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Higher-dimensional performance of port-based teleportation

View Article: PubMed Central - PubMed

ABSTRACT

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/d2 for large d, confirming the performance of one lower bound from the literature.

No MeSH data available.


The performance of PBT for N = 2, 3, 4.Here we plot the success probability S (dashed lines) and entanglement fidelity Fe (solid lines) of PBT for N = 2, 3, 4 as a function of dimension d. As d increases, the success probability for the POVM approaches one, for increasing N we find this success probability decreases.
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f2: The performance of PBT for N = 2, 3, 4.Here we plot the success probability S (dashed lines) and entanglement fidelity Fe (solid lines) of PBT for N = 2, 3, 4 as a function of dimension d. As d increases, the success probability for the POVM approaches one, for increasing N we find this success probability decreases.

Mentions: We plot these measures of success probability in Fig. 2. Although only calculated for small N, we find that: (i) S quickly approaches one as d increases; (ii) the entanglement fidelity Fe goes to zero asymptotically with d with roughly the exponent of −2; and (iii) the average fidelity F is only slightly higher than Fe (note that F ≥ Fe must always hold). Across common values of N and d these results agree with the original analysis of PBT1.


Higher-dimensional performance of port-based teleportation
The performance of PBT for N = 2, 3, 4.Here we plot the success probability S (dashed lines) and entanglement fidelity Fe (solid lines) of PBT for N = 2, 3, 4 as a function of dimension d. As d increases, the success probability for the POVM approaches one, for increasing N we find this success probability decreases.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC5015100&req=5

f2: The performance of PBT for N = 2, 3, 4.Here we plot the success probability S (dashed lines) and entanglement fidelity Fe (solid lines) of PBT for N = 2, 3, 4 as a function of dimension d. As d increases, the success probability for the POVM approaches one, for increasing N we find this success probability decreases.
Mentions: We plot these measures of success probability in Fig. 2. Although only calculated for small N, we find that: (i) S quickly approaches one as d increases; (ii) the entanglement fidelity Fe goes to zero asymptotically with d with roughly the exponent of −2; and (iii) the average fidelity F is only slightly higher than Fe (note that F ≥ Fe must always hold). Across common values of N and d these results agree with the original analysis of PBT1.

View Article: PubMed Central - PubMed

ABSTRACT

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/d2 for large d, confirming the performance of one lower bound from the literature.

No MeSH data available.