This document goals at explaining why (sections 1-4) we're resulted in ponder heavily the duality method of robust interactions, either from analogy with the same method of the speculation of nuclear reactions, and as a potential manner out of the disagreeable deadlock into which quantum relativistic theories of robust interactions appear to be pressured. subsequent we will talk about how (sections 5-6) we cross approximately discovering options to the limitations of a twin thought and what their houses are. ultimately, a few principles could be offered touching on the place (section 7) all this may carry us within the close to destiny.
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Extra resources for An introduction to dual models of strong interaction and their physical motivations
If we allow entanglement over blocks of a large length we thus recover the full classical capacity: Cc,1 (T ) ≤ Cc(T ) = sup 1 Cc,1 (T ⊗ ) . 21) It is not clear, whether equality holds here. ”. At the moment all partial results known to me seem to say that this is not the case. Comparison with other error criteria Coming now to the quantum capacity Cq (T ), we have relate our definition to more current ones. One version, first stated by Bennett is very similar to the one given above, but differs slightly in the error quantity, which is required to go to zero.
The ancilla form of a channel T is obtained by tensoring the Hilbert spaces Cm and Cn ⊗ C with suitable tensor factors Ca and Cb , so that ma = n b. One picks pure states in ψa ∈ Ca and ψb ∈ Cb and looks for a unitary extension of the map V φ ⊗ ψa = (V φ) ⊗ ψb . There are many ways to do this, and this is a weakness of the ancilla approach in practical computations: one is always forced to specify an initial state ψa of the ancilla, and many matrix elements of the unitary interaction, which in the end drop out of all results.
One picks pure states in ψa ∈ Ca and ψb ∈ Cb and looks for a unitary extension of the map V φ ⊗ ψa = (V φ) ⊗ ψb . There are many ways to do this, and this is a weakness of the ancilla approach in practical computations: one is always forced to specify an initial state ψa of the ancilla, and many matrix elements of the unitary interaction, which in the end drop out of all results. As the uniqueness clause in the Stinespring Theorem shows, it is the isometry V which neatly captures the relevant part of the ancilla picture.