## Can Two Differently Prepared Mixed Quantum-Ensembles be Discriminated Via Measurement Variance ?

**Authors:** C S Sudheer Kumar

Alice prepares two large qubit-ensembles E1 and E2 in the following states: She individually prepares each qubit of E1 in |0> or |1>, the eigenstates of Pauli-z operator Z, depending on the outcome of an unbiased coin toss. Similarly, she individually prepares each qubit of E2 in |+> or |-> the eigenstates of Pauli-x operator X. Bob, who is aware of the above states preparation procedures, but knows neither which of the two is E1 nor Alice's outcomes of coin tosses, needs to discriminate between the two maximally mixed ensembles. Here we argue that Bob can partially purify the mixed states (E1, E2), using the information supplied by central limit theorem. We will show that, subsequently Bob can discriminate between ensembles E1 and E2 by individually rotating each qubit state about the x-axis on Bloch sphere by a random angle, and then projectively measuring Z. By these operations, the variance of sample mean of Z measurement outcomes corresponding to the ensemble E1 gets reduced. On the other hand, qubit states in E2 are invariant under the x-rotations and therefore the variance remains unaltered. Thus Bob can discriminate between the two maximally mixed ensembles. We analyse the above problem both analytically as well as numerically, and show that the latter supports the former.

**Comments:** 21 Pages.

**Download:** **PDF**

### Submission history

[v1] 2017-02-06 14:22:10

[v2] 2017-04-23 13:45:58

**Unique-IP document downloads:** 31 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*