Hi everybody! I'm studying this paper "Unambiguous discrimination among quantum operations" http://pra.aps.org/abstract/PRA/v73/i4/e042301 and they state that(adsbygoogle = window.adsbygoogle || []).push({});

Ok, it's well known, but then I took a review of the notes to my course of quantum information and i found this not proven proposition: It is well known that a set of

quantum states can be perfectly distinguished if and only if

they are orthogonal to each other.

Well, I'm not able to arrange a sounded proof of this simple proposition: i guess i have to choose a base and decompose spectrally the operator but i'm not able to go on. could someone be so kind to show me how to do or at least to suggest me a book or a paper where i could find a proof? consider two states \rho_1 and \rho_2 (density operators) of a finite quantum system: if exists a projector \Pi_1 such that trace(\rho_1\Pi_1)=1 and trace(\rho_2\Pi_1)=0 then the two states are disntinguishable with certainty if and only if supp(\rho_1) is orthogonal to supp(\rho_2)

Thank!

**Physics Forums - The Fusion of Science and Community**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Theorem on projective measurement and 100% distinguishable states

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

Loading...

Similar Threads - Theorem projective measurement | Date |
---|---|

I Projection Postulate vs Quantum Randomness | Feb 14, 2018 |

I Bell's Theorem and Reality | Feb 13, 2018 |

A Time independence of a Noether charge in QFT? | Feb 10, 2018 |

A Probability of obtaining general quantum measurement outcome | Feb 5, 2018 |

A Fundamental Theorem of Quantum Measurements | Jan 24, 2018 |

**Physics Forums - The Fusion of Science and Community**