Hendrik B. Coldenstrodt-Ronge

Measuring measurement : theory and practice

Recent efforts have applied quantum tomography techniques to the calibration and characterization of complex quantum detectors using minimal assumptions. In this work, we provide detail and insight concerning the formalism, the experimental and theoretical challenges and the scope of these tomographical tools. Our focus is on the detection of photons with avalanche photodiodes and photon-number resolving detectors and our approach is to fully characterize the quantum operators describing these detectors with a minimal set of well-specified assumptions. The formalism is completely general and can be applied to a wide range of detectors.

Mapping coherence in measurement via full quantum tomography of a hybrid optical detector

Quantum states and measurements exhibit wave-like (continuous) or particle-like (discrete) character. Hybrid discrete–continuous photonic systems are key to investigating fundamental quantum phenomena1,2,3, generating superpositions of macroscopic states4, and form essential resources for quantum-enhanced applications5 such as entanglement distillation6,7 and quantum computation8, as well as highly efficient optical telecommunications9,10. Realizing the full potential of these hybrid systems requires quantum-optical measurements sensitive to non-commuting observables such as field quadrature amplitude and photon number11,12,13. However, a thorough understanding of the practical performance of an optical detector interpolating between these two regions is absent. Here, we report the implementation of full quantum detector tomography, enabling the characterization of the simultaneous wave and photon-number sensitivities of quantum-optical detectors. This yields the largest parameterization to date in quantum tomography experiments, requiring the development of novel theoretical tools. Our results reveal the role of coherence in quantum measurements and demonstrate the tunability of hybrid quantum-optical detectors. By developing full quantum detector tomography, researchers simultaneously characterize the wave- and photon-number sensitivities of quantum-optical detectors to yield the largest ever parametrization in a quantum tomography experiment. The presented results reveal the role of coherence in quantum measurements and demonstrate the tunability of hybrid quantum-optical detectors.

Photon Number Statistics of Multimode Parametric Down-Conversion

We experimentally analyze the complete photon number statistics of parametric down-conversion and ascertain the influence of multimode effects. Our results clearly reveal a difference between single-mode theoretical description and the measured distributions. Further investigations assure the applicability of loss-tolerant photon number reconstruction and prove strict photon number correlation between signal and idler modes.

A proposed testbed for detector tomography

Measurement is the only part of a general quantum system that has yet to be characterised experimentally in a complete manner. Detector tomography provides a procedure for doing just this; an arbitrary measurement device can be fully characterised, and thus calibrated, in a systematic way without access to its components or its design. The result is a reconstructed POVM containing the measurement operators associated with each measurement outcome. We consider two detectors, a single-photon detector and a photon-number counter, and propose an easily realised experimental apparatus to perform detector tomography on them. We also present a method of visualising the resulting measurement operators.

Quantum detector tomography of a time-multiplexed superconducting nanowire single-photon detector at telecom wavelengths.

Superconducting nanowire single-photon detectors (SNSPDs) are widely used in telecom wavelength optical quantum information science applications. Quantum detector tomography allows the positive-operator-valued measure (POVM) of a single-photon detector to be determined. We use an all-fiber telecom wavelength detector tomography test bed to measure detector characteristics with respect to photon flux and polarization, and hence determine the POVM. We study the SNSPD both as a binary detector and in an 8-bin, fiber based, Time-Multiplexed (TM) configuration at repetition rates up to 4 MHz. The corresponding POVMs provide an accurate picture of the photon number resolving capability of the TM-SNSPD.

Integrated photonic sensing

Loss is a critical roadblock to achieving photonic quantum-enhanced technologies. We explore a modular platform for implementing integrated photonics experiments and consider the effects of loss at different stages of these experiments, including state preparation, manipulation and measurement. We frame our discussion mainly in the context of quantum sensing and focus particularly on the use of loss-tolerant Holland–Burnett states for optical phase estimation. In particular, we discuss spontaneous four-wave mixing in standard birefringent fibre as a source of pure, heralded single photons and present methods of optimizing such sources. We also outline a route to programmable circuits that allows the control of photonic interactions even in the presence of fabrication imperfections and describe a ratiometric characterization method for beam splitters, which allows the characterization of complex circuits without the need for full process tomography. Finally, we present a framework for performing state tomography on heralded states using lossy measurement devices. This is motivated by a calculation of the effects of fabrication imperfections on precision measurement using Holland–Burnett states.

Recursive quantum detector tomography

Conventional tomographic techniques are becoming increasingly infeasible for reconstructing the operators of quantum devices of growing sophistication. We describe a novel tomographic procedure using coherent states, which begins by reconstructing the diagonals of the operator and then each successive off-diagonal in a recursive manner. Each recursion is considerably more efficient than reconstructing the operator in its entirety, and each successive recursion involves fewer parameters. We apply our technique to reconstruct the positive-operator-valued measure corresponding to a recently developed

Continuous phase stabilization and active interferometer control using two modes

We present a computer-based active interferometer stabilization method that can be set to an arbitrary phase difference and does not rely on modulation of the interfering beams. The scheme utilizes two orthogonal modes propagating through the interferometer with a constant phase difference between them to extract a common relative phase and generate a linear feedback signal. Switching times of 50 ms over a range of 0–6π radians at 632.8 nm are experimentally demonstrated. The relative interferometer phase can be stabilized up to several days to within ± 3°.

Homodyne state tomography with photon number resolving detectors

We introduce a complete tomographic reconstruction scheme geared toward low photon-number states. To demonstrate this method we reconstruct various single-mode coherent states.

Chapter 7 - Hybrid Detectors

This chapter presents an overview of efforts to improve photon-counting detection systems through the use of hybrid detection techniques such as spatial- and time-multiplexing of conventional detectors, and frequency up-conversion. It reviews the basic operation for these methods and illustrates their utility in a number of applications showing new or improved capabilities compared with conventional methods.