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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Limitations of quantum process tomography

Lynden K. Shalm, Morgan W. Mitchell, Aephraim M. Steinberg

Published Jan 11, 2005• 1 citation
Publisher

Abstract

Quantum process tomography is often cited as providing all the information that can be known about a given quantum process. In this paper we have shown that even if two processes appear identical under process tomography, it is possible to distinguish them using an interferometric setup. Using this setup, it is possible to gain more information about a process than just tomography provides.

DOI
10.1117/12.583241

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Quantum process tomography is often cited as providing all the information that can be known about a given quantum process. In this paper we have shown that even if two processes appear identical under process tomography, it is possible to distinguish them using an interferometric setup. Using this setup, it is possible to gain more information about a process than just tomography provides.
Abstract The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a possible reconstruction of the underlying process. The tomography is typically performed by processing an overcomplete set of measurements and extracting the process matrix from maximum-likelihood estimation. Here, we introduce Fourier Quantum Process Tomography, a technique which requires a reduced number of measurements, and benchmark its performance against the standard maximum-likelihood approach. Fourier Quantum Process Tomography is based on measuring probability distributions in two conjugate spaces for different state preparations and projections. Exploiting the concept of phase retrieval, our scheme achieves a complete and robust characterization of the setup by processing a near-minimal set of measurements. We experimentally test the technique on different space-dependent polarization transformations, reporting average fidelities higher than 90% and significant computational advantage.
Quantum process tomography, a primitive in many quantum information processing tasks, can be cast within the framework of the theory of design of experiments (DOE), a branch of classical statistics that deals with the relationship between inputs and outputs of an experimental setup. Such a link potentially gives access to the many ideas of the rich subject of classical DOE for use in quantum problems. The classical techniques from DOE, however, cannot be directly applied to the quantum process tomography due to the basic structural differences between the classical and quantum estimation problems. Here we properly formulate quantum process tomography as a DOE problem and examine several examples to illustrate the link and the methods. In particular, we discuss the common issue of nuisance parameters and point out interesting features in the quantum problem absent in the usual classical setting.
As the method to completely characterize quantum dynamical processes, quantum process tomography (QPT) is vitally important for quantum information processing and quantum control, where the faithfulness of quantum devices plays an essential role. Here via weak measurements, we present a new QPT scheme characterized by its directness and parallelism. Comparing with the existing schemes, our scheme needs a simpler state preparation and much fewer experimental setups. Furthermore, each parameter of the quantum process is directly determined from only five experimental values in our scheme, meaning that our scheme is robust against the accumulation of errors.
Quantum process tomography might be the most important paradigm shift which has yet to be translated fully into theoretical chemistry. Its fundamental strength, long established in quantum information science, offers a wealth of information about quantum dynamic processes which lie at the heart of many (if not all) chemical processes. However, due to its complexity its application to real chemical systems is currently beyond experimental reach. Furthermore, it is susceptible to errors due to experimental and theoretical inaccuracies and disorder has long been thought to be an obstacle in its applicability. Here, I present the first results of a study into the use of quantum light for quantum process tomography. By using a toy model and comparing numerical simulations to theoretical predictions the possible enhancement of using non-conventional light is studied. It is found, however, that disorder is necessary make the use of quantum light suitable for process tomography and that, in contrast to conventional wisdom, disorder can make the results more accurate than in an ordered system.
A fundamental task in photonics is to characterise an unknown optical process, defined by properties such as birefringence, spectral response, thickness and flatness. Amongst many ways to achieve this, single-photon probes can be used in a method called quantum process tomography (QPT). Furthermore, QPT is an essential method in determining how a process acts on quantum mechanical states. For example for quantum technology, QPT is used to characterise multi-qubit processors and quantum communication channels; across quantum physics QPT of some form is often the first experimental investigation of a new physical process, as shown in the recent research into coherent transport in biological mechanisms. However, the precision of QPT is limited by the fact that measurements with single-particle probes are subject to unavoidable shot noise---this holds for both single photon and laser probes. In situations where measurement resources are limited, for example, where the process is rapidly changing or the time bandwidth is constrained, it becomes essential to overcome this precision limit. Here we devise and demonstrate a scheme for tomography which exploits non-classical input states and quantum interferences; unlike previous QPT methods our scheme capitalises upon the possibility to use simultaneously multiple photons per mode. The efficiency---quantified by precision per photon used---scales with larger photon number input states. Our demonstration uses four-photon states and our results show a substantial reduction of statistical fluctuations compared to traditional QPT methods---in the ideal case one four-photon probe state yields the same amount of statistical information as twelve single probe photons.