Every true quantum experiment relies on interference effects, which are the physical manifestation of the superposition principle of quantum mechanics. In our work [WY], for the first time, we are able to derive universal measures of how strong the coherence of superposition is in any given quantum state. We do this by viewing superposition as a resource, and consider how it can be manipulated under so-called ‘incoherent’ operations [BCP].

Our main findings are simple formulas for how much pure coherence is contained in a given quantum state, by answering two fundamental questions: How efficiently can one transform the state into pure coherence (distillation)? And how efficient is the reverse process (formation)? It turns out that any quantum state that is not itself incoherent, however noisy it is, has some bit of pure coherence that can be extracted from it. At the same time, distillation and formation are in general not inverses to each other. Rather, there is irreversible loss of coherence in any cyclic process of first forming a noisy state from pure coherence and then distilling that coherence back to pure.

Traditionally, the degree of coherence is linked to the visibility of interference fringes in characteristic standardized experiments: double or multi-slit setups, interferometers, etc. In contrast, our approach quantifies the strength of coherence not with respect to a certain standard task, but by the performance at the best experiment tailored to the specific resource state.

In subsequent work [SCR+], we made a fruitful comparison between the resource of coherence, and another major manifestation of quantumness, entanglement, which intuitively is the natural form of quantum coherence as correlation. We did this by studying their interplay and mutual tradeoff in the basic quantum information task of “state merging”, a fundamental primitive protocol unifying data compression and error correction. We found various bounds on the tradeoff, suggesting that entanglement can be much more powerful than mere coherence.

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