ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Mon, 23 May 2022 09:08:36 GMT2022-05-23T09:08:36Z5051- Mutually unbiased bases in six dimensions: The four most distant baseshttps://scholarbank.nus.edu.sg/handle/10635/112466Title: Mutually unbiased bases in six dimensions: The four most distant bases
Authors: Raynal, P.; Lü, X.; Englert, B.-G.
Abstract: We consider the average distance between four bases in six dimensions. The distance between two orthonormal bases vanishes when the bases are the same, and the distance reaches its maximal value of unity when the bases are unbiased. We perform a numerical search for the maximum average distance and find it to be strictly smaller than unity. This is strong evidence that no four mutually unbiased bases exist in six dimensions. We also provide a two-parameter family of three bases which, together with the canonical basis, reach the numerically found maximum of the average distance, and we conduct a detailed study of the structure of the extremal set of bases. © 2011 American Physical Society.
Mon, 06 Jun 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1124662011-06-06T00:00:00Z
- Encoding many qubits in a rotorhttps://scholarbank.nus.edu.sg/handle/10635/115089Title: Encoding many qubits in a rotor
Authors: Raynal, P.; Kalev, A.; Suzuki, J.; Englert, B.-G.
Abstract: We propose a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. We then discuss the feasibility of this scheme and suggest several candidates for its implementation. The proposed scheme is immediately generalizable to qudits of any finite dimension. © 2010 The American Physical Society.
Thu, 20 May 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1150892010-05-20T00:00:00Z
- Optimal Lewenstein-Sanpera decomposition of two-qubit states using semidefinite programminghttps://scholarbank.nus.edu.sg/handle/10635/115850Title: Optimal Lewenstein-Sanpera decomposition of two-qubit states using semidefinite programming
Authors: Thiang, G.C.; Raynal, P.; Englert, B.-G.
Abstract: We use the language of semidefinite programming and duality to derive necessary and sufficient conditions for the optimal Lewenstein-Sanpera decomposition (LSD) of two-qubit states. We first provide a simple and natural derivation of the Wellens-Ku equations for full-rank states. Then, we obtain a set of necessary and sufficient conditions for the optimal decomposition of rank-3 states. This closes the gap between the full-rank case, where optimality conditions are given by the Wellens-Ku equations, and the rank-2 case, where the optimal decomposition is analytically known. We also give an analytic expression for the optimal LSD of a special class of rank-3 states. Finally, our formulation ensures efficient numerical procedures to return the optimal LSD for any arbitrary two-qubit state. © 2009 The American Physical Society.
Wed, 11 Nov 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1158502009-11-11T00:00:00Z
- Mutually unbiased bases for the rotor degree of freedomhttps://scholarbank.nus.edu.sg/handle/10635/115196Title: Mutually unbiased bases for the rotor degree of freedom
Authors: Lü, X.; Raynal, P.; Englert, B.-G.
Abstract: We consider the existence of a continuous set of mutually unbiased bases for the continuous and periodic degree of freedom that describes motion on a circle (rotor degree of freedom). By a singular mapping of the circle to the line, we find a first, but somewhat unsatisfactory, continuous set which does not relate to an underlying Heisenberg pair of complementary observables. Then, by a nonsingular mapping of the discrete angular momentum basis of the rotor onto the Fock basis for linear motion, we construct such a Heisenberg pair for the rotor and use it to obtain a second, fully satisfactory, set of mutually unbiased bases. © 2012 American Physical Society.
Tue, 22 May 2012 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1151962012-05-22T00:00:00Z
- Encoding qubits in a rotorhttps://scholarbank.nus.edu.sg/handle/10635/115415Title: Encoding qubits in a rotor
Authors: Kalev, A.; Raynal, P.; Suzuki, J.; Englert, B.-G.
Abstract: We present a scheme for encoding many qubits in a single rotor, that is, a continuous and periodic degree of freedom. A key feature of this scheme is its ability to manipulate and entangle the encoded qubits with a single operation on the system. We also show, using quantum error-correcting codes, how to protect the qubits against small errors in angular position and momentum which may affect the rotor. Finally, we propose a possible realization of qubits encoded in orbital angular momentum of a single photon. © 2011 American Institute of Physics.
Sat, 01 Jan 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1154152011-01-01T00:00:00Z