We propose an alternative framework for quantifying coherence. The framework is based on a natural property of coherence, the additivity of coherence for subspace-independent states, which is described by an operation-independent equality rather than operation-dependent inequalities and therefore applicable to various physical contexts. Our framework is compatible with all the known results on coherence measures but much more flexible and convenient for applications, and by using it many open questions can be resolved.We propose an alternative framework for quantifying coherence. The framework is based on a natural property of coherence, the additivity of coherence for subspace-independent states, which is described by an operation-independent equality rather than operation-dependent inequalities and therefore applicable to various physical contexts. Our framework is compatible with all the known results on coherence measures but much more flexible and convenient for applications, and by using it many open questions can be resolved.

arXiv:1606.03181Physical Review ADec 27, 2016185 citations

Diagnosing quantum channel decoherence via vector coherent mode decomposition

Kenneth A. Menard

High-dimensional quantum key distribution (HD-QKD) is limited by atmospheric turbulence, which scrambles the spatial modes used to encode information. A critical challenge is the lack of general methods to diagnose how this decoherence occurs. We apply the vector coherent mode decomposition (VCMD)-a numerical framework that represents a partially coherent beam as an incoherent superposition of its natural, orthogonal eigenmodes-as a powerful diagnostic engine for this problem. We simulate a qudit state propagating through a turbulent channel and use VCMD to quantify the decay of channel fidelity and reveal the exact spatial structure of the dominant error modes. This provides a complete modal fingerprint of the channel's decoherence mechanism. To establish the framework's credibility, we first validate its accuracy against a benchmark suite, including unmasking a deceptive "Masked Gaussian" beam and quantifying the purity of a decohered optical skyrmion. While the theory of vector coherence is established, this work consolidates it into a practical, basis-independent framework and applies it to discover the physical error modes of a turbulent quantum channel, a task for which conventional, basis-dependent methods are ill-suited.High-dimensional quantum key distribution (HD-QKD) is limited by atmospheric turbulence, which scrambles the spatial modes used to encode information. A critical challenge is the lack of general methods to diagnose how this decoherence occurs. We apply the vector coherent mode decomposition (VCMD)-a numerical framework that represents a partially coherent beam as an incoherent superposition of its natural, orthogonal eigenmodes-as a powerful diagnostic engine for this problem. We simulate a qudit state propagating through a turbulent channel and use VCMD to quantify the decay of channel fidelity and reveal the exact spatial structure of the dominant error modes. This provides a complete modal fingerprint of the channel's decoherence mechanism. To establish the framework's credibility, we first validate its accuracy against a benchmark suite, including unmasking a deceptive "Masked Gaussian" beam and quantifying the purity of a decohered optical skyrmion. While the theory of vector coherence is established, this work consolidates it into a practical, basis-independent framework and applies it to discover the physical error modes of a turbulent quantum channel, a task for which conventional, basis-dependent methods are ill-suited.

Journal of the Optical Society of America ADec 23, 20254 citations

Quantifying coherence of quantum channels based on the

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