相关论文: Factorization of numbers with Gauss sums: III. Alg…

We present a simple and general factorization law for quantum systems shared by two parties, which describes the time evolution of entanglement upon passage of either component through an arbitrary noisy channel. The robustness of…

We ask how quantum correlations can be distributed among many subsystems. To address this, we define entanglement sharing schemes (ESS) where certain pairs of subsystems allow entanglement to be recovered via local operations, while other…

In polynomial optimization problems, nonnegativity constraints are typically handled using the sum of squares condition. This can be efficiently enforced using semidefinite programming formulations, or as more recently proposed by Papp and…

A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not…

We study the parameterized complexity of algorithmic problems whose input is an integer set $A$ in terms of the doubling constant $C := |A + A|/|A|$, a fundamental measure of additive structure. We present evidence that this new…

The sparse factorization of a large matrix is fundamental in modern statistical learning. In particular, the sparse singular value decomposition and its variants have been utilized in multivariate regression, factor analysis, biclustering,…

Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement…

Classifying states as entangled or separable is a highly challenging task, while it is also one of the foundations of quantum information processing theory. This task is higly nontrivial even for relatively simple cases, such as two-qutrit…

Considering pure quantum states, entanglement concentration is the procedure where from $N$ copies of a partially entangled state, a single state with higher entanglement can be obtained. Getting a maximally entangled state is possible for…

Two novel measurement-based, quantum clustering algorithms are proposed based on quantum parallelism and entanglement. The first algorithm follows a divisive approach. The second algorithm is based on unsharp measurements, where we…

Quantum computing devices are believed to be powerful in solving the prime factorization problem, which is at the heart of widely deployed public-key cryptographic tools. However, the implementation of Shor's quantum factorization algorithm…

We give a polynomial time approximation scheme (PTAS) for computing the supremum of a Gaussian process. That is, given a finite set of vectors $V\subseteq\mathbb{R}^d$, we compute a $(1+\varepsilon)$-factor approximation to $\mathop…

We study the capacity of entanglement as an alternative to entanglement entropies in estimating the degree of entanglement of quantum bipartite systems over fermionic Gaussian states. In particular, we derive the exact and asymptotic…

Quantum computational algorithms exploit quantum mechanics to solve problems exponentially faster than the best classical algorithms. Shor's quantum algorithm for fast number factoring is a key example and the prime motivator in the…

We study the results of a compiled version of Shor's factoring algorithm on the ibmqx5 superconducting chip, for the particular case of $N=15$, $21$ and $35$. The semi-classical quantum Fourier transform is used to implement the algorithm…

Entanglement plays a crucial role in quantum processes particularly those pertaining to quantum information and computation. An analytical expression for an entanglement measure defined in terms of success rate of Grover's search algorithm…

We provide several applications of a previously introduced isomorphism between physical operations acting on two systems and entangled states [1]. We show: (i) how to implement (weakly) non-local two qubit unitary operations with a small…

Simulating quantum systems constructively furthers our understanding of qualitative and quantitative features which may be analytically intractable. In this letter, we directly simulate and explore the entanglement structure present in a…

Detection of entanglement in quantum states is one of the most important problems in quantum information processing. However, it is one of the most challenging tasks to find a universal scheme which is also desired to be optimal to detect…

We introduce GCIS, a grammar compression algorithm based on the induced suffix sorting algorithm SAIS, introduced by Nong et al. in 2009. Our solution builds on the factorization performed by SAIS during suffix sorting. We construct a…