Related papers: Convertibility of Observables
The problem of determining whether two states are equivalent by local unitary (LU) operations is important for quantum information processing. In this paper we propose an alternative perspective to study this problem by comparing the…
We discuss the uniqueness of quantum states compatible with given results for measuring a set of observables. For a given pure state, we consider two different types of uniqueness: (1) no other pure state is compatible with the same…
Quantum reference frame transformations have been proposed to provide a means by which to translate descriptions of quantum systems relative to each other. At present, there are several differing frameworks for describing quantum reference…
A new class of state transformations that are quantum mechanically prohibited is introduced. These can be seen as the generalization of the universal-NOT transformation which, for all pure inputs state of a given Hilbert space produces pure…
The problem of unambiguously distinguishing among nonorthogonal but linearly independent quantum states can be solved by mapping the set of nonorthogonal quantum states onto a set of orthogonal ones, which can then be distinguished without…
The separability from spectrum problem asks for a characterization of the eigenvalues of the bipartite mixed states {\rho} with the property that U^*{\rho}U is separable for all unitary matrices U. This problem has been solved when the…
Adiabatic process has found many important applications in modern physics, the distinct merit of which is that it does not need accurate control over the timing of the process. However, it is a slow process, which limits the application in…
We consider a perturbation of an ``integrable'' Hamiltonian and give an expression for the canonical or unitary transformation which ``simplifies'' this perturbed system. The problem is to invert a functional defined on the Lie- algebra of…
This note is intended to foster a discussion about the extent to which typical problems arising in quantum information theory are algorithmically decidable (in principle rather than in practice). Various problems in the context of…
A formula for the commutator of tensor product matrices is used to shows that, for qubits, compatibility of quantum multiparty observables almost never implies local compatibility at each site and to predict when this happens/does not…
We show that multipartite quantum states that have a positive partial transpose with respect to all bipartitions of the particles can outperform separable states in linear interferometers. We introduce a powerful iterative method to find…
A two-dimensional quantum system with anyonic excitations can be considered as a quantum computer. Unitary transformations can be performed by moving the excitations around each other. Measurements can be performed by joining excitations in…
The general transformation of the product of coherent states $\prod_{i=1}^N|\alpha_i>$ to the output state $\prod_{i=1}^M|\beta_i>$ ($N=M$ or $N\neq M$), which is realizable with linear optical circuit, is characterized with a linear map…
Let $T$ be an absolutely continuous polynomially bounded operator, and let $\theta$ be a singular inner function. It is shown that if $\theta(T)$ is invertible and some additional conditions are fulfilled, then $T$ has nontrivial…
Quantum states encoded in microwave photons or qubits can be effectively manipulated, whereas optical photons can be coherently transferred via optical fibre and waveguide. The reversible conversion of quantum states between microwave and…
This paper examines whether unitary evolution alone is sufficient to explain emergence of the classical world from the perspective of computability theory. Specifically, it looks at the problem of how the choice related to the measurement…
Determining whether a quantum state is separable or entangled is a problem of fundamental importance in quantum information science. This is a brief review in which we consider the problem for states in infinite dimensional Hilbert spaces.…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
We study the compatibility (or joint measurability) of quantum observables in a setting where the experimenter has access to multiple copies of a given quantum system, rather than performing the experiments on each individual copy…
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…