Estimating the spectrum of a density matrix with LOCC

The asymptotic spectrum of LOCC transformations

We study exact, non-deterministic conversion of multipartite pure quantum states into one-another via local operations and classical communication (LOCC) and asymptotic entanglement transformation under such channels. In particular, we consider the maximal number of copies of any given target state that can be extracted exactly from many copies of any given initial state as a function of the exponential decay in success probability, known as the converese error exponent. We give a formula for the optimal rate presented as an infimum over the asymptotic spectrum of LOCC conversion. A full under…

Distilling entanglement from arbitrary resources

We obtain the general formula for the optimal rate at which singlets can be distilled from any given noisy and arbitrarily correlated entanglement resource, by means of local operations and classical communication (LOCC). Our formula, obtained by employing the quantum information spectrum method, reduces to that derived by Devetak and Winter, in the special case of an i.i.d. resource. The proofs rely on a one-shot version of the so-called "hashing bound," which in turn provides bounds on the one-shot distillable entanglement under general LOCC.

对于固定谱，极大纠缠混合态并不总是存在

Maximally entangled mixed states for a fixed spectrum do not always exist

本文研究了固定谱混合态集合中是否存在极大纠缠态，通过分析秩为2状态，证明在特定特征值下不存在能在LOCC或非纠缠操作下转换为所有等谱状态的极大纠缠态。

Quantum state representation based on combinatorial Laplacian matrix of star-relevant graph

We consider the density matrices derived from combinatorial laplacian matrix of graphs. Specifically, the star-relevant graph, which means adding certain edges on peripheral vertices of star graph, is the focus of this paper. Initially, we provide the spectrum of the density matrices corresponding to star-like graph(i.e., adding an edge on star graph) and present that the Von Neumann entropy will increase under the graph operation(adding an edge on star graph) and the graph operation cannot simulated by local operation and classical communication (LOCC). Subsequently, we illustrate the spectru…

Estimation of unitary quantum operations

The problem of optimally estimating an unknown unitary quantum operation with the aid of entanglement is addressed. The idea is to prepare an entangled pair, apply the unknown unitary to one of the two parts and then measure the joint output state. This measurement could be an entangled one or it could be separable (e.g., LOCC). A comparison is made between these possibilities and it is shown that by using non-separable measurements one can improve the accuracy of the estimation by a factor of $2(d+1)/d$ where $d$ is the dimension of the Hilbert space on which $U$ acts.

Estimating the spectrum of a density operator

Given N quantum systems prepared according to the same density operator ρ, we propose a measurement on the N-fold system which approximately yields the spectrum of ρ. The projections of the proposed observable decompose the Hilbert space according to the irreducible representations of the permutations on N points, and are labeled by Young frames, whose relative row lengths estimate the eigenvalues of ρin decreasing order. We show convergence of these estimates in the limit N\to\infty, and that the probability for errors decreases exponentially with a rate we compute explicitly.