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LOCC, or local operations and classical communication, is a method in quantum information theory where a local (product) operation is performed on part of the system, and where the result of that operation is "communicated" classically to another part where usually another local operation is performed. An example of this is distinguishing two Bell pairs, such as the following:
Contents
Let's say the two-qubit system is separated, where the first qubit is given to Alice and the second is given to Bob. Assume that Alice measures the first qubit, and obtains the result 0. We still don't know which Bell pair we were given. Alice sends the result to Bob over a classical channel, where Bob measures the second qubit, also obtaining 0. Bob now knows that since the joint measurement outcome is
These measurements contrasts with nonlocal or entangled measurements, where a single measurement is performed in
Entanglement convertibility
Nielsen has derived a general condition to determine whether one pure state of a bipartite quantum system may be transformed into another using only LOCC. Full details may be found in the paper referenced earlier, the results are sketched out here.
Consider two particles in a Hilbert space of dimension
The
In more concise notation:
This is a more restrictive condition that local operations cannot increase the degree of entanglement. It is quite possible that converting between
Catalytic conversion
Just after Nielsen published his theorem of majorization, the catalytic transformation by LOCC was proposed. Consider the states,
These states are written in the form of Schmidt decomposition and in a descending order. We compare the sum of the coefficients of
In the table, red color is put if
Now we consider the product states
Similarly, we make up the table:
The color in the