相关论文: Progress on the Kretschmann-Schlingemann-Werner Co…

Consider quantum channels with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. Any such channel must satisfy the constraint $rd_2\geq d_1$, and the parameter regime $rd_2=d_1$ is called the boundary regime. In this…

This work presents a differentiable geometric parameterization of quantum channels in Kraus representation, which can be efficiently probed to find an unknown quantum channel. We explore its feasibility in finding the quasi inverse…

Most general dynamics of an open quantum system is commonly represented by a quantum channel, which is a completely positive trace-preserving map (CPTP or Kraus map). Well-known are the representations of quantum channels by Choi matrices…

We introduce an axiomatic approach for channel divergences and channel relative entropies that is based on three information-theoretic axioms of monotonicity under superchannels (i.e. generalized data processing inequality), additivity…

In this paper, Wielandt's inequality for classical channels is extended to quantum channels. That is, an upper bound to the number of times a channel must be applied, so that it maps any density operator to one with full rank, is found.…

We prove that if $u\in C^0(B_1)$ satisfies $F(x,D^2u) \le 0$ in $B_1\subset \mathbb{R}^2$, in the viscosity sense, for some fully nonlinear $(\lambda, \Lambda)$-elliptic operator, then $u \in W^{2,\varepsilon}(B_{1/2})$, with appropriate…

It is established that both discrete and continuous semigroups of unital quantum channels are eventually mixed unitary. This result is novel even for the subclass of Schur maps and stands in sharp contrast to the resolution of the…

A set of quantum measurements exhibits quantum contextuality when any consistent value assignment to the measurement outcomes leads to a contradiction with quantum theory. In the original Kochen-Specker-type of argument the measurement…

In this paper, we introduce a new type of Finsler metrics, called $(\alpha_1,\alpha_2)$-metrics. We define the notion of the good datum of a homogeneous $(\alpha_1,\alpha_2)$-metric and use that to study the geometric properties. In…

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

We obtain results for the spectral optimisation of Neumann eigenvalues on rectangles in $\mathbb{R}^2$ with a measure or perimeter constraint. We show that the rectangle with measure $1$ which maximises the $k$'th Neumann eigenvalue…

Is it always possible to explain random stochastic transitions between states of a finite-dimensional system as arising from the deterministic quantum evolution of the system? If not, then what is the minimal amount of randomness required…

We prove that $$ \|X(|u|^2)\|_{L^3_{t,\ell}}\leq C\|f\|_{L^2(\mathbb{R}^2)}^2, $$ where $u(x,t)$ is the solution to the linear time-dependent Schr\"odinger equation on $\mathbb{R}^2$ with initial datum $f$, and $X$ is the (spatial) X-ray…

Given a pair of elliptic curves $E_1,E_2$ over a field $k$, we have a natural map $\text{CH}^1(E_1)_0\otimes\text{CH}^1(E_2)_0\to\text{CH}^2(E_1\times E_2)$, and a conjecture due to Beilinson predicts that the image of this map is finite…

For any bounded convex domain $\Omega$ with $C^{2}$ boundary in $\mathbb{C}^{n}$, we show that there exist positive constants $C_{1}$ and $C_{2}$ such that \[ C_{1}\sqrt{\dfrac{K\left(w,w\right)}{\delta\left(w\right)}}\leq\left\Vert…

An issue which has attracted increasing attention in contemporary researches are Kirkwood--Dirac quasiprobabilities. List of their use includes many questions of quantum physics. Applications of complex tight frames in quantum information…

We address the problem of unambiguous comparison of a pair of unknown qudit unitary channels. Using the framework of process positive operator valued measures (PPOVM) we characterize all solutions and identify the optimal ones. We prove…

Inevitably, assessing the overall performance of a quantum computer must rely on characterizing some of its elementary constituents and, from this information, formulate a broader statement concerning more complex constructions thereof.…

In quadratic gravity, with a positive Weyl squared coefficient, the extra spin-2 sector is shown to correspond to a dual inverted harmonic oscillator, instead of a ghost. Using the Wightman spectrum condition, we prove that the associated…

Assuming the polynomial hierarchy is infinite, we prove a sufficient condition for determining if uniform and polynomial size quantum circuits over a non-universal gate set are not efficiently classically simulable in the weak…