Final answer:
Yes, one can project on an orthogonal basis for a multipartite system through local measurements and classical communication, within the field of quantum information science and subject to certain limitations related to the quantum state's properties.
Step-by-step explanation:
The concept of projecting on an orthogonal basis for a multipartite system using local measurements and classical communication is primarily associated with the field of quantum information science, which is a part of physics. In quantum mechanics, a multipartite system refers to a system that is composed of multiple, distinct subsystems, which may be entangled. An orthogonal basis is a set of vectors that are all perpendicular to each other, and in quantum mechanics, these vectors represent distinguishable states of the system.
To perform a projection onto an orthogonal basis in a multipartite system using local operations, each party must perform local measurements on their respective subsystems. These measurements are described by local observables, which project the state of each subsystem onto an element of a local basis. The use of classical communication allows the parties to share their measurement results and correlate their individual projections, thereby effectively projecting the state of the entire system onto the desired orthogonal basis.
It's important to note that while local measurements and classical communication (known as LOCC) can be used to perform certain projections, there may be limitations depending on the specific structure and entanglement properties of the quantum state in question. Such tasks fall under the study of quantum information theory and quantum computation.