We introduce a geometric entropy for quantum preparations, defined as the logarithm of the Hilbert-space volume of pure states compatible with a given set of constraints. This construction extends Boltzmann's counting perspective to the quantum setting, where compatible states need not be orthogonal and the relevant notion of"number of states"is naturally replaced by a volume in state space. We analyze three classes of constraints: restriction to a subspace, fixed expectation values, and coarse-grained subsystem descriptions. For representative examples, including subspace projection, spin expectation values, partial trace, and an imperfect detector map, we obtain explicit scaling laws and closed-form expressions for the associated volumes. The resulting framework provides a geometric measure of quantum ignorance at the level of the preparation and complements entropy notions based on density matrices and coarse graining.
Textbook quantum superposition refers to the feature that certain linear combinations of Hilbert space rays, each representing a valid quantum state, are themselves valid states. This notion is not operational, and it relies on the underlying Hilbert space formalism. Recent proposals for experimental tests of indefinit...
Recently, we introduced a geometric object analogous to an orthonormal frame in the Cartan formalism to study the parameter space of quantum systems; we called it N-bein, with N being the number of parameters that characterize the quantum system. Acting as the ‘square root’ of the quantum geometric tensor (QGT), the N-...
Jorge Romero, Carlos A. Velasquez, J. Vergara· Journal of Physics A: Mathem...· 0 citations
We propose that quantum mechanics emerges as the effective description of a deterministic physical reality from the perspective of an internal observer that constitutes a subsystem of a finite closed world. Because such an observer cannot access the complete ontological state of the world to which it belongs, its descr...
A. Belinsky, Alexandr Kaminsky· Laser Physics Letters· 0 citations
We study the one-sided time evolution of thermofield double (TFD) states in random matrix theory, where the Hamiltonian is taken to be a $D\times D$ random matrix drawn from a unitarily invariant emsemble of Hermitian matrices. We argue that the Krylov basis with the maximally entangled state taken as the initial vecto...
The geometry of quantum states is a fundamental research area with applications ranging from band theory in condensed matter to variational algorithms in quantum information. Due to their relative simplicity, pure states are usually studied, while mixed ones are needed in general, for instance to allow for finite tempe...
We argue for the universality of quantum theory using a dynamical consistency argument, within a specific Hamiltonian setting. We analyse two different types of coupling between simple quantum harmonic oscillators. Each illustrates an aspect of the free and interacting quantum fields and shows the inadequacy of semicla...
C. Marletto, V. Vedral· 0 citations
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