PRL: New approach will develop quantum sensors beyond standard quantum limits

A quantum sensor is a device that can use quantum behaviors such as quantum entanglement, coherence, and superposition to enhance the measurement capabilities of classical detectors. For example, the LIGO gravitational wave detector utilizes entangled states of light to enhance the distance measurement capabilities of its interferometer arm, enabling it to detect distance variations 10,000 times smaller than the width of a proton. Typically, quantum sensors use systems prepared in special quantum states called probe states. Finding the ideal probe state for a particular measurement has been the focus of many research efforts.

Now, Jarrod Reilly and his colleagues at the University of Colorado at Boulder have developed a new framework for optimizing this search. This approach helps develop quantum sensors that go beyond the standard quantum limit: The standard quantum limit is the minimum noise level of a device that can be obtained without the need for special quantum state preparation, and can therefore significantly improve measurement sensitivity.

The capabilities of quantum sensors are rapidly expanding and are increasingly moving from the laboratory to the real world. As a result, the technology is expected to play an important role in numerous fields. Quantum sensors can detect a wide range of parameters, from magnetic fields to temperature, and are expected to improve the sensitivity of devices such as single-photon detectors, laser imaging, sounding and ranging (LIDAR) detectors, and atomic clocks that are the basis of the Global Positioning System (GPS).

In many devices, quantum sensors play a crucial role in parameter estimation. In general, quantum parameter estimation consists of three steps: first, a quantum system (e.g., a quantum bit or a collection of quantum bits) is prepared in an optimal detection state; second, the detection state undergoes unitary evolution, a step also known as quantum evolution. This unitary evolution can be regarded as "sensitivity tuning", where the probe state changes according to the values of the relevant parameters. Therefore, this step encodes information about the parameters into the probe state. Third, optimal measurements are performed to extract parameter information.

How to find the optimal probe state for a given system or relevant parameter is a growing concern in the quantum sensor community. For a given quantum sensor, the decision of which probe state to use is usually made by finding the state with the largest quantum Fisher information (QFI), which is the quantum analog of Fisher information that measures the information about some unknown parameter carried by some observable. The QFI of a quantum probe state assesses its sensitivity to changes in the parameter of interest, and is therefore considered a key indicator of the reliability of quantum probe states used in quantum sensors. The higher the QFI of the probe state, the more accurate the measurement of the parameter of interest.

The approach of Reilly and his colleagues inverts this search protocol: instead of finding the best probe state for a given measurement, their framework searches for the best measurement for a given probe state. This approach also uses QFI, allowing them to assess the full potential of a given probe state for all quantum sensing applications. In their approach, the researchers used probe states. Their QFI matrix (QFIM) is then determined.

After diagonalizing this matrix, they found that the optimal generator for that probe state can be determined for a specific quantum sensing purpose. Thus, the generator can be considered as a specific measurement or quantum operation which, when applied to a quantum probe state, maximizes the estimation accuracy parameter associated with the system under test.

To understand more broadly how the method works, consider the problem of trying to find the longest route a ball rolling down a hill can take in a fixed amount of time. In the classical world, the answer is simple: the path will map to the route with the greatest slope, so the search needs to find that path. In the quantum world, the answer is more complex. The "quantum mountain" has a large number of dimensions, making brute-force search difficult.

But Reilly and colleagues' approach uses a similar idea to the classical approach: finding the optimal trajectory of the probe state in space and time, in a way that is reminiscent of how the classical theory of general relativity predicts the path of light by finding the optimal trajectory in curved spacetime. Using geometric concepts, they determined which transformations cause a particular entangled quantum system to evolve in the fastest way, and thus which parameters the state is most sensitive to.

In addition to improving current quantum sensors, Reilly and colleagues' approach has the potential to open the door to the use of quantum sensors for multiparameter estimation-which is needed for many imaging and metrology applications. Their proposal introduces a new perspective on quantum sensing by emphasizing the importance of high-precision measurements for selecting the correct generator for a given quantum state. Research and development in this area is likely to lead to innovative breakthroughs in the coming years, advancing quantum technology and our understanding of quantum mechanics.