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arXiv:1308.3254 · Physics Letters A

Optimal processing of reversible quantum channels

Alessandro Bisio, Giacomo Mauro D’Ariano, Paolo Perinotti, Michal Sedlák

Published Apr 28, 2014• 15 citations
arXivHTMLPDF
DOI
10.1016/j.physleta.2014.04.042

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Telecloning and its reverse process, referred to as remote quantum-information concentration (RQIC), have been attracting considerable interest because of their potential applications in quantum-information processing. The previous RQIC protocols were focused on the reverse process of the optimal universal telecloning. We here study the reverse process of ancilla-free phase-covariant telecloning (AFPCT). It is shown that the quantum information originally distributed into two spatially separated qubits from a single qubit via the optimal AFPCT procedure can be remotely concentrated back to a single qubit with a certain probability by using an asymmetric W state as the quantum channel.
We introduce the resource-theoretic free energy of a quantum channel as the maximal work extractable from the channel as its output equilibrates to a thermal state and its reference system remains locally intact. It is proportional to the relative entropy between the given channel and the absolutely thermal channel. It attains a clear operational meaning as twice the asymptotic rates of athermality distillation and formation under Gibbs-preserving superchannels, which map one absolutely thermal channel to another for a given bath, thereby revealing the asymptotic reversibility of the resource theory of athermality for quantum channels. Consequently, we establish that the optimal extractable work in converting one channel to another through the asymptotic athermality distillation and formation tasks equals the difference in their free energies. We call this optimal work the thermodynamic work capacity of channel conversion. Quantum information processing and computing fundamentally concern the manipulation and transformation of quantum channels, which encompass quantum states, their transformations, and measurements. A quantitative characterization of the optimal thermodynamic work gain or expenditure in quantum information processing constitutes a key step toward formulating thermodynamics of quantum processes.
Reversible quantum channels play a fundamental role in quantum dynamics and quantum information processing. A quantum channel is reversible if there exists another quantum channel acting as its left inverse. Due to their intrinsic significance and wide applications, it is desirable to characterize reversible quantum channels from diverse perspectives. In this work, we study reversible quantum channels on finite-dimensional Hilbert spaces, with particular emphasis on the case of different input and output dimensions. We systematically present twenty-one equivalent characterizations of reversible quantum channels from algebraic, geometrical, and information-theoretical perspectives. Among these characterizations, some are well known, while others, implicit in the literature or formulated in other contexts, are clarified here; the Choi-state characterization is derived in this work. Specifically, we prove that the Choi states of reversible quantum channels admit three equivalent forms: the spectral, direct-sum, and tensor-product representations. These twenty-one equivalent characterizations establish a comprehensive framework for reversible quantum channels, provide diverse insights into the structural and information-theoretic properties of quantum channels, and facilitate applications of reversibility in quantum information processing such as quantum error correction, quantum teleportation, and quantum thermodynamics.