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Determining a quantum state by means of a single apparatus
A E Allahverdyan1, R Balian, Th M Nieuwenhuizen
1Institute for Theoretical Physics, Valckenierstraat 65, 1018 XE Amsterdam, The Netherlands.
Physical Review Letters
|April 20, 2004
Summary
This study introduces a method to determine an unknown quantum system state (rho) by interacting it with a known auxiliary system. Repeated measurements of combined observables allow for precise state determination, particularly for spin systems.
Area of Science:
- Quantum mechanics
- Quantum information science
- Quantum state determination
Background:
- Characterizing unknown quantum states is fundamental for quantum information processing.
- Traditional methods often require complex setups or multiple measurement devices.
Purpose of the Study:
- To develop a method for determining an unknown quantum state using a known auxiliary system.
- To establish a one-to-one mapping between the quantum state and observable probabilities.
Main Methods:
- Utilizing controlled interaction between the system (S) and an auxiliary system (A).
- Measuring eigenvalues of a single, factorized observable of the combined system (S+A).
- Employing repeated measurements with a single apparatus.
Main Results:
- A one-to-one mapping is established between the density matrix (rho) and measurement probabilities.
- For spin systems, simultaneous measurement of z-components after interaction suffices.
- Robust experimental setups identified for initially pure or disordered auxiliary states.
Conclusions:
- The proposed method enables efficient quantum state determination through interaction and measurement.
- The technique is particularly effective for spin systems with specific couplings and external fields.
- This approach offers a practical pathway for quantum state characterization.