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

Springer eBooks

Blind Separation of Quantum States: Estimating Two Qubits from an Isotropic Heisenberg Spin Coupling Model

Yannick Deville, Alain Deville

Published Dec 18, 2007• 25 citations
Publisher
DOI
10.1007/978-3-540-74494-8_88

Related papers

Maximum Likelihood Blind Separation of Two Quantum States (QUBITS) with Cylindrical-Symmetry Heisenberg Spin Coupling

Yannick Deville, Alain Deville

Blind source separation (BSS) and quantum information processing (QIP) are two recent and rapidly evolving fields. No connection has ever been made between them to our knowledge, except in our initial paper, However, future practical QIP systems will probably involve "observed mixtures", in the BSS sense, of quantum states (qubits), e.g. associated to coupled spins. We here investigate how individual qubits may be retrieved from cylindrical-symmetry Heisenberg-coupled versions of them, and we show the relationship between this problem and classical BSS. We thus introduce a new nonlinear mixture model for qubits, motivated by actual quantum physical devices. We analyze the invertibility and ambiguities of this model. We propose practical data processing methods for (i) estimating the mixing parameter with a maximum likelihood approach and (ii) performing inversion to retrieve the sources. This yields a major extension as compared to our previous paper, not only in terms of considered spin coupling model, but also because we here introduce a much more powerful mixture estimation procedure.

IEEE International Conference on Acoustics Speech and Signal Processing•Mar 1, 2008•8 citations

Decoherence and entanglement of a pair of coupled qubits

Mohammad Mehdi Sahrapour, Nancy Makri

Bulletin of the American Physical Society•Mar 23, 2011•0 citations

The Blind Version of Quantum Process Tomography: Operating with Unknown Input Values

Yannick Deville, Alain Deville

System identification and inversion are two closely related problems, which lead to various configurations. In the quantum framework, system identification was only studied in the non-blind (or supervised) mode, i.e. with known input states (in addition to known output states). It is then called quantum process tomography. We here develop its blind (or unsupervised) version, operating with unknown (unentangled) input states (which are here not controlled by an automated loop). Our approach takes advantage of the blind quantum source separation (i.e. blind multi-qubit system inversion) methods based on disentanglement that we recently introduced. It is detailed for Heisenberg spin coupling and could be extended to other classes of processes. It estimates the parameter values of the Heisenberg Hamiltonian.

IFAC-PapersOnLine•Jul 1, 2017•9 citations

Entangled two-spin qubits

Richard J. Fitzgerald

Physics Today•Apr 19, 2012•0 citations

Effect of indirect dependencies on "Maximum likelihood blind separation of two quantum states (qubits) with cylindrical-symmetry Heisenberg spin coupling"

Yannick Deville, Alain Deville

In a previous paper [1], we investigated the Blind Source Separation (BSS) problem, for the nonlinear mixing model that we introduced in that paper. We proposed to solve this problem by using a maximum likelihood (ML) approach. When applying the ML approach to BSS problems, one usually determines the analytical expressions of the derivatives of the log-likelihood with respect to the parameters of the considered mixing model. In the literature, these calculations were mainly considered for linear mixtures up to now. They are more complex for nonlinear mixtures, due to dependencies between the considered quantities. Moreover, the notations commonly employed by the BSS community in such calculations may become misleading when using them for nonlinear mixtures, due to the above-mentioned dependencies. In this document, we therefore explain this phenomenon, by showing the effect of indirect dependencies on the application of the ML approach to the mixing model considered in [1]. This yields the explicit expression of the complete derivative of the log-likelihood associated to that mixing model.

arXiv:0906.0062•May 30, 2009•1 citation

QUANTUM MECHANICS OF QUBITS

WORLD SCIENTIFIC eBooks•Jul 21, 2019•0 citations
Blind source separation (BSS) and quantum information processing (QIP) are two recent and rapidly evolving fields. No connection has ever been made between them to our knowledge, except in our initial paper, However, future practical QIP systems will probably involve "observed mixtures", in the BSS sense, of quantum states (qubits), e.g. associated to coupled spins. We here investigate how individual qubits may be retrieved from cylindrical-symmetry Heisenberg-coupled versions of them, and we show the relationship between this problem and classical BSS. We thus introduce a new nonlinear mixture model for qubits, motivated by actual quantum physical devices. We analyze the invertibility and ambiguities of this model. We propose practical data processing methods for (i) estimating the mixing parameter with a maximum likelihood approach and (ii) performing inversion to retrieve the sources. This yields a major extension as compared to our previous paper, not only in terms of considered spin coupling model, but also because we here introduce a much more powerful mixture estimation procedure.
System identification and inversion are two closely related problems, which lead to various configurations. In the quantum framework, system identification was only studied in the non-blind (or supervised) mode, i.e. with known input states (in addition to known output states). It is then called quantum process tomography. We here develop its blind (or unsupervised) version, operating with unknown (unentangled) input states (which are here not controlled by an automated loop). Our approach takes advantage of the blind quantum source separation (i.e. blind multi-qubit system inversion) methods based on disentanglement that we recently introduced. It is detailed for Heisenberg spin coupling and could be extended to other classes of processes. It estimates the parameter values of the Heisenberg Hamiltonian.
In a previous paper [1], we investigated the Blind Source Separation (BSS) problem, for the nonlinear mixing model that we introduced in that paper. We proposed to solve this problem by using a maximum likelihood (ML) approach. When applying the ML approach to BSS problems, one usually determines the analytical expressions of the derivatives of the log-likelihood with respect to the parameters of the considered mixing model. In the literature, these calculations were mainly considered for linear mixtures up to now. They are more complex for nonlinear mixtures, due to dependencies between the considered quantities. Moreover, the notations commonly employed by the BSS community in such calculations may become misleading when using them for nonlinear mixtures, due to the above-mentioned dependencies. In this document, we therefore explain this phenomenon, by showing the effect of indirect dependencies on the application of the ML approach to the mixing model considered in [1]. This yields the explicit expression of the complete derivative of the log-likelihood associated to that mixing model.