Related papers: Limits on the Observable Dynamics of Mixed States
We show that bipartite concurrence for rank-2 mixed states of qubits is written by an observable which can be exactly and directly measurable in experiment by local projective measurements, provided that four copies of the composite quantum…
Understanding how higher-order interactions affect collective behavior is a central problem in nonlinear dynamics and complex systems. Most works have focused on a single higher-order coupling function, neglecting other viable choices. Here…
A general matrix approach to study entangled states is presented, based on operator completeness relations. Bases of unitary operators are considered, with focus on irreducible representations of groups. Bell measurements for teleportation…
We address perfect discrimination of two separable states. When available states are restricted to separable states, we can theoretically consider a larger class of measurements than the class of measurements allowed in quantum theory. The…
Observing and controlling complex networks are of paramount interest for understanding complex physical, biological and technological systems. Recent studies have made important advances in identifying sensor or driver nodes, through which…
Uncertainty and entanglement are both profound and key concepts in quantum theory. For three observables, the tightest uncertainty constants for both product and summation forms are revealed. In this work, we give an alternative proof for…
For many quantum information protocols such as state transfer, entanglement transfer and entanglement generation, standard notions of controllability for quantum systems are too strong. We introduce the weaker notion of accessible pairs,…
In this work, we consider the dynamics of repairable systems characterized by three distinct states: one signifying normal operational states, another representing degraded conditions and a third denoting failed conditions. These systems…
We propose an extended quantum mechanical formalism that is based on a wave operator $\vr$, which is related to the ordinary density matrix via $\rho=\vr\vr^\dagger$. This formalism allows a (generalized) unitary evolution between pure and…
Consider the initial-boundary value problem for a strictly hyperbolic, genuinely nonlinear, Temple class system of conservation laws % $$ u_t+f(u)_x=0, \qquad u(0,x)=\ov u(x), \qquad {{array}{ll} &u(t,a)=\widetilde u_a(t),…
We derive several uncertainty relations for two arbitrary unitary operators acting on physical states of a Hilbert space. We show that our bounds are tighter in various cases than the ones existing in the current literature. Using the…
Uncertainty relations are old, yet potentially rewarding to explore. By introducing a quantity called the uncertainty matrix, we provide a link between purity and observable incompatibility, and derive several stronger uncertainty relations…
We give upper bounds on limit multiplicities of certain non-tempered representations of unitary groups $U(a,b)$. These include some cohomological representations, and we give applications to the growth of cohomology of cocompact arithmetic…
We introduce algebraic sets in the products of complex projective spaces for the mixed states in multipartite quantum systems as their invariants under local unitary operations. The algebraic sets have to be the union of the linear…
An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characterise stability in permutations using action traces. We…
Minimum error state discrimination between two mixed states \rho and \sigma can be aided by the receipt of "classical side information" specifying which states from some convex decompositions of \rho and \sigma apply in each run. We…
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…
It is shown that any separable state on Hilbert space ${\cal H}={\cal H}_1\otimes{\cal H}_2$, can be written as a convex combination of N pure product states with $N\leq (dim{\cal H})^2$. Then a new separability criterion for mixed states…
An extensive generalization of the ordinary and quasi-eikonal methods is presented for the $pp$ and $\bar pp$ elastic scattering amplitudes, which takes into account in a phenomenological way all intermediate multiparticle states involving…
The standard state-dependent Heisenberg-Robertson uncertainly-relation lower bound fails to capture the quintessential incompatibility of observables as the bound can be zero for some states. To remedy this problem, we establish a class of…