance,it is known that Quantum Illumination sensors operate better inthe presence of strong atmospheric attenuation and backgroundsolar radiation. On the other hand, NOON-state quantum inter-ferometers have better performance in the absence of atmosphericattenuation.

Indeed, a standard quantum interferometer that uses non-entangled states can be used to perform high precision measure-ments of a induced phase δϕ, which can result from not knowingthe distance to some target δx. That is:

δϕ = kδx =2πx

λ(3)

where λ is the wavelength of the photons. In this case, the inputstates to the interferometer are N individual photon states of theform:

|ψ〉 = |1〉 ⊗ |1〉 ⊗ |1〉 ⊗ ...⊗ |1〉︸ ︷︷ ︸N

(4)

and the current induced in the detector is simply given by:

∆In ∝ cos(δϕ) (5)

The Rayleigh limit basically implies that in order to properly distinguish a measured value, we can only lookat the maximum values of ∆I. As shown in Figure 2, the distance between the two neighboring maxima in∆I is δϕm = 2π, and as a consequence, the minimum distance displacement that can be measured with thisinterferometer is δx = λ.

Figure 4: The current in the detector∆I with respect to the angular dis-placement δϕ. The injection of N = 3NOON states into the system causessuper-oscillations, which lead to a 3-fold improvement over the Rayleighlimit.

On the other hand, if we use entangled NOON states, the current inthe detector is given by:

∆Ie ∝ cos(Nδϕ) (6)

where N is the number of photons.16 The effect of entanglement is tointroduce super-oscillations, as the expression for ∆Ie oscillates fasterby a factor N than the current ∆In for non-entangled photons. Thesesuper-oscillations are shown in Figure 4 for the case N = 3. As aconsequence, the minimum distance displacement that can be measuredis now given by:

δx =λ

N(7)

In other words, the use of NOON entangled states helps the detectorto beat the Rayleigh limit δx = λ by a factor of N .

Similarly, the shot noise limit, which bounds the performance of mostof our classical sensing devices is given by:

δϕ ≥ δϕsnl = O(

1√N

)(8)

where again, N represents the number of non-entangled photons used by the sensing device. However, NOONstate interferometry is limited by the Heisenberg limit:

δϕ ≥ δϕhl = O(

1

N

)(9)

and therefore, NOON state interferometry helps the detector to beat the shot noise limit δϕsnl by a quadraticfactor.

Figure 5: The sensitivity of an interfer-ometer with N non-entangled photons islimited by the shot noise limit (SNL),while interferometers using NOON statesare bounded by the Heisenberg limit(HL). However, in the presence of at-mospheric attenuation, the performanceof the NOON state interferometer is de-graded.

Unfortunately, the performance of NOON state interferometryis severely degraded in the presence of an attenuating media.11

For example, Figure 5 shows the shot noise limit (snl), which isthe sensitivity bound for a sensor with N non-entangled photons.Also shown is the Heisenberg limit (HL), which is the sensitivitybound for a sensor with N entangled photons in NOON states.However, in the presence of attenuation, the sensitivity boundincreases with N . And for N ≈ 24, the sensitivity bound ofthe entangled photon sensor is actually worse than for the non-entangled system.

Even though there have been proposals to circumvent the degrad-ing effects of the environment, NOON state interferometry seemsto be better geared to operate in low attenuation environments.Such is the case of outer space. Indeed, over the first 150 km, thedensity of the atmosphere decreases by 9 order of magnitude∗.And outside Earth’s atmosphere, the density of outer space isof less than one hydrogen atom per cubit meter. This implies aphoton mean free path of about 1023 km for signal photons trav-eling in outer space. As a consequence, one should consider thepossibility of deploying quantum sensors based on NOON interferometry in orbit around Earth.

∗Let us recall that, for instance, the International Space station is at 340 km, the Hubble Space Telescope at 595 km,and the GPS satellites at 20,350 km.

6. SPACE-BASED QUANTUM RADAR FOR SMALL NEOS

As we have discussed, in the absence of atmospheric attenuation, quantum sensors are able to have betterperformance than their classical counterparts. First, it is possible to have super-resolution, as NOON stateinterferometry can beat the Rayleigh limit by a factor of N. This is an important feature to detect and discriminatesmall objects. And second, these quantum sensors are able to beat the shot noise limit by a quadratic factor.

Figure 6: Depiction of proposed quantumdetection satellite (not yet deployed).13

To take advantage of a quantum sensor with these characteris-tics, we have investigated the theoretical possibility of having anetwork of space-borne quantum sensors in orbit around Earth.These satellites would be composed of a power source, a communi-cation system, a quantum sensor, and any required maneuveringboosters. The sensing system is relatively simple, as it wouldbe reduced to a quantum interferometer and a source of NOONstates. If all the raw detection data is broadcasted to a ground sta-tion, the satellite itself does not require sophisticated data anal-ysis hardware. In such a case, the principal source of continuousenergy consumption is the generation of entangled photons.

Furthermore, these quantum sensors can achieve a O(√N) im-

provement in performance, or equivalently, a O(√N) reduction

in number of photons necessary to achieve the same level of performance as traditional classical systems. Thismeans that in principle quantum sensors have much lower power requirements, hence significantly lower expectedcost12 compared with most classical alternatives.

7. CONCLUSIONS

Quantum sensing appears to be the best option offered by modern science to perform a multitude of detectiontasks in the space environment. We described a basic system of orbiting quantum sensors which could be usedfor a variety of missions such as missile defense, Earth defense against comets and asteroids, and debris trackingfor the safe removal and passage of spacecrafts. Due to the nature of quantum sensing, these satellite networksystem would have reduced cost and higher performance than what can be achieved with today’s technology.However, many theoretical and experimental questions remain open.

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