Phase States, a Fully Separable Basis in the n-Qubit Computational Space

The article examines the Pegg–Barnett phase eigenstates and their embedding into an n-qubit computational framework using a Fock–binary mapping under condition that the truncated Hilbert space dimension is a power of two. In this setting, the phase eigenstates form a complete orthonormal basis of fully separable states, with each state factorizing into independent single-qubit components. As a result, all bipartite entanglement entropies vanish, and the reduced density matrices obtained by tracing over any subset of qubits remain pure. We further analyze the effects of dimension reduction by tracing out qubits: individual basis states remain pure under this process, while superpositions generally become mixed unless their coefficients satisfy a specific matching condition. These features establish phase states as a unique entanglement-free basis with potential applications in digitized quantum fields, qubit-based representations of bosonic modes, and controlled information processing where the management of entropy and correlations is crucial.