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SPIE Optics Education and Outreach

Quantum state tomography made easy (Conference Presentation)

Andrew Forbes, Adam Vallés

Published Sep 17, 2018• 0 citations
Publisher

Abstract

Quantum state tomography (QST) allows one to probe an unknown quantum state and is a ubiquitous tool in many quantum laboratories. Unfortunately it is a time consuming and complex procedure, and thus consequently is seldom demonstrated in teaching laboratories. Here we outline a simple demonstration of the essential features of QST in a manner that allows for its implementation in undergraduate laboratories. We exploit the fact that non-separability, the quintessential feature of entangled quantum states, is in fact not unique to quantum mechanics. Using this, we construct a 3D printed version of an equivalent system for QST but with bright classical light, and demonstrate all the essential features of this tool. The source code to print the elements and run the QST are all available on-line from our website. We hope that this will inspire the introduction of “practical” quantum mechanics into the teaching curriculum.

DOI
10.1117/12.2320455

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Quantum state tomography (QST) allows one to probe an unknown quantum state and is a ubiquitous tool in many quantum laboratories. Unfortunately it is a time consuming and complex procedure, and thus consequently is seldom demonstrated in teaching laboratories. Here we outline a simple demonstration of the essential features of QST in a manner that allows for its implementation in undergraduate laboratories. We exploit the fact that non-separability, the quintessential feature of entangled quantum states, is in fact not unique to quantum mechanics. Using this, we construct a 3D printed version of an equivalent system for QST but with bright classical light, and demonstrate all the essential features of this tool. The source code to print the elements and run the QST are all available on-line from our website. We hope that this will inspire the introduction of “practical” quantum mechanics into the teaching curriculum.
A tomographic measurement is a ubiquitous tool for estimating the properties of quantum states, and its application is known as quantum state tomography (QST). The process involves manipulating single photons in a sequence of projective measurements, often to construct a density matrix from which other information can be inferred, and is as laborious as it is complex. Here we unravel the steps of a QST and outline how it may be demonstrated in a fast and simple manner with intense (classical) light. We use scalar beams in a time reversal approach to simulate the outcome of a QST and exploit non-separability in classical vector beams as a means to treat the latter as a “classically entangled” state for illustrating QSTs directly. We provide a complete do-it-yourself resource for the practical implementation of this approach, complete with tutorial video, which we hope will facilitate the introduction of this core quantum tool into teaching and research laboratories alike. Our work highlights the value of using intense classical light as a means to study quantum systems and in the process provides a tutorial on the fundamentals of QSTs.
Quantum state tomography (QST) is a fundamental technique for characterizing quantum states, crucial for validating quantum technologies. However, traditional QST methods often suffer from limitations in measurement efficiency and accuracy, particularly when dealing with complex quantum systems. This work presents an advanced approach to QST utilizing entangled photon sources and a meticulously designed measurement strategy. The core of this method lies in exploiting the correlations inherent in entangled photon pairs to significantly enhance the reconstruction process. We detail a novel scheme that minimizes measurement errors and maximizes the information extracted from each measurement, leading to a substantial improvement in both the accuracy and resolution of the reconstructed quantum state. The theoretical framework outlines the key equations and algorithms used for state reconstruction, focusing on a practical implementation. The results presented suggest a pathway towards more robust and reliable QST, paving the way for more accurate characterization of quantum systems and the development of advanced quantum applications.
Quantum state tomography (QST) is an essential tool for characterizing an unknown quantum state. Recently, QST has been performed for entangled qudits based on orbital angular momentum, time-energy uncertainty, and frequency bins. Here, we propose a QST for time-bin qudits, with which the number of measurement settings scales linearly with dimension d . Using the proposed scheme, we performed QST for a four-dimensional time-bin maximally entangled state with 16 measurement settings. We successfully reconstructed the density matrix of the entangled qudits, with which the average fidelity of the state was calculated to be 0.950.
Quantum state tomography (QST) aims at estimating a quantum state from averaged quantum measurements made on copies of that state. Most quantum algorithms rely on QST at some point and it is a well-explored topic in the literature, mostly for mixed states. In this paper we focus on the QST of a pure quantum state using parallel unentangled measurements. Pure states are a small but useful subset of all quantum states, and their tomography requires fewer measurements and is essentially a phase recovery problem. Parallel unentangled measurements are easy to implement in practice because they allow the user to measure each qubit individually, e.g., using one-qubit Pauli measurements. We propose two sets of quantum measurements that one can make on a pure state as well as the algorithms that use the measurement outcomes in order to identify the state. We also discuss how those estimates can be fine tuned by finding the state that maximizes the likelihood of the measurements with different variants of the likelihood. The performances of the proposed three types of QST methods are validated by means of detailed numerical tests, including for mixed states that are close to being pure.
Quantum state tomography (QST) estimates an unknown quantum state from a measurement process typically performed on identical copies of the target state and plays a core role in characterizing quantum information systems. However, because quantum measurement outcomes are probabilistic, QST methods often require many shots per basis to achieve high-fidelity estimates, which hinders scalability to many-qubit applications and slows the transmission of quantum information. A more efficient procedure is therefore required for modern-day quantum operations in quantum computing, communications, and sensing. We address this need with an adaptive QST approach that measures a single-qubit state in a wide set of bases. We include bases beyond the Pauli triad {X,Y,Z} by leveraging the infinite-dimensional Hilbert space of quantum mechanics, increasing the likelihood of producing highly polarized measurement outcomes and finding an optimally informative basis. With this basis, the state can be identified with fewer measurements by focusing on directions that most reduce uncertainty of the state. In addition to theoretical innovation in [9], we experimentally verify in a simplified photonic realization using 13 bases that having many more available measurement bases than the Pauli triad benefits QST. This engineering implementation demonstrates that adaptive QST is both efficient in performance and practical to implement.
Quantum State Tomography (QST) offers a novel approach to understanding complex systems by leveraging quantum mechanics. This paper introduces a quantum state tomography algorithm designed for efficiently mapping the state of a complex system based on measurements. The core mechanism involves utilizing quantum superposition and entanglement to create a probabilistic model of the system's state, enabling rapid, less-precise assessment. The algorithm's potential lies in its ability to overcome the computational limitations of traditional state tomography, opening new avenues for analyzing and interpreting intricate systems. This work demonstrates the feasibility of QST through a theoretical analysis and preliminary implementation, highlighting its promise for various scientific and engineering applications.