# UPBSepDistinguishable

 Other toolboxes required UPBSepDistinguishable Determines whether or not a UPB is distinguishable by separable measurements CVX LocalDistinguishability 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