14,008 research outputs found

    Coherifying quantum channels

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    Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required by quantum theory to explain a given stochastic process? Here, we address this problem by studying possible coherifications of a quantum channel Φ\Phi, i.e., we look for channels ΦC\Phi^{\mathcal{C}} that induce the same classical transitions TT, but are "more coherent". To quantify the coherence of a channel Φ\Phi we measure the coherence of the corresponding Jamio{\l}kowski state JΦJ_{\Phi}. We show that the classical transition matrix TT can be coherified to reversible unitary dynamics if and only if TT is unistochastic. Otherwise the Jamio{\l}kowski state JΦCJ_\Phi^{\mathcal{C}} of the optimally coherified channel is mixed, and the dynamics must necessarily be irreversible. To assess the extent to which an optimal process ΦC\Phi^{\mathcal{C}} is indeterministic we find explicit bounds on the entropy and purity of JΦCJ_\Phi^{\mathcal{C}}, and relate the latter to the unitarity of ΦC\Phi^{\mathcal{C}}. We also find optimal coherifications for several classes of channels, including all one-qubit channels. Finally, we provide a non-optimal coherification procedure that works for an arbitrary channel Φ\Phi and reduces its rank (the minimal number of required Kraus operators) from d2d^2 to dd.Comment: 20 pages, 8 figures. Published versio

    Direct Characterization of Quantum Dynamics: General Theory

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    The characterization of the dynamics of quantum systems is a task of both fundamental and practical importance. A general class of methods which have been developed in quantum information theory to accomplish this task is known as quantum process tomography (QPT). In an earlier paper [M. Mohseni and D. A. Lidar, Phys. Rev. Lett. 97, 170501 (2006)] we presented a new algorithm for Direct Characterization of Quantum Dynamics (DCQD) of two-level quantum systems. Here we provide a generalization by developing a theory for direct and complete characterization of the dynamics of arbitrary quantum systems. In contrast to other QPT schemes, DCQD relies on quantum error-detection techniques and does not require any quantum state tomography. We demonstrate that for the full characterization of the dynamics of n d-level quantum systems (with d a power of a prime), the minimal number of required experimental configurations is reduced quadratically from d^{4n} in separable QPT schemes to d^{2n} in DCQD.Comment: 17 pages, 6 figures, minor modifications are mad
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