Time-frequency (TF) filtering of analog signals has played a crucial role in the development of radio-frequency communications and is currently being recognized as an essential capability for communications, both classical and quantum, in the optical frequency domain. How best to design optical time-frequency (TF) filters to pass a targeted temporal mode (TM), and to reject background (noise) photons in the TF detection window? The solution for ‘coherent’ TF filtering is known—the quantum pulse gate—whereas the conventional, more common method is implemented by a sequence of incoherent spectral filtering and temporal gating operations. To compare these two methods, we derive a general formalism for two-stage incoherent time-frequency filtering, finding expressions for signal pulse transmission efficiency, and for the ability to discriminate TMs, which allows the blocking of unwanted background light. We derive the tradeoff between efficiency and TM discrimination ability, and find a remarkably concise relation between these two quantities and the time-bandwidth product of the combined filters. We apply the formalism to two examples—rectangular filters or Gaussian filters—both of which have known orthogonal-function decompositions. The formalism can be applied to any state of light occupying the input temporal mode, e.g., ‘classical’ coherent-state signals or pulsed single-photon states of light. In contrast to the radio-frequency domain, where coherent detection is standard and one can use coherent matched filtering to reject noise, in the optical domain direct detection is optimal in a number of scenarios where the signal flux is extremely small. Our analysis shows how the insertion loss and SNR change when one uses incoherent optical filters to reject background noise, followed by direct detection, e.g. photon counting. We point out implications in classical and quantum optical communications. As an example, we study quantum key distribution, wherein strong rejection of background noise is necessary to maintain a high quality of entanglement, while high signal transmission is needed to ensure a useful key generation rate.
Quantum systems are promising candidates for sensing of weak signals as they can be highly sensitive to external perturbations, thus providing excellent performance when estimating parameters of external fields. However, when trying to detect weak signals that are hidden by background noise, the signal-to-noise ratio is a more relevant metric than raw sensitivity. We identify, under modest assumptions about the statistical properties of the signal and noise, the optimal quantum control to detect an external signal in the presence of background noise using a quantum sensor. Interestingly, for white background noise, the optimal solution is the simple and well-known spin-locking control scheme. Using numerical techniques, we further generalize these results to the case of background noise with a Lorentzian spectrum. We show that for increasing correlation time, pulse based sequences, such as CPMG, are also close to the optimal control for detecting the signal, with the crossover dependent on the signal frequency. These results show that an optimal detection scheme can be easily implemented in near-term quantum sensors without the need for complicated pulse shaping.
more » « less- NSF-PAR ID:
- 10218771
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Quantum Information
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2056-6387
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract: 100 words Jurors are increasingly exposed to scientific information in the courtroom. To determine whether providing jurors with gist information would assist in their ability to make well-informed decisions, the present experiment utilized a Fuzzy Trace Theory-inspired intervention and tested it against traditional legal safeguards (i.e., judge instructions) by varying the scientific quality of the evidence. The results indicate that jurors who viewed high quality evidence rated the scientific evidence significantly higher than those who viewed low quality evidence, but were unable to moderate the credibility of the expert witness and apply damages appropriately resulting in poor calibration. Summary: <1000 words Jurors and juries are increasingly exposed to scientific information in the courtroom and it remains unclear when they will base their decisions on a reasonable understanding of the relevant scientific information. Without such knowledge, the ability of jurors and juries to make well-informed decisions may be at risk, increasing chances of unjust outcomes (e.g., false convictions in criminal cases). Therefore, there is a critical need to understand conditions that affect jurors’ and juries’ sensitivity to the qualities of scientific information and to identify safeguards that can assist with scientific calibration in the courtroom. The current project addresses these issues with an ecologically valid experimental paradigm, making it possible to assess causal effects of evidence quality and safeguards as well as the role of a host of individual difference variables that may affect perceptions of testimony by scientific experts as well as liability in a civil case. Our main goal was to develop a simple, theoretically grounded tool to enable triers of fact (individual jurors) with a range of scientific reasoning abilities to appropriately weigh scientific evidence in court. 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