arXiv subjects

Shiang Yong Looi

Publications and source records attributed to Shiang Yong Looi.

6 recordsLinked to original sources

arXiv2011

Tripartite Entanglement in Qudit Stabilizer States and Application in Quantum Error Correction

Consider a stabilizer state on $n$ qudits, each of dimension $D$ with $D$ being a prime or a squarefree integer, divided into three mutually disjoint sets or parts. Generalizing a result of Bravyi et al. [J. Math. Phys. \textbf{47}, 062106 (2006)] for qubits (D=2), we show that up to local unitaries on the three parts the state can be written as a tensor product of unentangled single-qudit states, maximally entangled EPR pairs, and tripartite GHZ states. We employ this result to obtain a complete characterization of the properties of a class of channels associated with stabilizer error-correcting codes, along with their complementary channels.

quant-ph↗

arXiv2011

SOMIM: An open-source program code for the numerical Search for Optimal Measurements by an Iterative Method

SOMIM is an open-source code that implements a Search for Optimal Measurements by using an Iterative Method. For a given set of statistical operators, SOMIM finds the POVMs that maximizes the accessed information, and thus determines the accessible information and one or all of the POVMs that retrieve it. The maximization procedure is a steepest-ascent method that follows the gradient in the POVM space, and uses conjugate gradients for speed-up.

quant-ph↗

arXiv2010

Construction of Equientangled Bases in Arbitrary Dimensions via Quadratic Gauss Sums and Graph States

Recently [Karimipour and Memarzadeh, Phys. Rev. A 73, 012329 (2006)] studied the problem of finding a family of orthonormal bases in a bipartite space each of dimension $D$ with the following properties: (i) The family continuously interpolates between the product basis and the maximally entangled basis as some parameter $t$ is varied, and (ii) for a fixed $t$, all basis states have the same amount of entanglement. The authors derived a necessary condition and provided explicit solutions for $D \leq 5$ but the existence of a solution for arbitrary dimensions remained an open problem. We prove that such families exist in arbitrary dimensions by providing two simple solutions, one employing the properties of quadratic Gauss sums and the other using graph states. The latter can be generalized to multipartite equientangled bases with more than two parties.

quant-ph↗

arXiv2010

Location of quantum information in additive graph codes

The location of quantum information in various subsets of the qudit carriers of an additive graph code is discussed using a collection of operators on the coding space which form what we call the information group. It represents the input information through an encoding operation constructed as an explicit quantum circuit. Partial traces of these operators down to a particular subset of carriers provide an isomorphism of a subgroup of the information group, and this gives a precise characterization of what kinds of information they contain. All carriers are assumed to have the same dimension D, an arbitrary integer greater than 1.

quant-ph↗

arXiv2008

Quantum Error Correcting Codes Using Qudit Graph States

Graph states are generalized from qubits to collections of $n$ qudits of arbitrary dimension $D$, and simple graphical methods are used to construct both additive and nonadditive quantum error correcting codes. Codes of distance 2 saturating the quantum Singleton bound for arbitrarily large $n$ and $D$ are constructed using simple graphs, except when $n$ is odd and $D$ is even. Computer searches have produced a number of codes with distances 3 and 4, some previously known and some new. The concept of a stabilizer is extended to general $D$, and shown to provide a dual representation of an additive graph code.

quant-ph↗

arXiv2005

The Singapore Protocol: Incoherent Eavesdropping Attacks

We thoroughly analyse the novel quantum key distribution protocol introduced recently in quant-ph/0412075, which is based on minimal qubit tomography. We examine the efficiency of the protocol for a whole range of noise parameters and present a general analysis of incoherent eavesdropping attacks with arbitrarily many steps in the iterative key generation process. The comparison with the tomographic 6-state protocol shows that our protocol has a higher efficiency (up to 20%) and ensures the security of the established key even for noise parameters far beyond the 6-state protocol's noise threshold.

quant-ph↗