Optimal measurements for reaching quantum fisher information in mixed quantum optical states
Abstract
The discipline of quantum-limited optical precision measurement has historically focused on the development of non-classical, active sensing techniques whereby non-classical states (such as entangled states) are generated by a transmitter and directed toward a target and reflected back toward the receiver where it is measured to extract an estimation of the parameter of interest. The work that we are proposing in this Short-Term Innovative Research (STIR) grant aims to investigate the fundamental quantum-limited sensitivity for the detection of photon-starved optical mixed states. Our previous work focused on fundamental limits to state discrimination of mixed quantum states. We propose to extend that work here examining the problem of parameter estimation using photon-starved mixed quantum states. The limit to the precision of parameter estimation is represented by the variance of a measurement. For a specific measurement implementation the limit to the variance can be calculated using a quantity called Fisher information (FI). Fundamentally, the variance on any measurement is limited by quantum mechanics, and therefore the quantum Fisher information (QFI) calculates a variance directly from the quantum mechanical representation of the state being measured. Our research objectives for this proposed project will start with the calculation of the FI and QFI for several mixed state sensing problems. Our investigation will include non-classical states as well as classical coherent states mixed with thermal light. Next, we will calculate the symmetric logarithmic derivative (SLD) function for these sensing scenarios, and determine the eigenvectors of the SLD function. These eigenvectors give a measurement basis in which the QFI bound can be reached, minimizing the measurement variance. These measurement vectors are likely to be abstract, however, so we will investigate optical operators that can rotate the received quantum state such that the SLD function is diagonal in the Fock basis, rendering direct photon number measurement the optimal measurement for minimizing the measurement variance. Finally, we will leverage the quantum sensing testbed, which was constructed under previous support from ARO, and implement a quantum sensing experiment. In the experiment we will limit ourselves to displacement operations for rotation of the received quantum state attempting to diagonalize the SLD in the Fock basis. We will use photon number measurement followed by estimation to determine the parameter of interest and directly measure the variance of our measurement.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 20, 2020
- Source ID
- W911NF2010235
Entities
People
- Jonathan Habif
Organizations
- Army Contracting Command
- United States Army
- University of Southern California