[quant-ph/0509174]

Reduced density matrices are a powerful tool in the analysis of entanglement structure, approximate or coarse-grained dynamics, decoherence, and the emergence of classicality. It is straightforward to produce a reduced density matrix with the partial-trace map by “tracing out” part of the quantum state, but in many natural situations this reduction may not be achievable. We investigate the general problem of identifying how the quantum state reduces given a restriction on the observables. For example, in an experimental setting, the set of observables that can actually be measured is usually modest (compared to the set of all possible observables) and their resolution is limited. In such situations, the appropriate state-reduction map can be defined via a generalized bipartition, which is associated with the structure of irreducible representations of the algebra generated by the restricted set of observables. The definition of quantum state reductions can also be extended beyond algebras of observables. To accomplish this task, we introduce a more flexible notion of bipartition, the partial bipartition, which describes coarse-grainings preserving information about a limited set (not necessarily algebra) of observables. We describe a variational method to choose the coarse-grainings most compatible with a specified Hamiltonian, which exhibit emergent classicality in the reduced state space. We apply this construction to the concrete example of the 1-D Ising model. Our results have relevance for quantum information, bulk reconstruction in holography, and quantum gravity. [1909.12851] 

I explain why there is a quantum reality problem and why we are motivated to seek precise solutions that are physically natural, respect fundamental symmetries and are empirically confirmable. I discuss a proposal involving late time measurements of photons or other massless particles. I also explain how this and other proposals motivate new types of physical law, involving statistical constraints, that are natural foils against which to test standard cosmological ideas. [1608.04805, 1311.0249]

We study the question of how to decompose Hilbert space into a preferred tensor-product factorization without any pre-existing structure other than a Hamiltonian operator, in particular the case of a bipartite decomposition into “system” and “environment.” Such a decomposition can be defined by looking for subsystems that exhibit quasi-classical behavior. The correct decomposition is one in which pointer states of the system are relatively robust against environmental monitoring (their entanglement with the environment does not continually and dramatically increase) and remain localized around approximately-classical trajectories. We present an in-principle algorithm for finding such a decomposition by minimizing a combination of entanglement growth and internal spreading of the system. Both of these properties are related to locality in different ways. Extensions of this paradigm to include degrees of freedom which do not form a tensor factor of Hilbert space are also discussed. [2005.12938]

[2111.12700, 1701.01107]

We define a version of quantum complexity designed to measure, at any instant of time, the spatial structure of entanglement in a state vector. Decomposition of a state vector into branches is then found by minimizing a linear combination of the mean squared quantum complexity of a candidate set of branches and the corresponding classical entropy of the ensemble of branch weights. In a non-relativistic formulation of this proposal, branching occurs repeatedly over time, with each branch splitting successively into further sub-branches among which the branch followed by the real world is chosen randomly according to the Born rule. In a Lorentz covariant version, the real world is a single random draw from the set of branches at asymptotically late time, restored to finite time by sequentially retracing the set of branching events implied by the late time choice. [2105.04545]