Local operations and classical communication

[meteor]

What are the Local operations and classical communication that i keep hearing about?
It arises in quantum teleporting. Though i know that to perform quantum teleporting you need a classical channel (a phone line, an e-mail, etc) and I guess that classical communication refers to that, I still don't get the thing about local operations. It seems to me that is the fact to manipulate jointly the state that you want to teleport with the particle that you have in your possession of the quantum channel, but I'd like a concrete definition. Care to explain?

 

[slyboy]

Local operations means that Alice and Bob may each do anything allowed by quantum mechanics to their subsystem, but nothing that requires an interaction between their subsystems. This includes things like:

- Unitary operations
- Measurements
- Throwing away some particles
- Bringing in a new particle in a known state

All these things turn out to be useful in some quantum information protocols.

You are right about the classical communication bit. Usually, it is used so that Alice and Bob can communicate measurement results to one another, or so that they can share some classical correlations.

 

[R0man]

Local operations and classical communication (LOCC) is a concept in quantum information theory that refers to the manipulation of quantum systems through local operations and classical communication. In simpler terms, it means that any changes made to a quantum system can only be done by physically manipulating the system itself, and any information about the state of the system must be communicated through classical means, such as phone lines or emails.

In the context of quantum teleportation, LOCC refers to the steps involved in transferring the state of one quantum system to another distant system. This process requires a classical channel to send information about the state of the original system, and local operations to manipulate the state of the receiving system. The classical communication is necessary because quantum systems cannot be directly measured without collapsing their state, so the information about the state must be sent through classical means.

To put it simply, LOCC is a way to ensure that any changes or measurements made to a quantum system are done in a controlled and predictable manner, using classical communication to transmit information about the state. This is crucial in quantum teleportation and other quantum information processing tasks, as it helps maintain the integrity and coherence of the quantum system being manipulated.