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

Computer Science and Information Technologies (CSIT)

Reconstruction of quantum information after the measurement

Sergey S. Poghosyan, Taksu Cheon

Published Sep 1, 2013• 0 citations
Publisher

Abstract

We consider a weak value expansion of the Hermitian operator in terms of a set of operators formed from biorthogonal basis. The utility of the expansion is showcased with examples of spin one-half and spin one systems, where irreversible subset of stochastic matrices describing projective measurement on a mixed state is identified.
DOI
10.1109/csitechnol.2013.6710344

Related papers

Weak value expansion of quantum operators and its application in stochastic matrices

Taksu Cheon, Sergey S. Poghosyan

It is shown that any Hermitian operator can be expanded in terms of a set of operators formed from biorthogonal basis, and the expansion coefficients are given as products of weight functions and weak values, shedding a new light on the physical interpretation of the weak value. The utility of our approach is showcased with examples of spin one-half and spin one systems, where irreversible subset of stochastic matrices describing projective measurement on a mixed state is identified.

arXiv:1306.4767•Jun 20, 2013•2 citations

Quantum tomography via nonorthogonal basis and weak values

Juan J Díaz, Isabel Sainz, A. B. Klimov

Using a relation between a biorthogonal set of equiseparable bases and the weak values of the density matrix we derive an explicit formula for its tomographic reconstruction completely analogous to the standard mutually unbiased bases expansion.

arXiv:1602.04073•Physical Review A•Jun 26, 2015•4 citations

Hermitian conjugate measurement

Hiroaki Terashima, Masahito Ueda

We propose a class of probabilistic reversing operations on the state of a system that was disturbed by a weak measurement. It can approximately recover the original state from the disturbed state especially with an additional information gain using the Hermitian conjugate of the measurement operator. We illustrate the general scheme by considering a quantum measurement consisting of spin systems with an experimentally feasible interaction and show that the reversing operation simultaneously increases both the fidelity to the original state and the information gain with such a high probability of success that their average values increase simultaneously.

arXiv:0709.1210•Physical Review A•Jan 13, 2010•7 citations

Expanding Hermitian operators in a basis of projectors on coherent spin states

Stefan Weigert

The expectation values of a Hermitian operator in (2 s +1) 2 specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2 s +1) 2 coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system. The result guarantees that (almost) any experimentally desirable choice of directions is appropriate for reconstructing the state of a quantum spin by means of a Stern–Gerlach apparatus.

arXiv:quant-ph/9907101•Journal of Optics B Quantum and Semiclassical Optics•Oct 16, 2004•3 citations

Weak measurements in non-Hermitian systems

A. Matzkin

'Weak measurements'—involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement—are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the standard definition of the 'weak value' of an observable must be modified. These studies are undertaken in the context of bound-state scattering theory, a non-Hermitian formalism for which the involved Hilbert spaces are unambiguously defined and the metric operators can be explicitly computed. Numerical examples are given for a model system. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.

arXiv:1204.3296•Journal of Physics A Mathematical and Theoretical•Oct 23, 2012•8 citations

Complete characterization of post-selected quantum statistics using weak measurement tomography

Holger Friedrich Hofmann

The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back action, the quantum state reconstruction is also valid for the postselected subensembles usually considered in weak measurement paradoxes. It is shown that postselection can then be identified with a statistical decomposition of the initial density matrix into transient density matrices conditioned by the anticipated measurement outcomes. This result indicates that it is possible to ascribe the properties determined by the final measurement outcome to each individual quantum system before the measurement has taken place. The ``collapse'' of the pure state wave function in a measurement can then be understood in terms of the classical ``collapse'' of a probability distribution as new information becomes available.

arXiv:0907.0533•Physical Review A•Jan 6, 2010•59 citations
We propose a class of probabilistic reversing operations on the state of a system that was disturbed by a weak measurement. It can approximately recover the original state from the disturbed state especially with an additional information gain using the Hermitian conjugate of the measurement operator. We illustrate the general scheme by considering a quantum measurement consisting of spin systems with an experimentally feasible interaction and show that the reversing operation simultaneously increases both the fidelity to the original state and the information gain with such a high probability of success that their average values increase simultaneously.
The expectation values of a Hermitian operator in (2 s +1) 2 specific coherent states of a spin are known to determine the operator unambiguously. As shown here, (almost) any other set of (2 s +1) 2 coherent state projectors also provide a basis for self-adjoint operators. This is proved by considering the determinant of the Gram matrix associated with the coherent state projectors as a Hamiltonian of a fictitious classical spin system. The result guarantees that (almost) any experimentally desirable choice of directions is appropriate for reconstructing the state of a quantum spin by means of a Stern–Gerlach apparatus.
'Weak measurements'—involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement—are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the standard definition of the 'weak value' of an observable must be modified. These studies are undertaken in the context of bound-state scattering theory, a non-Hermitian formalism for which the involved Hilbert spaces are unambiguously defined and the metric operators can be explicitly computed. Numerical examples are given for a model system. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to 'Quantum physics with non-Hermitian operators'.
The reconstruction of quantum states from a sufficient set of experimental data can be achieved with arbitrarily weak measurement interactions. Since such weak measurements have negligible back action, the quantum state reconstruction is also valid for the postselected subensembles usually considered in weak measurement paradoxes. It is shown that postselection can then be identified with a statistical decomposition of the initial density matrix into transient density matrices conditioned by the anticipated measurement outcomes. This result indicates that it is possible to ascribe the properties determined by the final measurement outcome to each individual quantum system before the measurement has taken place. The ``collapse'' of the pure state wave function in a measurement can then be understood in terms of the classical ``collapse'' of a probability distribution as new information becomes available.