arXiv:2403.18210

A unified view of direct measurement of quantum states, processes, and measurements

Kazuhisa Ogawa, TAKUMI MATSUURA, Akihisa Tomita

Published Mar 27, 2024• 0 citations

Abstract

The dynamics of a quantum system are characterized by three components: quantum state, quantum process, and quantum measurement. The proper measurement of these components is a crucial issue in quantum information processing. Recently, direct measurement methods have been proposed and demonstrated wherein each complex matrix element of these three components is obtained separately, without the need for quantum tomography of the entire matrix. Since these direct measurement methods have been proposed independently, no theoretical framework has been presented to unify them despite the time symmetry of quantum dynamics. In this study, we propose a theoretical framework to systematically derive direct measurement methods for these three components. Following this framework and further utilizing the basis-shift unitary transformation, we have derived the most efficient direct measurement method using qubit probes. Additionally, we have experimentally demonstrated the feasibility of the direct measurement method of quantum states using optical pulse trains.

DOI: 10.48550/arxiv.2403.18210

Related papers

Unified Framework for Direct Characterization of Kraus Operators, Observables, Density Matrices, and Weak Values Without Weak Interaction

Sahil Sahil, S Sohail

Generalized quantum measurements, described by positive operator-valued measures (POVMs), are essential for modeling realistic processes in open quantum systems. While quantum process tomography can fully characterize a POVM, it is resource-intensive and impractical when only specific POVM elements or matrix elements of a particular POVM element are of interest. Direct quantum measurement tomography offers a more efficient alternative but typically relies on weak interactions and complex structures of the system, environment, and probe as the dimension of the system increases, limiting its precision and scalability. Furthermore, characterizing a POVM element alone is insufficient to determine the underlying physical mechanism, as multiple Kraus operators can yield the same measurement statistics. In this work, we present a unified framework for the direct characterization of individual matrix elements of Kraus operators associated with specific POVM elements and arbitrary input states without requiring weak interaction, complex structures of the system-environment-probe or full process and state tomography. This framework naturally extends to projective measurements, enabling direct observable tomography, and to the characterization of unitary operations. Our method also captures modular and weak values of observables and Kraus operators, without invoking weak interaction approximations. We demonstrate potential implementations in optical systems, highlighting the experimental feasibility of our approach.

arXiv:2510.07789Oct 8, 20250 citations

Direct characterization of coherence of quantum detectors by sequential measurements

Liang Xu, Huichao Xu, Jie Xie +4 more

The quantum properties of quantum measurements are indispensable resources in quantum information processing and have drawn extensive research interest. The conventional approach to revealing quantum properties relies on the reconstruction of entire measurement operators by quantum detector tomography. However, many specific properties can be determined by a part of the matrix components of the measurement operators, which makes it possible to simplify the characterization process. We propose a general framework to directly obtain individual matrix elements of the measurement operators by sequentially measuring two noncompatible observables. This method allows us to circumvent the complete tomography of the quantum measurement and extract the required information. We experimentally implement this scheme to monitor the coherent evolution of a general quantum measurement by determining the off-diagonal matrix elements. The investigation of the measurement precision indicates the good feasibility of our protocol for arbitrary quantum measurements. Our results pave the way for revealing the quantum properties of quantum measurements by selectively determining the matrix components of the measurement operators.

arXiv:2111.10325Advanced PhotonicsNov 29, 20219 citations

Quantum Measurement on a Budget

Dylan H. Mahler

Quantum computation - the use of quantum systems as bits, or qubits, to perform computation - has been proven to be exponentially faster than what is thought possible with classical computation for several tasks. Quantum computers have the unique ability to store an amount of information that is exponential in the number of constituent particles used to encode that information. This property, which is arguably where quantum computers derive their power, makes it very difficult to characterize quantum systems. In order to fully characterize an unknown quantum state, a series of measurements must be performed on it and the state deduced from the results of those measurements. This process, called quantum tomography, is known to require exponential resources in the number of qubits. Both the number of measurements - the measurement complexity - and the number of times each measurement must be repeated - the sample complexity - present serious challenges when performing tomography. In addition, the measurement apparatus itself, which is usually a quantum system, must be characterized leading to even more experimental complexity. Here, I present three experiments which aim to reduce the experimental complexity of quantum tomography. The first aims to reduce the number of measurements needed to locate the decoherence-free subspaces of a noisy quantum channel. The process of locating these subspaces, which would normally require full process tomography, is performed with quadratically fewer measurement settings. The second experiment aims to characterize both an uncalibrated measurement apparatus and an unknown quantum state at the same time. With a specific model of measurement, it is found that an uncalibrated parameter of the measurement can be directly extracted using a single measurement. In the third experiment, I perform an experiment in which the optimal sample complexity for quantum state tomography is obtained using adaptivity: the ability to change measurement settings part way through an experiment. All three experiments were performed using the polarization degree of freedom of photons generated by spontaneous parametric downconversion. The source of photon pairs and the measurement techniques used are described in detail, along with the theory of quantum distinguishability and its relevance to tomography.

Jun 1, 20150 citations

Diagrammatic representation of direct measurement systems of quantum states, processes, and measurements

Kazuhisa Ogawa, H. Kobayashi, Akihisa Tomita

A diagrammatic representation that intuitively shows the relation between measurement systems using qubit probes and their outcomes is introduced. This representation enables us to design direct measurement systems of quantum states, processes, and measurements systematically.

The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meetingJan 1, 20190 citations

Efficient non-destructive direct characterization of arbitrary many-body quantum channels

Zhiyuan Wang, Qing He, Zijing Zhang

Quantum process tomography (QPT) is a crucial technique for characterizing unknown quantum channels. However, traditional QPT methods encounter scalability problems as the particle numbers increase, requiring exponentially more state preparations and measurement operators. The characteristics of sparse target channels (e.g., multiqubit phase-shift gates) can be obtained by measuring only a few specific matrix elements without requiring global QPT. Therefore, direct quantum channel characterization is vital. This paper proposes a direct protocol for both qubit and qudit systems that extracts specific process matrix elements without full reconstruction. The measurement operator requirements remain independent of system size and dimensionality. Notably, the proposed protocol uses nondestructive measurements and preserves qubits after evolution through unknown processes for potential reuse, making it uniquely promising for applications such as real-time monitoring of noise processes in quantum error correction and real-time feedback control requiring quantum state preservation. To validate the theoretical correctness of our approach, we conducted experimental demonstrations of both the unitary and non-unitary processes of single qubits using a nuclear magnetic resonance system on the SpinQ quantum cloud platform. The experimental results confirmed the correctness and effectiveness of the proposed method.

npj Quantum InformationDec 14, 20251 citation

Dynamic Time Matrix and Quantum Measurement

Jincheng Zhang

This paper explores the intersection of dynamic time matrices and quantum measurement, presenting a novel approach to modeling quantum system dynamics in time-dependent environments. We introduce a dynamic time matrix framework that explicitly links quantum measurements to the evolution of time matrices, offering a new perspective on how measurement influences the state of a quantum system. The core mechanism involves the concept of "time quantum jumps," which mathematically represent the dynamic transformation of the time matrix itself, thereby providing a robust mathematical tool for studying quantum systems. This work aims to advance our understanding of quantum systems' behavior by providing a more intuitive and mathematically rigorous framework for investigating time-dependent quantum processes.

Aug 31, 20260 citations