Packaged Quantum States for Gauge-Invariant Quantum Computation and Communication

Packaged quantum states are gauge-invariant states in which all internal quantum numbers (IQNs) form an inseparable block. This feature gives rise to novel packaged entanglements that encompass all IQNs, which is important both for fundamental physics and for quantum technology. Here we develop a framework for gauge-invariant quantum information processing based on packaged quantum states. We propose the necessary and sufficient conditions for a valid packaged superposition state of a single particle and multi-particle. We then present the details of constructing gauge-invariant packaged qubits (or qudits), packaged gates, and packaged circuits (which commute with the total charge operator). These serve as alternative foundation for gauge-invariant quantum information science. We then adapt conventional quantum error-correction codes, quantum algorithms, and quantum communication protocols to the ($d \times D$)-dimensional hybrid-packaged subspace. This high-dimensional hybrid-packaged subspace is flexible for pruning and scaling to match available physics systems. Thus, packaged quantum information processing becomes feasible and testable. Our results show that the gauge-invariant packaged quantum states may provide a possible route toward robust, fault-tolerant, and secure quantum technologies.