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Physical Review A

Relative tomography of an unknown quantum state

Dmitri S. Mogilevtsev, Jaroslav Řeháček, Z. Hradil

Published Feb 3, 2009• 26 citations
Publisher

Abstract

We propose a tomography scheme capable of reconstructing the quantum state of an unknown mode of light. The complex mode structure of the investigated field is expressed by a single number---the mismatch between the probe and signal. This parameter is estimated as a part of the quantum tomography protocol. This opens up ways for reconstructions utilizing interference between independent sources.

DOI
10.1103/physreva.79.020101

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We propose a tomography scheme capable of reconstructing the quantum state of an unknown mode of light. The complex mode structure of the investigated field is expressed by a single number---the mismatch between the probe and signal. This parameter is estimated as a part of the quantum tomography protocol. This opens up ways for reconstructions utilizing interference between independent sources.
Any measurement scheme involving interference of quantum states of the electromagnetic field necessarily mixes information about the spatiotemporal structure of these fields and quantum states in the recorded data. We show that in this case, a trade-off is possible between extracting information about the quantum states and the structure of the underlying fields, with the modal overlap being either a goal or a convenient tool of the reconstruction. We show that varying quantum states in a controlled way allows one to infer temporal profiles of modes. Vice versa, for the known quantum state of the probe and controlled variable overlap, one can infer the quantum state of the signal. We demonstrate this trade-off by performing an experiment using the simplest on–off detection in an unbalanced weak homodyning scheme. For the single-mode case, we demonstrate experimentally inference of the overlap and a few-photon signal state. Moreover, we show theoretically that the same single-detector scheme is sufficient even for arbitrary multi-mode fields.
As one of the fundamental tools in the quantum information field, quantum state tomography can be utilized to reconstruct any unknown state. Usually, it needs a tomographically complete set of measurements and meantime it requires that all measurements are fully characterized. Here we propose a semi-measurement-device-independent quantum state tomography protocol, which only needs one characterized measurement and a trusted ancillary system. Furthermore, we carry out corresponding experimental demonstrations by using linear optics, and obtain the average state fidelity as high as 0.973, verifying the effectiveness of the scheme.
Abstract We address state reconstruction by photon-number-resolving detectors, and demonstrate that they may be effectively exploited to perform quantum tomography of states of light. In particular, we find that the pattern function technique, originally developed for optical homodyne tomography, may be also applied to discrete data. Our results open new perspectives for quantum-state reconstruction in the mesoscopic regime, and pave the way to the use of photon-number-resolving-based detection schemes in Quantum Information science.
We discuss the data-pattern tomography for reconstruction of entangled states of light. We show that for a moderate number of probe coherent states it is possible to achieve high accuracy of representation not only for single-mode states but also for two-mode entangled states. We analyze the stability of these representations to the noise and demonstrate the conservation of the purity and entanglement. Simulating the probe and signal measurements, we show that systematic error inherent for representation of realistic signal response with finite sets of responses from probe states still allows one to infer reliably the signal states preserving entanglement.
In quantum state tomography, one potential source of error is uncontrolled contact of the system with a heat bath whose detailed properties are not known, and whose impact on the system moreover varies between different runs of the experiment. Precisely these variations provide a handle for reconstructing the system's effective relaxation dynamics. I propose a pertinent estimation scheme which is based on a steepest-descent ansatz and maximum likelihood. After reconstructing the relaxation dynamics, the original quantum state of the system can be constrained to a curve in state space.