# Quantum Information: What Is It All About?

## Abstract

**:**

## 1. Introduction

## 2. Classical Information Theory

## 3. Quantum Probabilities

## 4. Quantum Measurements

## 5. Incompatible Properties

#### 5.1. Issues of Logic

#### 5.2. Compatible and Incompatible

#### 5.3. The Single Framework Rule

## 6. Quantum Information Theory I

## 7. Quantum Information Theory II

## 8. Conclusions

## Acknowledgments

## Conflicts of Interest

## References

- Bell, J.S. Against measurement. In Sixty-Two Years of Uncertainty; Miller, A.I., Ed.; Plenum Press: New York, NY, USA, 1990; pp. 17–31. [Google Scholar] Reprinted in Speakable and Unspeakable in Quantum Mechanics, 2nd ed.; Cambridge University Press: Cambridge, UK, 2004; pp. 213–231.
- Von Neumann, J. Mathematical Foundations of Quantum Mechanics; Princeton University Press: Princeton, NJ, USA, 1955. [Google Scholar]
- Griffiths, R.B. What quantum measurements measure. Phys. Rev. A
**2017**, 96, 32110. [Google Scholar] [CrossRef] - Birkhoff, G.; von Neumann, J. The logic of quantum mechanics. Ann. Math.
**1936**, 37, 823–843. [Google Scholar] [CrossRef] - Griffiths, R.B. Consistent Quantum Theory; Cambridge University Press: Cambridge, UK, 2002. [Google Scholar]
- Griffiths, R.B. Quantum locality. Found. Phys.
**2011**, 41, 705–733. [Google Scholar] [CrossRef] - Griffiths, R.B. The New Quantum Logic. Found. Phys.
**2014**, 44, 610–640. [Google Scholar] [CrossRef] - Isham, C.J. Quantum logic and the histories approach to quantum theory. J. Math. Phys.
**1994**, 35, 2157–2185. [Google Scholar] [CrossRef] - Griffiths, R.B. The Consistent Histories Approach to Quantum Mechanics. Stanford Encyclopedia of Philosophy, 2014. Available online: http://plato.stanford.edu/entries/qm-consistent-histories/ (accessed on 29 November 2017).
- Griffiths, R.B. A consistent quantum ontology. Stud. Hist. Philos. Mod. Phys.
**2013**, 44, 93–114. [Google Scholar] [CrossRef] - Gell-Mann, M.; Hartle, J.B. Classical equations for quantum systems. Phys. Rev. D
**1993**, 47, 3345–3382. [Google Scholar] [CrossRef] - Omnès, R. Understanding Quantum Mechanics; Princeton University Press: Princeton, NJ, USA, 1999. [Google Scholar]
- Cover, T.M.; Thomas, J.A. Elements of Information Theory, 2nd ed.; Wiley: New York, NY, USA, 2006. [Google Scholar]
- Griffiths, R.B. Consistent quantum measurements. Stud. Hist. Philos. Mod. Phys.
**2015**, 52, 188–197. [Google Scholar] [CrossRef] - Nielsen, M.A.; Chuang, I.L. Quantum Computation and Quantum Information; Cambridge University Press: Cambridge, UK, 2000. [Google Scholar]
- Griffiths, R.B. Types of quantum information. Phys. Rev. A
**2007**, 76, 062320. [Google Scholar] [CrossRef] - Renes, J.M.; Dupuis, F.; Renner, R. Efficient polar coding of quantum information. Phys. Rev. Lett.
**2012**, 109, 050504. [Google Scholar] [CrossRef] [PubMed] - Coles, P.J.; Piani, M. Complementary sequential measurements generate entanglement. Phys. Rev. A
**2014**, 89, 010302. [Google Scholar] [CrossRef] - Bennett, C.H.; Brassard, G.; Crépeau, C.; Jozsa, R.; Peres, A.; Wootters, W.K. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett.
**1993**, 70, 1895–1899. [Google Scholar] [CrossRef] [PubMed] - Griffiths, R.B.; Niu, C.-S. Semiclassical Fourier transform for quantum computation. Phys. Rev. Lett.
**1996**, 76, 3228–3231. [Google Scholar] [CrossRef] [PubMed]

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**MDPI and ACS Style**

Griffiths, R.B.
Quantum Information: What Is It All About? *Entropy* **2017**, *19*, 645.
https://doi.org/10.3390/e19120645

**AMA Style**

Griffiths RB.
Quantum Information: What Is It All About? *Entropy*. 2017; 19(12):645.
https://doi.org/10.3390/e19120645

**Chicago/Turabian Style**

Griffiths, Robert B.
2017. "Quantum Information: What Is It All About?" *Entropy* 19, no. 12: 645.
https://doi.org/10.3390/e19120645