# Difference between revisions of "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

## Source code

Click on "expand" to the right to view the MATLAB source code for this function.

## References

1. 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
2. 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
3. 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.