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One central study that constitutes a major branch of quantum resource theoryis the hierarchy of states. This provides a broad understanding ofresourcefulness in certain tasks in terms of efficiency. Here, we investigatethe maximal superposition states, i.e., golden states, of the resource theoryof superposition. Golden states in the resource theory of coherence are verywell established; however, it is a very challenging task for superposition dueto the nonorthogonality of the basis states. We show that there are sets ofinner product settings that admit a golden state in high-dimensional systems.We bridge the gap between the resource theory of superposition and coherence inthe context of golden states by establishing a continuous relation by means ofa Gram matrix. In addition, immediate corollaries of our framework provide arepresentation of maximal states which reduces to the maximal state of thecoherence in the orthonormal limit of pure basis states.

Golden states in resource theory of superposition