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Universal Superposition of Orthogonal States (edit)
Revision as of 16:56, 19 March 2019
, 19 March 2019→Pseudo Code
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###'''Then:''' Accept the round | ###'''Then:''' Accept the round | ||
###'''Else:''' Reject. | ###'''Else:''' Reject. | ||
### The successful output is in the form: </br> | |||
<math>|\Psi\rangle = C(\alpha |\psi\rangle + \beta e^{i\eta} |\psi^\perp\rangle)</math></br> | <math>|\Psi\rangle = C(\alpha |\psi\rangle + \beta e^{i\eta} |\psi^\perp\rangle)</math></br> | ||
<math>e^{i\eta}</math> is a relative phase which is <math>\frac{\langle1|\psi\rangle}{\langle0|\psi^\perp\rangle}</math></br> | <math>e^{i\eta}</math> is a relative phase which is <math>\frac{\langle1|\psi\rangle}{\langle0|\psi^\perp\rangle}</math></br> | ||
#'''Mixed Output Case:''' Always accept. The protocol is perfect. | ##'''Mixed Output Case:''' | ||
###Always accept. The protocol is perfect. | |||
### The output will be:<math>|\Psi^{\mu,\nu} \rangle = C (\alpha |\psi\rangle + \beta e^{i\eta_{\mu,\nu}} |\psi^\perp\rangle) </math>, <math>e^{i\eta_{\mu,\nu}}</math> is a relative phase which depends on the outputs of the measurements but in all cases, the superposition has the desired form and weights. | |||
==Further Information== | ==Further Information== | ||
# [https://arxiv.org/abs/1708.04360 DKK(2017)] The above protocol | # [https://arxiv.org/abs/1708.04360 DKK(2017)] The above protocol | ||
# [https://arxiv.org/abs/1505.04955 OGHW(2016)] The first paper that talks about and proves the no-superposition theorem. Also in this paper, they present a probabilistic protocol for superposing two arbitrary (but not completely unknown) states where we know the overlaps of them with a fixed reference state. this protocol, is also restricted to a set of input states. | # [https://arxiv.org/abs/1505.04955 OGHW(2016)] The first paper that talks about and proves the no-superposition theorem. Also in this paper, they present a probabilistic protocol for superposing two arbitrary (but not completely unknown) states where we know the overlaps of them with a fixed reference state. this protocol, is also restricted to a set of input states. | ||