# UPBSepDistinguishable

UPBSepDistinguishable | |

Determines whether or not a UPB is distinguishable by separable measurements | |

Other toolboxes required | CVX |
---|---|

Related functions | LocalDistinguishability |

Function category | Distinguishing objects |

` UPBSepDistinguishable` is a function that determines whether or not a given UPB is perfectly distinguishable by separable measurements. This question is interesting because it is known that all UPBs are indistinguishable by LOCC measurements

^{[1]}, and all UPBs are distinguishable by PPT measurements. Separable measurements lie between these two classes.

## Syntax

`DIST = UPBSepDistinguishable(U,V,W,...)`

## Argument descriptions

`U,V,W,...`: Matrices, each with the same number of columns as each other, whose columns are the local vectors of the UPB.

## Examples

### Qutrit UPBs are distinguishable

It was shown in ^{[2]} that all UPBs in $\mathbb{C}^3 \otimes \mathbb{C}^3$ are distinguishable by separable measurements. We can verify this fact for the "Tiles" UPB as follows:

```
>> [u,v] = UPB('Tiles'); % generates the "Tiles" UPB
>> UPBSepDistinguishable(u,v)
ans =
1
```

### The Feng UPB is indistinguishable

It was shown in ^{[3]} that the UPB in $\mathbb{C}^4 \otimes \mathbb{C}^4$ found by K. Feng is indistinguishable by separable measurements. We can confirm this fact as follows:

```
>> [u,v] = UPB('Feng4x4'); % generates the "Feng" UPB
>> UPBSepDistinguishable(u,v)
ans =
0
```

## Source code

Click here to view this function's source code on github.

## References

- ↑ C. Bennett, D. DiVincenzo, T. Mor, P. Shor, J. Smolin, and B. Terhal. Unextendible product bases and bound entanglement.
*Physical Review Letters*, 82(26):5385–5388, 1999. E-print: arXiv:quant-ph/9808030 - ↑ D. DiVincenzo, T. Mor, P. W. Shor, J. Smolin, and B. Terhal. Unextendible product bases, uncompletable product bases and bound entanglement.
*Communications in Mathematical Physics*, 238(3):379–410, 2003. E-print: arXiv:quant-ph/9908070 - ↑ S. Bandyopadhyay, A. Cosentino, N. Johnston, V. Russo, J. Watrous, and N. Yu.
*Limitations on separable measurements by convex optimization*. E-print: arXiv:1408.6981 [quant-ph], 2014.