Recent progress in the resource theory of asymmetry and its applications

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Symmetry and symmetry breaking are among the central themes in physics and have attracted the interest of many physicists. Recently, the resource theory of asymmetry (RTA) [1-4], which approaches these issues from the perspective of resource theories, has been actively studied.

In the past few years, several foundational advances have been made in this framework. In particular, the iid-complete monotone that plays a role analogous to entanglement entropy has been identified for arbitrary compact Lie groups [2] as well as for arbitrary finite groups [3]. The resolution for compact Lie groups includes, as a corollary, a solution to the Marvian–Spekkens conjecture [4].

Building on this theoretical foundation, several developments related to the Wigner–Araki–Yanase (WAY) theorem [5-7] have also been obtained. These include extensions of the WAY theorem to the implementation of arbitrary unitary gates [8], and a unification of the WAY-type theorems, i.e. the WAY theorem, the Eastin–Knill theorem (a fundamental limitation on error correction under symmetry) [9], and the above unitary-gate results. The unification is formulated a universal trade-off inequality relating symmetry, irreversibility, and quantumness for arbitrary quantum dynamics [10]. Using this tradeoff relation, the WAY-type limitations can now be applied, for example, to quantum thermodynamics[11] and black hole evaporation [10] etc.

If time permits, I will also briefly touch upon some other recent developments, such as extensions of the above tradeoff and the WAY theorem to general resource theory beyond symmetry [12].