Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1504.06000 · Physical Review A

Process tomography via sequential measurements on a single quantum system

Humairah Bassa, Sandeep K. Goyal, Sujit K. Choudhary, Hermann Uys, Lajos Diósi, Thomas Konrad

Published Sep 3, 2015• 14 citations
arXivHTMLPDF

Abstract

We utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters is encoded into a continuous-variable classical system which is coupled to the two-level quantum system via a generalized Hamiltonian. This combined estimate of the quantum state and dynamical parameters is updated by using the information obtained from sequential measurements on the quantum system and, after a sufficient waiting period, faithful state monitoring and parameter determination is obtained. Numerical evidence is used to demonstrate the convergence of the state estimate to the true state of the hybrid system.

DOI
10.1103/physreva.92.032102

Related papers

Selective continuous-variable quantum process tomography

Virginia Feldman, Ariel Bendersky

Quantum process tomography is a useful tool for characterizing quantum processes. This task is essential for the development of different areas, such as quantum information processing. In this work, we present a protocol for selective continuous-variable quantum process tomography. Our proposal allows one to selectively estimate any element of an unknown continuous-variable quantum process in the position representation, without requiring the complete reconstruction of the process. By resorting to controlled squeezing and translation operations, and adaptatively discretizing the process, a direct measure of an estimate of any process element can be obtained. Furthermore, we show, supported by numerical simulations, how the protocol can be used to partially reconstruct on a region a continuous-variable quantum process.

arXiv:2410.17516•Physical Review A•Apr 4, 2025•1 citation

Quantum state tomography from a sequential measurement of two variables in a single setup

Antonio Di Lorenzo

We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{B}$, the eigenstates of which form bases connected by a discrete Fourier transform. The state can be pure or mixed, the dimension of the Hilbert space and the coupling strength are arbitrary, and the experimental setup is fixed. The concept of Moyal quasicharacteristic function is introduced for finite-dimensional Hilbert spaces.

arXiv:1303.7154•Physical Review A•Oct 17, 2013•13 citations

Quantum process tomography of unitary maps from time-delayed measurements

Irene López Gutiérrez, Felix Dietrich, Christian B. Mendl

Abstract Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known initial states together with time-delayed measurements for reconstructing the unitary map and corresponding Hamiltonian of the time dynamics. The overarching mathematical framework and feasibility guarantee of our method is provided by the Takens embedding theorem. We explain in detail how the reconstruction of a single-qubit Hamiltonian works in this setting and provide numerical methods and experiments for general few-qubit and lattice systems with local interactions. In particular, the method allows to find the Hamiltonian of a two qubit system by observing only one of the qubits.

arXiv:2112.09021•Quantum Information Processing•Jun 22, 2023•5 citations

Continuous Measurement Quantum State Tomography of Atomic Ensembles

Riofrio Almeida, A R Carlos

Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, ${}^{133}$Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace ($F=3 \oplus F=4$), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.

•Jan 1, 2012•3 citations

Continuous Measurement Quantum State Tomography of Atomic Ensembles

Carlos A. Riofrío

Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, ${}^{133}$Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace ($F=3 \oplus F=4$), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.

arXiv:1111.5627•Nov 23, 2011•2 citations

Identification of quantum closed systems via the quantum process tomography

Weiwei Zhou, S. G. Schirmer, Hongwei Xie +1 more

The dynamics of an unknown closed quantum system can be characterized by a Hamiltonian. We discuss the identification of this Hamiltonian from quantum process tomography data at several time points for systems with a time-independent Hamiltonian. Quantum process tomography (QPT) yields a set of unitary operators and allows us to convert the identification problem into an estimation problem for the eigenfrequencies of the system. Spectral decomposition of Hermitian and unitary operators shows that process tomography needs to be performed at least at two different time points and the identifiability of the Hamiltonian depends on the choice of these points. Sufficient conditions on the timing to ensure complete identifiability of the Hamiltonian are presented under the assumption that unitary matrices obtained from QPT are exact without numerical errors.

Chinese Control Conference (CCC)•Jul 25, 2012•0 citations
We utilize a discrete (sequential) measurement protocol to investigate quantum process tomography of a single two-level quantum system, with an unknown initial state, undergoing Rabi oscillations. The ignorance of the dynamical parameters is encoded into a continuous-variable classical system which is coupled to the two-level quantum system via a generalized Hamiltonian. This combined estimate of the quantum state and dynamical parameters is updated by using the information obtained from sequential measurements on the quantum system and, after a sufficient waiting period, faithful state monitoring and parameter determination is obtained. Numerical evidence is used to demonstrate the convergence of the state estimate to the true state of the hybrid system.
Quantum process tomography is a useful tool for characterizing quantum processes. This task is essential for the development of different areas, such as quantum information processing. In this work, we present a protocol for selective continuous-variable quantum process tomography. Our proposal allows one to selectively estimate any element of an unknown continuous-variable quantum process in the position representation, without requiring the complete reconstruction of the process. By resorting to controlled squeezing and translation operations, and adaptatively discretizing the process, a direct measure of an estimate of any process element can be obtained. Furthermore, we show, supported by numerical simulations, how the protocol can be used to partially reconstruct on a region a continuous-variable quantum process.
We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables, $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{A}$ and $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{B}$, the eigenstates of which form bases connected by a discrete Fourier transform. The state can be pure or mixed, the dimension of the Hilbert space and the coupling strength are arbitrary, and the experimental setup is fixed. The concept of Moyal quasicharacteristic function is introduced for finite-dimensional Hilbert spaces.
Abstract Quantum process tomography conventionally uses a multitude of initial quantum states and then performs state tomography on the process output. Here we propose and study an alternative approach which requires only a single (or few) known initial states together with time-delayed measurements for reconstructing the unitary map and corresponding Hamiltonian of the time dynamics. The overarching mathematical framework and feasibility guarantee of our method is provided by the Takens embedding theorem. We explain in detail how the reconstruction of a single-qubit Hamiltonian works in this setting and provide numerical methods and experiments for general few-qubit and lattice systems with local interactions. In particular, the method allows to find the Hamiltonian of a two qubit system by observing only one of the qubits.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133{}^{133}133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4F=3 \oplus F=4F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.
Quantum state tomography is a fundamental tool in quantum information processing. It allows us to estimate the state of a quantum system by measuring different observables on many identically prepared copies of the system. This is, in general, a very time-consuming task that requires a large number of measurements. There are, however, systems in which the data acquisition can be done more efficiently. In fact, an ensemble of quantum systems can be prepared and manipulated by external fields while being continuously and collectively probed, producing enough information to estimate its state. This provides a basis for continuous measurement quantum tomography. In this protocol, an ensemble of identically prepared systems is collectively probed and controlled in a time-dependent manner to create an informationally complete continuous measurement record. The measurement history is then inverted to determine the state at the initial time. We use two different estimation methods: maximum likelihood and compressed sensing. The general formalism is applied to the case of reconstruction of the quantum state encoded in the magnetic sub-levels of a large-spin alkali atom, 133{}^{133}133Cs. We apply this protocol to the case of reconstruction of states in the full 16-dimensional electronic-ground subspace (F=3⊕F=4F=3 \oplus F=4F=3⊕F=4), controlled by microwaves and radio-frequency magnetic fields. We present an experimental demonstration of continuous measurement quantum tomography in an ensemble of cold cesium atoms with full control of its 16-dimensional Hilbert space. We show the exquisite level of control achieved in the lab and the excellent agreement between the theory discussed in this dissertation and the experimental results. This allows us to achieve fidelities >95% for low complexity quantum states, and >92% for arbitrary random states, which is a formidable accomplishment for a space of this size.
The dynamics of an unknown closed quantum system can be characterized by a Hamiltonian. We discuss the identification of this Hamiltonian from quantum process tomography data at several time points for systems with a time-independent Hamiltonian. Quantum process tomography (QPT) yields a set of unitary operators and allows us to convert the identification problem into an estimation problem for the eigenfrequencies of the system. Spectral decomposition of Hermitian and unitary operators shows that process tomography needs to be performed at least at two different time points and the identifiability of the Hamiltonian depends on the choice of these points. Sufficient conditions on the timing to ensure complete identifiability of the Hamiltonian are presented under the assumption that unitary matrices obtained from QPT are exact without numerical errors.