Explaining Holevo Additivity: A Simple Guide

[ppnl]

Can someone give a simple explanation of what this is about:

http://scienceblogs.com/pontiff/2008/09/holevo_additivity_falls_the_qu.php

I think I have a reasonable understanding of a classical information channel. I think I have a bare minimum understanding of a quantum information channel as the term is used to explain quantum teleportation. But I don't understand what it means to transmit classical information through a quantum channel.

Can someone provide a simple explanation for the rest of us?

 

[my_wan]

I don't think thinking of a "quantum information channel" in terms of "quantum teleportation" is particularly useful, misleading at best. The thing not to do here with regard to this blog is to assume a "quantum information channel" and quantum information are synonymous. The difference between a quantum and classical information 'channel' is based solely on how that information is encoded and not on the type of information.

A classical information channel is simply one where a piece of information is encoded in bits that have a definite state, like the zero and one representation of a computer. You can use it to store and/or transmit your phone number for instance. A quantum information "channel" is one in which the information, like the phone number, is stored most popularly in qubits, or a quantum state that can be in a superposition of the two states (zero or one) at any given time. The difference is not the information, only the way the information is encoded. The advantages of a "quantum information channel" only becomes apparent in the processing, not the storage, of that information.

Unfortunately people who talk to the public about quantum systems oftens tries so hard to get the weirdness factor across they create a lot of confusion with regard to basic empirical facts. Theoretical constructs and basic empirical facts often get conflated.

 

[denian]

Holevo additivity is a concept in quantum information theory that deals with the amount of classical information that can be transmitted through a quantum channel. A classical information channel is a means of transmitting information, such as through a telephone line or a fiber optic cable. In a classical channel, the amount of information that can be transmitted is limited by the bandwidth or capacity of the channel.

In a quantum channel, information is transmitted using quantum systems, such as photons or atoms. These systems can exist in multiple states at the same time, allowing for the transmission of more information than a classical channel. However, the amount of information that can be transmitted through a quantum channel is limited by the laws of quantum mechanics.

Holevo additivity states that the maximum amount of classical information that can be transmitted through a quantum channel is equal to the sum of the individual capacities of each subsystem of the channel. This means that the total capacity of a quantum channel is not greater than the sum of its parts, unlike in classical channels where the total capacity can be increased by combining multiple channels.

This concept has important implications for quantum communication and cryptography, as it helps us understand the limitations of quantum channels and how to optimize their use for transmitting information. Overall, Holevo additivity is a fundamental principle in quantum information theory that helps us better understand the capabilities and limitations of quantum channels.