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Higher-dimensional performance of port-based teleportation

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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.


PBT protocol for teleporting entanglement.When the input system C is half of an entangled state σDC, PBT will ‘swap’ the entanglement so that now systems D and Bi (corresponding to port i in Bob’s possession) become entangled. The joint quantum state σDC will have been transferred to . Finally, if σDC is initially maximally entangled, then the ‘global’ fidelity (including the entanglement with system D) of this teleportation is given by the so-called entanglement fidelity8 for this process.
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f1: PBT protocol for teleporting entanglement.When the input system C is half of an entangled state σDC, PBT will ‘swap’ the entanglement so that now systems D and Bi (corresponding to port i in Bob’s possession) become entangled. The joint quantum state σDC will have been transferred to . Finally, if σDC is initially maximally entangled, then the ‘global’ fidelity (including the entanglement with system D) of this teleportation is given by the so-called entanglement fidelity8 for this process.

Mentions: Port-based teleportation (PBT)1 is a variation of conventional quantum teleportation, which can be used as a universal processor. In PBT, Alice (the sender) and Bob (the receiver) share N pairs of entangled quantum states (without loss of generality we assume these to be maximally entangled). Then Alice performs a joint measurement (a positive operator valued measurement, POVM, ) on her resource and the input quantum state that she wishes to teleport. Finally, Alice tells Bob the measurement outcome i ∈ {0, 1, …, N}. If i = 0 the teleportation is considered to have failed, otherwise, Alice’s input state will have been teleported to the ith entangled partner (or port) in Bob’s possession, see Fig. 1. Unlike conventional teleportation2, PBT does not require any corrective unitary operation at Bob’s side other than to discard the unused ports, however, it achieves this at the cost of requiring more entanglement, while simultaneously realising only a finite probability of success.


Higher-dimensional performance of port-based teleportation
PBT protocol for teleporting entanglement.When the input system C is half of an entangled state σDC, PBT will ‘swap’ the entanglement so that now systems D and Bi (corresponding to port i in Bob’s possession) become entangled. The joint quantum state σDC will have been transferred to . Finally, if σDC is initially maximally entangled, then the ‘global’ fidelity (including the entanglement with system D) of this teleportation is given by the so-called entanglement fidelity8 for this process.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: PBT protocol for teleporting entanglement.When the input system C is half of an entangled state σDC, PBT will ‘swap’ the entanglement so that now systems D and Bi (corresponding to port i in Bob’s possession) become entangled. The joint quantum state σDC will have been transferred to . Finally, if σDC is initially maximally entangled, then the ‘global’ fidelity (including the entanglement with system D) of this teleportation is given by the so-called entanglement fidelity8 for this process.
Mentions: Port-based teleportation (PBT)1 is a variation of conventional quantum teleportation, which can be used as a universal processor. In PBT, Alice (the sender) and Bob (the receiver) share N pairs of entangled quantum states (without loss of generality we assume these to be maximally entangled). Then Alice performs a joint measurement (a positive operator valued measurement, POVM, ) on her resource and the input quantum state that she wishes to teleport. Finally, Alice tells Bob the measurement outcome i ∈ {0, 1, …, N}. If i = 0 the teleportation is considered to have failed, otherwise, Alice’s input state will have been teleported to the ith entangled partner (or port) in Bob’s possession, see Fig. 1. Unlike conventional teleportation2, PBT does not require any corrective unitary operation at Bob’s side other than to discard the unused ports, however, it achieves this at the cost of requiring more entanglement, while simultaneously realising only a finite probability of success.

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.