Quantum Darwinism in a Composite System: Objectivity versus Classicality

Abstract

We investigate the implications of quantum Darwinism in a composite quantum system with interacting constituents exhibiting a decoherence-free subspace. We consider a two-qubit system coupled to an N-qubit environment via a dephasing interaction. For excitation preserving interactions between the system qubits, an analytical expression for the dynamics is obtained. It demonstrates that part of the system Hilbert space redundantly proliferates its information to the environment, while the remaining subspace is decoupled and preserves clear non-classical signatures. For measurements performed on the system, we establish that a non-zero quantum discord is shared between the composite system and the environment, thus violating the conditions of strong Darwinism. However, due to the asymmetry of quantum discord, the information shared with the environment is completely classical for measurements performed on the environment. Our results imply a dichotomy between objectivity and classicality that emerges when considering composite systems.

Why we should interpret density matrices as moment matrices: the case of (in)distinguishable particles and the emergence of classical reality

“…Quantum Darwinism tries to overcome this issue by interpreting pointer observables as information about a physical system that the environment selects and proliferates among m observers. Using the quantum de Finetti theorem, [48] proved that classical reality emerges at the increase of m. Indeed, the setting we used in the last example paper is similar to the one described in [49]: two-qubit system coupled to an N-qubit system.…”

Correlations, Information Backflow, and Objectivity in a Class of Pure Dephasing Models

“…Let us first study the establishment and spread of correlations in the considered scenarios. As discussed in detail in many publications [ 6 , 23 , 24 , 25 , 40 , 41 , 42 , 43 , 44 ], this feature might have an impact on the notion of objectivity for a quantum state, in the spirit of so-called quantum Darwinism [ 3 ] (see, for example, ref. [ 7 ] for a recent review and references therein).…”

Thermality versus Objectivity: Can They Peacefully Coexist?

“…The environment, when acting as a heat bath, can lead to the equilibration and thermalisation of quantum systems [5][6][7][8][9]. Meanwhile, in an approach to the quantumto-classical transition called Quantum Darwinism [10][11][12][13][14], the environment plays a key role in the process of how quantum systems appear classically objective [13,14]-whereby classical objective systems have properties that are equivalently independently verifiable by independent observers. In the realm of open quantum systems, whether one process or another occurs depends on multiple factors, including details of the system-environment interactions, initial states, time regimes, averaging, etc.…”