Coherence of quantum channels

Abstract

Coherence is a basic notion for quantum states. Instead of quantum states, in this work, We establish a resource theory for quantifying the coherence of Gaussian channels. To do this, we propose the definitions of incoherent Gaussian channels and incoherent Gaussian superchannels.

Validating and controlling quantum enhancement against noise by the motion of a qubit

“…makes the N-qubit state classical (diagonal) in the computational basis, which remains classical provided that each noisy channel is incoherent [68,69]. As a byproduct of the above main result, we have found the general behavior that larger velocities of the qubit strongly protect quantumness against noise.…”

“…As a matter of fact, one needs suitable blind intermediate measurements which make the system state classical (incoherent) so that it can remain classical for the remainder of the evolution. We remark that, once such measurements are found, they work for any open system dynamics arising from an incoherent channel, that is a channel incapable of creating quantum coherence in the state of the system [68,69]. Since one is interested in making the system state classical in the preferred computational basis, we find that the goal is inherently-accomplished by the nonselective projections…”

On coherence of quantum operations by using Choi-Jamiołkowski isomorphism

“…By Ref. [48], we have Lemma 1. If M is a coherence measure for quantum states in the Baumgratz-Cramer-Plenio (BCP) framework [10], then…”

“…It is well-know that in Hilbert space there is the phase-out operation, which can eliminate the coherence of the quantum state. Similarly, one can define the phase-out superoperation [48]. Since the incoherent states depend on the choice of the basis of the Hilbert space, so does the phase-out operation.…”

“…Obviously, we have the following result. e iθ iα |α i| on a single qubit [48], is largest in the unitary operations on a single qubit. Here θ iα is a real number.…”