Quantum state tomography from sequential measurement of two variables in a single setup

Abstract

We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way that their eigenstates may form bases connected by a discrete Fourier transform. The state can be pure or mixed, the dimension of the Hilbert space and the coupling strength are arbitrary, and the experimental setup is fixed. The concept of Moyal quasicharacteristic function is introduced for finite-dimensional Hilbert spaces.

16 pages, 2 figures, revtex4-1. Comments welcome. v2: sacrificed generality to clarity; v3: minor changes, references added

References in corpus (8)

• Full characterisation of polarisation states of light via direct measurement
• State tomography via weak measurements
• Sequential measurement of conjugate variables as an alternative quantum state tomography
• Quantum optical reconstruction scheme using weak values
• Correlations between detectors allow violation of the Heisenberg noise-disturbance principle for position and momentum measurements
• Quantum Mechanics of Successive Measurements with Arbitrary Meter Coupling
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Cited by in corpus (11)

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• Direct Reconstruction of the Quantum Density Matrix by Strong Measurements
• Stereographical visualization of a polarization state using weak measurements with an optical-vortex beam
• On the novelty, efficacy, and significance of weak measurements for quantum tomography
• Quantum State Interferography
• Relationship between subjecting the qubit to dynamical decoupling and to a sequence of projective measurements
• Weak values and weak coupling maximizing the output of weak measurements
• Improving direct state measurements by using rebits in real enlarged Hilbert spaces
• Postselection induced entanglement swapping from a vacuum--excitation entangled state to separate quantum systems
• Measurement of a spin-1 system
• Modified Kubo formula with a complex force term for weak measurement