Higher-dimensional performance of port-based teleportation

TY - JOUR

T1 - Higher-dimensional performance of port-based teleportation

AU - Wang, Zhiwei

AU - Braunstein, Samuel Leon

N1 - © Authors, 2016

PY - 2016/9/8

Y1 - 2016/9/8

N2 - Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction. However, its behavior for higher-dimensional systems has been hard to calculate explicitly beyond dimension d = 2. Indeed, relying on conventional Hilbert-space representations entails an exponential overhead with increasing dimension. Some general upper and lower bounds for various success measures, such as (entanglement) fidelity, are known, but some become trivial in higher dimensions. Here we construct a graph-theoretic algebra (a subset of Temperley-Lieb algebra) which allows us to explicitly compute the higher-dimensional performance of PBT for so-called “pretty-good measurements” with negligible representational overhead. This graphical algebra allows us to explicitly compute the success probability to distinguish the different outcomes and fidelity for arbitrary dimension d and low number of ports N, obtaining in addition a simple upper bound. The results for low N and arbitrary d show that the entanglement fidelity asymptotically approaches N/d^2 for large d, confirming the performance of one lower bound from the literature.

AB - Port-based teleportation (PBT) is a variation of regular quantum teleportation that operates without a final unitary correction. However, its behavior for higher-dimensional systems has been hard to calculate explicitly beyond dimension d = 2. Indeed, relying on conventional Hilbert-space representations entails an exponential overhead with increasing dimension. Some general upper and lower bounds for various success measures, such as (entanglement) fidelity, are known, but some become trivial in higher dimensions. Here we construct a graph-theoretic algebra (a subset of Temperley-Lieb algebra) which allows us to explicitly compute the higher-dimensional performance of PBT for so-called “pretty-good measurements” with negligible representational overhead. This graphical algebra allows us to explicitly compute the success probability to distinguish the different outcomes and fidelity for arbitrary dimension d and low number of ports N, obtaining in addition a simple upper bound. The results for low N and arbitrary d show that the entanglement fidelity asymptotically approaches N/d^2 for large d, confirming the performance of one lower bound from the literature.

KW - Port-based teleportation

KW - Quantum information

UR - http://www.nature.com/articles/srep33004

U2 - 10.1038/srep33004

DO - 10.1038/srep33004

M3 - Article

SN - 2045-2322

VL - 6

JO - Scientific Reports

JF - Scientific Reports

M1 - 33004

ER -