UPBSepDistinguishable

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 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.