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:quant-ph/9809018 · Journal of Physics A Mathematical and General

Reconstructing a pure state of a spinsthrough three Stern-Gerlach measurements

Jean-Pierre Amiet, Stefan Weigert

Published Jan 1, 1999• 43 citations
arXivHTMLPDF

Abstract

Consider a spin s prepared in a pure state. It is shown that, generically, the moduli of the spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by means of a standard Stern-Gerlach apparatus. It is therefore possible to reconstruct a generic pure state on the basis of 6s independent measured intensities.

DOI
10.1088/0305-4470/32/15/006

Related papers

Reconstructing the density matrix of a spinsthrough Stern - Gerlach measurements

Jean-Pierre Amiet, Stefan Weigert

The Pauli problem is solved for a spin of length s prepared in an arbitrary (unnormalized) mixed state which has free real parameters. The reconstruction of its density operator is possible if one knows the probabilities of the spin components along each of directions in space. These probabilties are directly accessible through measurements performed with a Stern - Gerlach apparatus. A multipole expansion of the density operator establishes the link between the matrix elements of and the measured intensities.

Journal of Physics A Mathematical and General•Aug 7, 1998•19 citations

Coherent states and the reconstruction of pure spin states

Jean-Pierre Amiet, Stefan Weigert

Coherent states provide an appealing method to reconstruct efficiently the pure state of a quantum mechanical spin s . A Stern-Gerlach apparatus is used to measure (4 s +1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeros of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stern-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase space which are smaller than .

Journal of Optics B Quantum and Semiclassical Optics•Aug 13, 1999•32 citations

Coherent States and the Reconstruction of Pure Spin States

Jean-Pierre Amiet, Stefan Weigert

Coherent states provide an appealing method to reconstruct efficiently a pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s+1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeroes of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stern-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase-space which are smaller than hbar.

arXiv:quant-ph/9904036•Apr 8, 1999•0 citations

Coherent states and the reconstruction of pure spin states

Jean-Pierre Amiet, Stefan Weigert

Coherent states provide an appealing method to reconstruct efficiently the pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s+1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeroes of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stern-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase-space which are smaller than ¯h. To determine the unknown state of a quantum system poses a problem which is interesting from a theoretical, an experimental, and a conceptual point of view. To set up a successful approach to state reconstruction (see [1] and [2] for reviews) means to identify a collection of observables, a quorum, such that their expectation values contain

•Oct 1, 1999•0 citations

Determination of pure spin state from three measurements

Igor D. Ivanović

The author shows that the state determination of a pure spin state can be obtained from the results of three Stern-Gerlach type measurements. If the initial state is m=0 state, the selection of measurements cannot be made in advance.

Journal of Physics A Mathematical and General•Jul 7, 1993•6 citations

Reconstructing the density matrix of a spinsthrough Stern-Gerlach measurements: II

Jean-Pierre Amiet, Stefan Weigert

The density matrix of a spin s is fixed uniquely if the probabilites to obtain the value s upon measuring . are known for 4 s ( s +1) appropriately chosen directions in space. These numbers are just the expectation values of the density operator in coherent spin states, and they are easily obtained in an experiment carried out with a Stern-Gerlach apparatus. Furthermore, the experimental data is non-redundant, and it can be inverted explicitly which allows for a parametrization of the statistical operator by the 4 s ( s +1) positive parameters.

arXiv:quant-ph/9903067•Journal of Physics A Mathematical and General•Jan 1, 1999•38 citations
Consider a spin s prepared in a pure state. It is shown that, generically, the moduli of the spin components along three directions in space determine the state unambiguously. These probabilities are accessible experimentally by means of a standard Stern-Gerlach apparatus. It is therefore possible to reconstruct a generic pure state on the basis of 6s independent measured intensities.
The Pauli problem is solved for a spin of length s prepared in an arbitrary (unnormalized) mixed state which has free real parameters. The reconstruction of its density operator is possible if one knows the probabilities of the spin components along each of directions in space. These probabilties are directly accessible through measurements performed with a Stern - Gerlach apparatus. A multipole expansion of the density operator establishes the link between the matrix elements of and the measured intensities.
Coherent states provide an appealing method to reconstruct efficiently the pure state of a quantum mechanical spin s . A Stern-Gerlach apparatus is used to measure (4 s +1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeros of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stern-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase space which are smaller than .
Coherent states provide an appealing method to reconstruct efficiently a pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s+1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeroes of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stern-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase-space which are smaller than hbar.
Coherent states provide an appealing method to reconstruct efficiently the pure state of a quantum mechanical spin s. A Stern-Gerlach apparatus is used to measure (4s+1) expectations of projection operators on appropriate coherent states in the unknown state. These measurements are compatible with a finite number of states which can be distinguished, in the generic case, by measuring one more probability. In addition, the present technique shows that the zeroes of a Husimi distribution do have an operational meaning: they can be identified directly by measurements with a Stern-Gerlach apparatus. This result comes down to saying that it is possible to resolve experimentally structures in quantum phase-space which are smaller than ¯h. To determine the unknown state of a quantum system poses a problem which is interesting from a theoretical, an experimental, and a conceptual point of view. To set up a successful approach to state reconstruction (see [1] and [2] for reviews) means to identify a collection of observables, a quorum, such that their expectation values contain
The density matrix of a spin s is fixed uniquely if the probabilites to obtain the value s upon measuring . are known for 4 s ( s +1) appropriately chosen directions in space. These numbers are just the expectation values of the density operator in coherent spin states, and they are easily obtained in an experiment carried out with a Stern-Gerlach apparatus. Furthermore, the experimental data is non-redundant, and it can be inverted explicitly which allows for a parametrization of the statistical operator by the 4 s ( s +1) positive parameters.