Conditional emergence of classical domain and branching of quantum histories

We outline the minimalistic measurement scheme (MMS) compatible with regular unitary evolution of a closed quantum system. Within this approach, a part of the system becomes informationally isolated (restricted) which leads to a natural emergence of the classical domain. This measurement scenario is a simpler alternative to environment-induced decoherence that reconciles unitarity of quantum mechanics (QM) with irreversible measurement process. In its basic version, MMS involves two ancilla qubits, A and X, entangled with each other and with the system S. Informational or thermodynamic cost of measurement is represented by the X qubit being isolated, i.e., becoming unavailable for future interactions with the rest of the system. Conditional upon this isolation, the A qubit, which plays the role of an apparatus, becomes classical and records the outcome of the measurement. Classicality is therefore both an emergent and reversible property, since breaking informational isolation of the X qubit would bring the apparatus back to the quantum realm. The MMS procedure may be used to perform von Neumann-style projective measurements or generalized ones, which corresponds to a positive-operator-valued measure (POVM). By repeating the same generalized measurement multiple times with different A and X qubits, one asymptotically approaches the wave-function collapse in the basis determined by the premeasurement process. We present a simple result for the total information extracted after N such weak measurements. Building upon MMS, we propose a construction that maps a history of a quantum system onto a set of A qubits. It resembles the consistent histories (CH) formulation of quantum mechanics but is distinct from it and is built entirely within the conventional QM. In particular, the consistency postulate of the CH formalism is not automatically satisfied but is rather an emerging property. Namely, each measurement event corresponds to the branching of mutually exclusive classical realities whose probabilities are additive. In a general case, however, the superposition between different histories is determined by the history density matrix.