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Ref. 2 the entangling power was defined using a different notation (Formula presented)
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In Ref. 2 the entangling power was defined using a different notation (Formula presented)
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The SUM gate may create entanglement of (Formula presented) from the state (Formula presented) This entanglement is the maximum because the SUM gate may be implemented nonlocally using this much entanglement via a generalization of the Gottesmann-Chuang 29 gate. Both the DSUM and SWAP gates create entanglement of (Formula presented) from initial states where the qudits acted upon are maximally entangled with ancillas; this entanglement is the maximum possible for a system of this dimension. Similarly, without ancillas the maximum possible entanglement is (Formula presented) and this may be created via the DSUM gate from the initial state (Formula presented)
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The SUM gate may create entanglement of (Formula presented) from the state (Formula presented) This entanglement is the maximum because the SUM gate may be implemented nonlocally using this much entanglement via a generalization of the Gottesmann-Chuang 29 gate. Both the DSUM and SWAP gates create entanglement of (Formula presented) from initial states where the qudits acted upon are maximally entangled with ancillas; this entanglement is the maximum possible for a system of this dimension. Similarly, without ancillas the maximum possible entanglement is (Formula presented) and this may be created via the DSUM gate from the initial state (Formula presented)
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