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arXiv:1804.02211 · Physical Review Letters

Quantum-Limited Loss Sensing: Multiparameter Estimation and Bures Distance between Loss Channels

Ranjith Nair

Published Dec 3, 2018• 79 citations
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Abstract

The problem of estimating multiple loss parameters of an optical system using the most general ancilla-assisted parallel strategy is solved under energy constraints. An upper bound on the quantum Fisher information matrix is derived assuming that the environment modes involved in the loss interaction can be accessed. Any pure-state probe that is number diagonal in the modes interacting with the loss elements is shown to exactly achieve this upper bound even if the environment modes are inaccessible, as is usually the case in practice. We explain this surprising phenomenon, and show that measuring the Schmidt bases of the probe is a parameter-independent optimal measurement. Our results imply that multiple copies of two-mode squeezed vacuum probes with an arbitrarily small nonzero degree of squeezing, or probes prepared using single-photon states and linear optics, can achieve quantum-optimal performance in conjunction with on-off detection. We also calculate explicitly the energy-constrained Bures distance between any two product loss channels. Our results are relevant to standoff image sensing, biological imaging, absorption spectroscopy, and photodetector calibration.

DOI
10.1103/physrevlett.121.230801

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The problem of estimating multiple loss parameters of an optical system using the most general ancilla-assisted parallel strategy is solved under energy constraints. An upper bound on the quantum Fisher information matrix is derived assuming that the environment modes involved in the loss interaction can be accessed. Any pure-state probe that is number diagonal in the modes interacting with the loss elements is shown to exactly achieve this upper bound even if the environment modes are inaccessible, as is usually the case in practice. We explain this surprising phenomenon, and show that measuring the Schmidt bases of the probe is a parameter-independent optimal measurement. Our results imply that multiple copies of two-mode squeezed vacuum probes with an arbitrarily small nonzero degree of squeezing, or probes prepared using single-photon states and linear optics, can achieve quantum-optimal performance in conjunction with on-off detection. We also calculate explicitly the energy-constrained Bures distance between any two product loss channels. Our results are relevant to standoff image sensing, biological imaging, absorption spectroscopy, and photodetector calibration.
We obtain universal (i.e., probe and measurement-independent) performance bounds on ancilla-assisted quantum sensing of multiple parameters of phase-covariant optical channels under energy and mode-number constraints. We first show that for any such constrained problem, an optimal ancilla-entangled probe can always be found whose reduced state on the modes probing the channel is diagonal in the photon-number basis. For parameters that are encoded in single-mode Gaussian channels, we derive a universal upper bound on the quantum Fisher information matrix that delineates the roles played by the energy and mode constraints. We illustrate our results for sensing of the transmittance of a thermal loss channel under both the no-passive-signature and passive-signature paradigms, and in the problem of sensing the noise variance of an additive-noise channel. In both cases, we show that two-mode squeezed vacuum probes are near-optimal under the constraints in the regime of low signal brightness, i.e., per-mode average photon number. More generally, our work sets down a uniform framework for readily evaluating universal limits for any sensing problem involving Gaussian channels.
Phase-insensitive optical amplifiers uniformly amplify each quadrature of an input field and are of both fundamental and technological importance. We find the quantum limit on the precision of estimating the gain of a quantum-limited phase-insensitive amplifier using a multimode probe that may also be entangled with an ancilla system. In stark contrast to the sensing of loss parameters, the average photon number N and number of input modes M of the probe are found to be equivalent and interchangeable resources for optimal gain sensing. All pure-state probes whose reduced state on the input modes to the amplifier is diagonal in the multimode number basis are proven to be quantum optimal under the same gain-independent measurement. We compare the best precision achievable using classical probes to the performance of an explicit photon-counting-based estimator on quantum probes and show that an advantage exists even for single-photon probes and inefficient photodetection. A closed-form expression for the energy-constrained Bures distance between two product amplifier channels is also derived.
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Abstract Lossy bosonic channels play an important role in a number of quantum information tasks, since they well approximate thermal dissipation in an experiment. Here, we characterize their metrological power in the idler-free and entanglement-assisted cases, using respectively single- and two-mode Gaussian states as probes. In the problem of estimating the loss parameter, we study the power-constrained quantum Fisher information (QFI) for generic temperature and loss parameter regimes, showing qualitative behaviours of the optimal probes. We show semi-analytically that the two-mode squeezed-vacuum state optimizes the QFI for any value of the loss parameter and temperature. We discuss the optimization of the total QFI, where the number of probes is allowed to vary by keeping the total power constrained. In this context, we elucidate the role of the ‘shadow-effect’, or passive signature, for reaching a quantum advantage. Finally, we discuss the implications of our results for the quantum illumination and quantum reading protocols.
This thesis presents three studies in quantum-enhanced sensing and target detection. The first study explores covert target detection using optical or microwave probes, establishing quantum-mechanical limits on the error probabilities of entanglement-assisted detection methods while maintaining the sender's covertness. It identifies the minimal energy required to preserve covertness and reduce error probabilities, compares two-mode squeezed vacuum probes and coherent states against these limits, and extends the analysis to discriminating thermal loss channels and non-adversarial quantum illumination. The second study focuses on phase-insensitive optical amplifiers, determining the quantum limit on the precision of gain estimation using multimode probes possibly entangled with ancillary systems. It finds that the average photon number and the number of input modes are interchangeable resources for achieving optimal gain sensing precision, contrasting classical probes with quantum probes and highlighting the advantages of the latter, even with single-photon inputs and inefficient photodetection. It also provides a closed-form expression for the energy-constrained Bures distance between two amplifier channels. The third study compares three probe states -- coherent state, two-mode squeezed vacuum (TMSV), and single-photon entangled state (SPES) -- in quantum-enhanced target detection, assessing their performance under signal energy constraints relevant to covert radar sensing. SPES is uniquely positioned as a practical probe due to its non-classical properties after thermal loss and ease of generation. Numerical analysis shows that at low signal energies, the error exponent of TMSV aligns with SPES, indicating comparable detection capabilities and that SPES surpasses the best classical state-the coherent state-in accuracy for certain signal strengths.