Related papers: Mapping the space of quantum expectation values
Let $\mathcal{H}_i$ be a finite dimensional complex Hilbert space of dimension $d_i$ associated with a finite level quantum system $A_i$ for $i = i, 1,2, ..., k$. A subspace $S \subset \mathcal{H} = \mathcal{H}_{A_{1} A_{2}... A_{k}} =…
Ergodicity has been one of the fundamental concepts underpinning our understanding of thermalization in isolated systems since the first developments in classical statistical mechanics. Recently, a similar notion has been introduced for…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
In the presence of Lindblad decoherence, i.e. dissipative effects in an open quantum system due to interaction with an environment, we examine the transition probabilities between the eigenstates in the two-level quantum system described by…
Consider a mixed quantum mechanical state, describing a statistical ensemble in terms of an arbitrary density operator $\rho$ of low purity, $\tr\rho^2\ll 1$, and yielding the ensemble averaged expectation value $\tr(\rho A)$ for any…
It is well-known that any two pure quantum states (in the same Hilbert space) can be mapped to any other using unitary transformations. However, previous approaches to this problem required two explicit bases for the Hilbert space, one each…
A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of…
One of the most central and controversial element of quantum mechanics is the use of non zero vectors of a Hilbert space (or, more generally, of one dimension subspaces) for representing the state of a quantum system. In particular, the…
Contents 1. Creation and annihilation operators for the system of indistinguishable particles 1.1 The permutation group and the states of a system of indistinguishable particles 1.2 Dimension of the Hilbert space of a system of…
Quantum state tomography is the standard technique for reconstructing a quantum state from experimental data. In the regime of finite statistics, experimental data cannot give perfect information about the quantum state. A common way to…
This paper starts by describing the dynamics of the electron-monopole system at both classical and quantum level by a suitable reduction procedure. This suggests, in order to realise the space of states for quantum systems which are…
Various problems concerning the geometry of the space $u^*(\cH)$ of Hermitian operators on a Hilbert space $\cH$ are addressed. In particular, we study the canonical Poisson and Riemann-Jordan tensors and the corresponding foliations into…
We consider the classical minisuperspace model describing a closed, homogeneous and isotropic Universe, with a positive cosmological constant. Upon canonical quantization, the infinite number of possible operator orderings in the quantum…
Non-Hermitian operators naturally arise in the description of open quantum systems, which exhibit features such as resonances and decay processes, where the associated eigenvalues are complex. Standard quantum algorithms, including the…
We consider an isolated, macroscopic quantum system. Let H be a micro-canonical "energy shell," i.e., a subspace of the system's Hilbert space spanned by the (finitely) many energy eigenstates with energies between E and E + delta E. The…
Ergodicity, the property that all allowed configurations are explored over time, plays a pivotal role in explaining the equilibrium behavior of classical dynamical systems. Yet, such a property is typically precluded in quantum systems…
A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
The theory of measurements continuous in time in quantum mechanics (quantum continual measurements) has been formulated by using the notions of instrument and positive operator valued measure, functional integrals, quantum stochastic…
The typicality approach and the Hilbert space averaging method as its technical manifestation are important concepts of quantum statistical mechanics. Extensively used for expectation values we extend them in this paper to transition…
We apply concepts of random differential geometry connected to the random matrix ensembles of the random linear operators acting on finite dimensional Hilbert spaces. The values taken by random linear operators belong to the Liouville…