# Optimal Measurements of Spin Direction

@article{Appleby2000OptimalMO, title={Optimal Measurements of Spin Direction}, author={David Marcus Appleby}, journal={International Journal of Theoretical Physics}, year={2000}, volume={39}, pages={2231-2252} }

The accuracy of a measurement of the spin direction of a spin-s particle ischaracterized for arbitrary half-integral s. The disturbance caused by themeasurement is also characterized. The approach is based on that taken in severalprevious papers concerning joint measurements of position and momentum. Asin those papers, a distinction is made between the errors of retrodiction andprediction. Retrodictive and predictive error relationships are derived. The POVMdescribing the outcome of a maximally… Expand

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It is proved that through a sequence of weak measurements of random directions of the collective spin component, sampled discretely or in a continuous measurement with random controls, one can approach the optimal bound of the spin-coherent-state positive-operator-valued-measure. Expand

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It is argued that, although the BLW approach (based on the Wasserstein two-deviation) has its uses, there are important physical situations where an operator approach is preferable, and the source of the difficulties is the problem of interpretation. Expand

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We present a correspondence between positive operator valued measures (POVMs) and sets of generalized coherent states. POVMs describe quantum observables and, similar to quantum states, quantum… Expand

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A systematic classification methodology is presented by using a sampling-based learning control (SLC) approach for quantum discrimination by simultaneously steering members belonging to different classes to their corresponding target states. Expand

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We introduce the concept of cloning for classes of observables and classify cloning machines for qubit systems according to the number of parameters needed to describe the class under investigation.… Expand

#### References

SHOWING 1-10 OF 27 REFERENCES

Measuring the quantum state of light

- Physics
- 1995

Abstract We analyse several schemes for measuring the quantum state of a single light mode. These schemes are useful for experimentalists to gain the maximum information about non-classical light… Expand

Quantum Mechanics on Phase Space

- Mathematics
- 1995

Preface. I: Basic quantum theory and the necessity for its revision. I.1. Classical mechanics of particles and fluids. I.2. Structure of a physical model: state, property (observable), measurement.… Expand

Quantum theory and measurement

- Physics
- 1983

The forty-nine papers collected here illuminate the meaning of quantum theory as it is disclosed in the measurement process. Together with an introduction and a supplemental annotated bibliography,… Expand

Operational Quantum Physics

- Mathematics
- 2001

Operational Quantum Physics offers a systematic presentation of quantum mechanics which makes exhaustive use of the full probabilistic structure of this theory. Accordingly the notion of an… Expand

Quantum Theory: Concepts and Methods

- Physics
- 1993

Preface. Part I: Gathering the Tools. 1. Introduction to Quantum Physics. 2. Quantum Tests. 3. Complex Vector Space. 4. Continuous Variables. Part II: Cryptodeterminism and Quantum Inseparability. 5.… Expand

Generalized Coherent States and Their Applications

- Mathematics
- 1986

I Generalized Coherent States for the Simplest Lie Groups.- 1. Standard System of Coherent States Related to the Heisenberg-Weyl Group: One Degree of Freedom.- 1.1 The Heisenberg-Weyl Group and Its… Expand

When is a quantum measurement

- Physics
- 1986

The measurement of a quantum system is not consummated until irreversible processes have destroyed all phase coherence between different possible outcomes of that measurement. It is inconsistent to… Expand

Int. J. Theor. Phys

- Int. J. Theor. Phys
- 1998

Commun. Math. Phys

- Commun. Math. Phys
- 1973

Proc. Phys. Math. Soc. Japan

- Proc. Phys. Math. Soc. Japan
- 1940