Related papers: Unitary Evolution Between Pure and Mixed States
Characterization of quantum measurements and dynamical processes is typically performed using pure state preparations. However, in realistic experimental settings, the preparation of pure states is often infeasible due to noise and system…
The simulation of many-body open quantum systems is key to solving numerous outstanding problems in physics, chemistry, material science, and in the development of quantum technologies. Near-term quantum computers may bring considerable…
We study bipartite unitary operators which stay invariant under the local actions of diagonal unitary and orthogonal groups. We investigate structural properties of these operators, arguing that the diagonal symmetry makes them suitable for…
We give the mathematical theory of duality computer in the density matrix formalism. This result complements the mathematical theory of duality computer of Gudder in the pure state formalism.
We introduce a task that we call partial decoupling, in which a bipartite quantum state is transformed by a unitary operation on one of the two subsystems and then is subject to the action of a quantum channel. We assume that the subsystem…
This work addresses a fundamental problem of controllability of open quantum systems, meaning the ability to steer arbitrary initial system density matrix into any final density matrix. We show that under certain general conditions open…
The minimal time required for a system to evolve between two different states is an important notion for developing ultra-speed quantum computer and communication channel. Here, we introduce a new metric for non-degenerate density operator…
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…
We develop a rigorous formalism for the description of the evolution of observables in quantum systems of particles. We construct a solution of the initial-value problem to the quantum dual BBGKY hierarchy of equations as an expansion over…
Given a pure state vector |x> and a density matrix rho, the function p(x|rho)=<x|rho|x> defines a probability density on the space of pure states parameterised by density matrices. The associated Fisher-Rao information measure is used to…
The split involution quantization scheme, proposed previously for pure second--class constraints only, is extended to cover the case of the presence of irreducible first--class constraints. The explicit Sp(2)--symmetry property of the…
In the framework of finite-dimensional Fock space models, for a predefined fixed mean number of particles $\bar{n}_{k}$, it is shown that there is a ``large'' multi-dimensional subspace $s_{\bar{n}_{k}}$ of initial pure states, in the space…
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…
Classical probability distributions on sets of sequences can be modeled using quantum states. Here, we do so with a quantum state that is pure and entangled. Because it is entangled, the reduced densities that describe subsystems also carry…
Realizing non-unitary transformations on unitary-gate based quantum devices is critically important for simulating a variety of physical problems including open quantum systems and subnormalized quantum states. We present a dilation based…
For the description of quantum evolution, the use of a manifestly time-dependent quantum Hamiltonian $\mathfrak{h}(t) =\mathfrak{h}^\dagger(t)$ is shown equivalent to the work with its simplified, time-independent alternative $G\neq…
Having a broad range of methods available for implementing unitary operations is crucial for quantum information tasks. We study a dissipative process commonly used to describe dissipatively coupled systems and show that the process can…
In Everettian quantum mechanics, justifications for the Born rule appeal to self-locating uncertainty or decision theory. Such justifications have focused exclusively on a pure-state Everettian multiverse, represented by a wave function.…
Any set of pure states living in an given Hilbert space possesses a natural and unique metric --the Haar measure-- on the group $U(N)$ of unitary matrices. However, there is no specific measure induced on the set of eigenvalues $\Delta$ of…
We will study rigorously the notion of mixed states and their density operators (or matrices.) We will also discuss the quantum-mechanical consequences of possible variations of Planck's constant h. This Review has been written having in…