Toward a fully relativistic theory of quantum information

Using negative partial information for quantum communication. (a) In these diagrams, time runs from top to bottom, and space is horizontal. The line marked “A" is Alice's space-time trajectory, while the line marked “B" is Bob's. Bob creates an eē pair (an Einstein-Podolski-Rosen pair) close to him, and sends the ebit over to Alice. Alice, armed with an arbitrary quantum state q, performs a joint measurement M on both e and q, and sends the two classical bits 2c she obtains from this measurement back to Bob (over a classical channel). When Bob receives these two cbits, he performs one out of four unitary transformations U on the anti-ebit he is still carrying, conditionally on the classical information he received. Having done this, he recovers the original quantum state q, which was "teleported" over to him. The partial information in e is one bit, while it is minus one for the antiebit. (b) In superdense coding, Alice sends two classical bits of information 2c over to Bob, but using only a single qubit in the quantum channel. This process is in a way the “dual" to the teleportation process, as Alice encodes the two classical bits by performing a conditional unitary operation U on the anti-ebit, while it is Bob that performs the measurement M on the ebit he kept and the qubit Alice sent.

Christoph Adami

Information theory is a statistical theory dealing with the relative state of detectors and physical systems.
Because of this physicality of information, the classical framework of Shannon needs to be extended to deal with quantum detectors, perhaps moving at relativistic speeds, or even within curved space-time.
Considerable progress toward such a theory has been achieved in the last fifteen years, while much is still not understood.
This review recapitulates some milestones along this road, and speculates about future ones.
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