Condensed Matter Seminar

J.M. Geremia
University of New Mexico

Thursday, October 11, 2007
1:00 pm in SPL 52

Using Real-Time Quantum State Estimation and Feedback to Implement a Cat-State Measurement without the Cat-State

Abstract: Measurements on quantum systems are inherently uncertain, and reaching the minimum uncertainty allowed by physics in any given setting generally requires one to measure in an optimal way. A great example of the importance of optimal measurements is quantum state discrimination. One must identify the state into which a quantum system was prepared given a list of possible states and one copy of the system to measure. This setting, often called the Helstrom Problem, lies at the foundation of quantum information science: given an initially mixed quantum system, it investigates the maximum purification that is possible through measurement. State discrimination also lies at the heart of communications theory.

By the method of positive operator valued measures, quantum information theoretic methods can be used to find the optimal measurement for state discrimination problems. Unfortunately, the optimal measurements found in this way are generally extremely difficult to perform because they would require one to perform impractically-complex unitary operations on the quantum system being measured. We will consider discriminating between two coherent states of a harmonic oscillator. In this case, the optimal measurement would require generating a cat-state, i.e. a superposition of macroscopically distinct coherent states. In all current settings, whether optical or in condensed matter, preparing high-fidelity superpositions of coherent states is impractical.

We instead consider an alternative approach based on real-time quantum feedback control, and we demonstrate that it is possible to achieve the quantum limit for coherent state discrimination by combining a continuous measurement of the harmonic oscillator number operator with feedback-mediated displacements. In this manner, feeedback is used to simulate the optimal measurement and achieve the quantum limit with ever generating a superposition state. Corroborating laboratory data obtained using optical coherent states will be presented.