Entanglement-enhanced lidars for simultaneous range and velocity measurements

Abstract

Lidar is a well-known optical technology for measuring a target's range and radial velocity. We describe two lidar systems that use entanglement between transmitted signals and retained idlers to obtain significant quantum enhancements in simultaneous measurements of these parameters. The first entanglement-enhanced lidar circumvents the Arthurs-Kelly uncertainty relation for simultaneous measurements of range and radial velocity from the detection of a single photon returned from the target. This performance presumes there is no extraneous (background) light, but is robust to the round-trip loss incurred by the signal photons. The second entanglement-enhanced lidar-which requires a lossless, noiseless environment-realizes Heisenberg-limited accuracies for both its range and radial-velocity measurements, i.e., their root-mean-square estimation errors are both proportional to 1/M when M signal photons are transmitted. These two lidars derive their entanglementbased enhancements from the use of a unitary transformation that takes a signal-idler photon pair with frequencies ω S and ω I and converts it to a signal-idler photon pair whose frequencies are (ω S + ω I )/2 and (ω S − ω I )/2. Insight into how this transformation provides its benefits is provided through an analogy to continuous-variable superdense coding. DOI: 10.1103/PhysRevA.96.040304 Quantum metrology [1-3] addresses measuring unknown parameters of a physical system using quantum-mechanical resources. A typical single-parameter scenario involves interrogating a physical system with M probes that undergo independent, identical interactions with the system. These probes then carry away information that can be used to estimate the parameter of interest. When the M probes are in a product state, the standard quantum limit (SQL)-with a root-meansquare (rms) estimation error proportional to 1/ √ M-can be achieved. Entangled probes, however, can realize the Heisenberg limit (HL) [2,3], viz., an rms estimation error that is proportional to 1/M [2][3][4][5][6][7]. SQL vs HL behavior for single-parameter estimation can arise, e.g., in measuring time delays [5], point-source separations [8][9][10][11], displacements [12][13][14], or magnetic fields [15].Significant complications occur, in the independent, identical interactions setting, when there are multiple unknown parameters [12][13][14][15]. In particular, if these parameters are associated with noncommuting observables, then the uncertainty principle would seem to forbid obtaining unlimited simultaneous knowledge of them from a single returned probe [16][17][18][19][20][21][22]. In such cases, quantum-enhanced accuracy can be obtained by entangling probes with locally stored idlers [12][13][14][23][24][25][26][27], in addition to the benefit derived from entangling different probes.In this Rapid Communication we address quantum metrology for a specific pair of parameters associated with noncommuting observables: the lidar problem of measuring both a target's range and its radial velocity. We describe tw...

Multiparameter Estimation in Networked Quantum Sensors

“…A magnetic field sensing problem is considered later. QSNs with non-commuting parameter generators -There are a variety of important estimation problems for which the generators do not commute [9,47,48], such as estimating the three spatial components of a magnetic field [9], or estimating completely unknown unitaries [48]. We now adapt Theorem 1 to the case of non-commuting parameter generators.…”

“…In our model, the generators of parameters imprinted on different sensors always commute, so only the generators of parameters encoded into the same sensor can be non-commuting. When estimating parameters with non-commuting generators, it is known that the optimal estimation protocol will generally require a probe that is entangled with an ancilla [47,48]. In a QSN, other sensors in the network can potentially play a similar role to ancillas, and so sensor-entanglement might reduce estimation uncertainty.…”

Quantum metrology in the presence of limited data

“…On the other hand, the number of times that we can interact with the system under study by performing several measurements is always finite and potentially small. This is a possibility that could arise, for instance, in tracking scenarios where we can only have access to a few observations before the object of interest is out of reach, as might be the case for quantum radar [13][14][15] or lidar [15][16][17].…”

Bayesian multiparameter quantum metrology with limited data

“…Real-world applications typically give rise to estimation problems with several unknown pieces of information. For instance, we may need to determine the range and velocity of a moving object [1], quantify phases and phase diffusion [2,3], reconstruct an image [4][5][6], estimate the components of a field [7], assess the spatial deformations of a grid of sources [8,9] or implement distributed sensing protocols using quantum networks [10][11][12][13][14][15]. In this context, many results in existing literature rely on the formalism provided by the multi-parameter Cramér-Rao bound [16][17][18][19][20].…”