Restrictions on quantum operations give rise to resource theories. Total lack of a shared reference frame for transformations associated with a group G between two parties is equivalent to having, in effect, an invariant channel between the parties and a corresponding superselection rule (SSR). The resource associated with the absence of the reference frame is known as 'frameness' or 'asymmetry'. We show that any entanglement monotone for pure bipartite states can be adapted as a pure-state frameness monotone for phase-invariant channels (equivalently U(1) superselection rules) and extended to the case of mixed states via the convex-roof extension. As an application, we construct a family of concurrence monotones for U(1)-frameness for general finite-dimensional Hilbert spaces. Furthermore we study 'frameness of formation' for mixed states analogous to entanglement of formation. In the case of a qubit, we show that it can be expressed as an analytical function of the concurrence analogously to the Wootters's formula for entanglement of formation. Our results highlight deep links between entanglement and frameness resource theories.

We develop a theory of charge-parity-time (CPT) frameness resources to circumvent CPT superselection. We construct and quantify such resources for spin-0, 1/2, 1, and Majorana particles and show that quantum information processing is possible even with CPT superselection. Our method employs a unitary representation of CPT inversion by considering the aggregate action of CPT rather than the composition of separate C, P, and T operations, as some of these operations involve problematic antiunitary representations.

In closed systems, dynamical symmetries lead to conservation laws. However, conservation laws are not applicable to open systems that undergo irreversible transformations. More general selection rules are needed to determine whether, given two states, the transition from one state to the other is possible. The usual approach to the problem of finding such rules relies heavily on group theory and involves a detailed study of the structure of the respective symmetry group. We approach the problem in a completely new way by using entanglement to investigate the asymmetry properties of quantum states. To this end, we embed the space state of the system in a tensor product Hilbert space, whereby symmetric transformations between two states are replaced with local operations on their bipartite images. The embedding enables us to use the well-studied theory of entanglement to investigate the consequences of dynamic symmetries. Moreover, under reversible transformations, the entanglement of the bipartite image states becomes a conserved quantity. These entanglement-based conserved quantities are new and different from the conserved quantities based on expectation values of the Hamiltonian symmetry generators. Our method is not group-specific and applies to general symmetries associated with any compact semi-simple Lie group.

We develop a complete resource theory of charge-parity-time (CPT) inversion symmetry for both massive and massless relativistic particles of arbitrary spin. We show that a unitary representation of CPT can be consistently constructed for all spins and develop the resource theory associated with CPT super-selection, thereby identifying and quantifying the resources required to lift the super-selection rule.