Test-measured Rényi divergences

01/14/2022
by   Milán Mosonyi, et al.
0

One possibility of defining a quantum Rényi α-divergence of two quantum states is to optimize the classical Rényi α-divergence of their post-measurement probability distributions over all possible measurements (measured Rényi divergence), and maybe regularize these quantities over multiple copies of the two states (regularized measured Rényi α-divergence). A key observation behind the theorem for the strong converse exponent of asymptotic binary quantum state discrimination is that the regularized measured Rényi α-divergence coincides with the sandwiched Rényi α-divergence when α>1. Moreover, it also follows from the same theorem that to achieve this, it is sufficient to consider 2-outcome measurements (tests) for any number of copies (this is somewhat surprising, as achieving the measured Rényi α-divergence for n copies might require a number of measurement outcomes that diverges in n, in general). In view of this, it seems natural to expect the same when α<1; however, we show that this is not the case. In fact, we show that even for commuting states (classical case) the regularized quantity attainable using 2-outcome measurements is in general strictly smaller than the Rényi α-divergence (which is unique in the classical case). In the general quantum case this shows that the above "regularized test-measured" Rényi α-divergence is not even a quantum extension of the classical Rényi divergence when α<1, in sharp contrast to the α>1 case.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/14/2021

Quantum Rényi divergences and the strong converse exponent of state discrimination in operator algebras

The sandwiched Rényi α-divergences of two finite-dimensional quantum sta...
research
11/01/2019

Update of a conditional probability by minimal divergence

The present paper investigates the situation that two events which are b...
research
07/16/2021

The strong converse exponent of discriminating infinite-dimensional quantum states

The sandwiched Rényi divergences of two finite-dimensional density opera...
research
09/07/2023

On the optimal error exponents for classical and quantum antidistinguishability

The concept of antidistinguishability of quantum states has been studied...
research
01/07/2022

Bregman divergence based em algorithm and its application to classical and quantum rate distortion theory

We formulate em algorithm in the framework of Bregman divergence, which ...
research
02/25/2018

Measuring quantum discord using the most distinguishable steered states

Any two-qubit state can be represented, geometrically, as an ellipsoid w...
research
05/27/2019

Private Learning and Regularized Optimal Transport

Private data are valuable either by remaining private (for instance if t...

Please sign up or login with your details

Forgot password? Click here to reset