I am trying to understand (Local operations and Classical communication) LOCC operations, but there is something I do not know.

My first question is, what is the difference between a LOCC operation and a LOCC protocol?

Second, suppose a state $\rho$, if a LOCC operation applied to it you get an ensemble {$p_i$,$\sigma_i$}, $\rho \overset{\text{LOCC}}{\rightarrow} \{p_i,\sigma_i\}$ ($p_i$ is the probability to obtain $\sigma_i$). How can I describe this $\sigma_i$ in a formula? Is this dependent on the LOCC protocol which was used? Is it correct when I say that the index $i$ is generally an index family, because it depends on the number of communication rounds?


I guess the terminology is not completely standardised, but I see it in the following way:

An LOCC operation is an element of the class LOCC, which contains all local quantum operations and classical communication. In other words, an LOCC operation would be doing a local quantum operation or doing some classical communication.

An LOCC protocol is just a sequence of such operations. Usually, a protocol implements a task, such as distillation of entanglement or the like.

How to describe the set of LOCC operations and/or protocols? The set of quantum operations, for instance, is the set of completely positive trace preserving maps, which has a nice description in terms of Kraus operators for instance. The set LOCC in contrast has no such easy mathematical description. Therefore, specifying $\rho \stackrel{\mathrm{LOCC}}{\rightarrow} \{p_i,\sigma_i\}$ is harder and usually, people consider special protocols and/or special subsets of operations and only then try to write down a general form of such operations.

I would recommend having a look at the following paper, which explains a lot about the set of LOCC operations: https://arxiv.org/abs/1210.4583


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.