ENTANGLEMENT SPECIFICATION:
TIME GOES BACKWARD AT THE OTHER SIDE OF THE BRIDGE
Bob Coecke
Consider a network in which appear only projectors on entangled states.
We show that we can apply classical functional reasoning, including
currying and GoI, on a ``virtual information flow'' where the functions
are not the projectors themselves but those functions obtained via the
isomorphism ${\cal V}\otimes{\cal W}\simeq[{\cal V}^*,{\cal W}]$ for the
corresponding entangled state on which we project. The flow is however
manifestly acausal but this remarkably doesn't seem to obstruct its
interpretation. The virtual information flows as if ``time goes backward
at the other side of the EPR-bridge''.
Then we provide a two-way compiler which translates entanglement
specification networks in an ordinary quantum computational setting of
measurements, unitary transformations and classical communication.
These two together provide a powerful tool for protocol and network
design, which unifies and simplifies the re-invention of teleportation,
entanglement swapping and many (new) others. Quantum information
processing can now be done in terms of a classical ``travelling
token''-interpretation, for which many high-level specification
languages are available.
Interesting is the fact that the passage from bipartite entanglement to
multipartite entanglement goes with the passage of a network with a
virtual flow to one with virtual function boxes.
We also reconsider the results in [1] in the light of these new ones and
it follows that we can produce a much more economical realisation of
Geometry of interaction for quantum systems.
[1] S. Abramsky and B. Coecke. Physical traces: Classical vs. quantum
information processing. ENTCS 69 - CTCS'02 issue. arXiv:cs.CG/0207057
[2] B. Coecke. Entanglement Spcification I: Acausal functionality and
protocol generation. OUCL Research Report. (2003)
[3] B. Coecke. Entanglement Spcification II: Virtual components. OUCL
Research Report. (2003)