相关论文: On Lieb's conjecture

We introduce a new notion of entropy for quantum states, called contextual entropy, and show how it unifies Shannon and von Neumann entropy. The main result is that from the knowledge of the contextual entropy of a quantum state of a…

Elaborating on a previous work by Marolf et al, we relate some exact results in quantum field theory and statistical mechanics to the Bekenstein universal bound on entropy. Specifically, we consider the relative entropy between the vacuum…

The correspondence principle plays a fundamental role in quantum mechanics, which naturally leads us to inquire whether it is possible to find or determine close classical analogs of quantum states in phase space -- a common meeting point…

We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An…

Extending a recent result by Frank and Lieb, we show an entropic uncertainty principle for mixed states in a Hilbert space relatively to pairs of positive operator valued measures that are independent in some sense. This yields…

We focus on quantum systems represented by a Hilbert space $L^2(A)$, where $A$ is a locally compact Abelian group that contains a compact open subgroup. We examine two interconnected issues related to Weyl-Heisenberg operators. First, we…

We consider a many-body Hilbert space with a fixed global charge and show that the typical entanglement entropy of a subsystem, at the leading and subleading order in the thermodynamic limit, can be expressed in terms of a single quantity…

The unitary group acting on the Hilbert space of three quantum bits admits a Lie subgroup, of elements which permute with the symmetric group of permutations. Under the action of such Lie subgroup, the Hilbert space splits into three…

It is suspected that the quantum evolution equations describing the micro-world as we know it are of a special kind that allows transformations to a special set of basis states in Hilbert space, such that, in this basis, the evolution is…

A SU(2) intertwiner with N legs can be interpreted as the quantum state of a convex polyhedron with N faces (when working in 3d). We show that the intertwiner Hilbert space carries a representation of the non-compact group SO*(2N). This…

Let S be the von Neumann entropy of a finite ensemble E of pure quantum states. We show that S may be naturally viewed as a function of a set of geometrical volumes in Hilbert space defined by the states and that S is monotonically…

Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…

We summarize a new realist interpretation of quantum theory that builds on the existing physical structure of the theory and allows experiments to have definite outcomes, but leaves the theory's basic dynamical content essentially intact.…

It has been argued that the entropy which one is computing in the isolated horizon framework of loop quantum gravity is closely related to the entanglement entropy of the gravitational field and that the calculation performed is not…

Taking several statistical examples, in particular one involving a choice of experiment, as points of departure, and making symmetry assumptions, the link towards quantum theory developed in Helland (2005a,b) is surveyed and clarified. The…

The structure of the state spaces of bipartite (N tensor N) quantum systems which are invariant under product representations of the group SO(3) of three-dimensional proper rotations is analyzed. The subsystems represent particles of…

Various parameterizations for the orbits under local unitary transformations of three-qubit pure states are analyzed. The interconvertibility, symmetry properties, parameter ranges, calculability and behavior under measurement are looked…

We consider quantum cosmology for toroidal universes in d+1 dimensions. The Hilbert space is the space of square-integrable automorphic forms for GL(d). The Hartle-Hawking state is defined as a Poincar\'e sum over the no-boundary…

We study the effect that the SU(2) symmetry, and the rich Hilbert space structure that it generates in lattice spin systems, has on the average entanglement entropy of highly excited eigenstates of local Hamiltonians and of random pure…

Entanglement for pure bipartite states is most commonly quantified in a state-by-state manner to each pure state of a bipartite system a scalar quantity, such as the von Neumann entropy of a reduced density matrix. This provides a precise…