# Power of unentangled measurements on two antiparallel spins

## Abstract

We consider a pair of antiparallel spins polarized in a random direction to encode quantum information. We wish to extract as much information as possible on the polarization direction attainable by an unentangled measurement, i.e., by a measurement whose outcomes are associated with product states. We develop analytically the upper bound 0.7935 bits to the Shannon mutual information obtainable by an unentangled measurement, which is definitely less than the value 0.8664 bits attained by an entangled measurement. This proves our main result, that not every ensemble of product states can be optimally distinguished by an unentangled measurement, if the measure of distinguishability is defined in the sense of Shannon. We also present results from numerical calculations and discuss briefly the case of parallel spins.

- Authors:

- Institute of Nuclear Research of the Hungarian Academy of Sciences, H-4001 Debrecen, P.O. Box 51 (Hungary)

- Publication Date:

- OSTI Identifier:
- 20982289

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. A; Journal Volume: 75; Journal Issue: 3; Other Information: DOI: 10.1103/PhysRevA.75.032343; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; INFORMATION THEORY; NUMERICAL ANALYSIS; POLARIZATION; QUANTUM CRYPTOGRAPHY; QUANTUM ENTANGLEMENT; QUANTUM INFORMATION; RANDOMNESS; SPIN; SPIN ORIENTATION

### Citation Formats

```
Vertesi, T.
```*Power of unentangled measurements on two antiparallel spins*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVA.75.032343.

```
Vertesi, T.
```*Power of unentangled measurements on two antiparallel spins*. United States. doi:10.1103/PHYSREVA.75.032343.

```
Vertesi, T. Thu .
"Power of unentangled measurements on two antiparallel spins". United States.
doi:10.1103/PHYSREVA.75.032343.
```

```
@article{osti_20982289,
```

title = {Power of unentangled measurements on two antiparallel spins},

author = {Vertesi, T.},

abstractNote = {We consider a pair of antiparallel spins polarized in a random direction to encode quantum information. We wish to extract as much information as possible on the polarization direction attainable by an unentangled measurement, i.e., by a measurement whose outcomes are associated with product states. We develop analytically the upper bound 0.7935 bits to the Shannon mutual information obtainable by an unentangled measurement, which is definitely less than the value 0.8664 bits attained by an entangled measurement. This proves our main result, that not every ensemble of product states can be optimally distinguished by an unentangled measurement, if the measure of distinguishability is defined in the sense of Shannon. We also present results from numerical calculations and discuss briefly the case of parallel spins.},

doi = {10.1103/PHYSREVA.75.032343},

journal = {Physical Review. A},

number = 3,

volume = 75,

place = {United States},

year = {Thu Mar 15 00:00:00 EDT 2007},

month = {Thu Mar 15 00:00:00 EDT 2007}

}