Quantum state embezzlement is the transformation $|\ensuremath{\mu}\ensuremath{\rangle}\ensuremath{\mapsto}|\ensuremath{\mu}\ensuremath{\rangle}|\ensuremath{\varphi}\ensuremath{\rangle}$ using only local operations, where $|\ensuremath{\varphi}\ensuremath{\rangle}$ and $|\ensuremath{\mu}\ensuremath{\rangle}$ are multipartite quantum states. Exact embezzlement is an impossible task since it implies the increase of entanglement without communication. Surprisingly, van Dam and Hayden [Phys. Rev. A 67, 060302 (2003)] find a universal embezzling family of states $|\ensuremath{\mu}\ensuremath{\rangle}$ that enables embezzlement in the bipartite setting with arbitrary precision as the dimension of $|\ensuremath{\mu}\ensuremath{\rangle}$ increases. Furthermore, the family is independent of the state $|\ensuremath{\varphi}\ensuremath{\rangle}$ to be embezzled. We study embezzlement in the bipartite setting. We present various requirements and consequences, and infinitely many universal embezzling families inequivalent to that proposed by van Dam and Hayden. We include numerical studies of up to 33-qubit large local systems.Quantum state embezzlement is the transformation $|\ensuremath{\mu}\ensuremath{\rangle}\ensuremath{\mapsto}|\ensuremath{\mu}\ensuremath{\rangle}|\ensuremath{\varphi}\ensuremath{\rangle}$ using only local operations, where $|\ensuremath{\varphi}\ensuremath{\rangle}$ and $|\ensuremath{\mu}\ensuremath{\rangle}$ are multipartite quantum states. Exact embezzlement is an impossible task since it implies the increase of entanglement without communication. Surprisingly, van Dam and Hayden [Phys. Rev. A 67, 060302 (2003)] find a universal embezzling family of states $|\ensuremath{\mu}\ensuremath{\rangle}$ that enables embezzlement in the bipartite setting with arbitrary precision as the dimension of $|\ensuremath{\mu}\ensuremath{\rangle}$ increases. Furthermore, the family is independent of the state $|\ensuremath{\varphi}\ensuremath{\rangle}$ to be embezzled. We study embezzlement in the bipartite setting. We present various requirements and consequences, and infinitely many universal embezzling families inequivalent to that proposed by van Dam and Hayden. We include numerical studies of up to 33-qubit large local systems.

arXiv:1311.6842Physical Review AOct 24, 201418 citations

O(N) -Universality Classes and the Mermin-Wagner Theorem

Alessandro Codello, Giulio D’Odorico

We study how universality classes of O(N)-symmetric models depend continuously on the dimension d and the number of field components N. We observe, from a renormalization group perspective, how the implications of the Mermin-Wagner-Hohenberg theorem set in as we gradually deform theory space towards d = 2. For a fractal dimension in the range 2 < d < 3, we find, for any N ≥ 1, a finite family of multicritical effective potentials of increasing order. Apart from the N = 1 case, these disappear in d = 2 consistently with the Mermin-Wagner-Hohenberg theorem. Finally, we study O(N = 0)-universality classes and find an infinite family of these in two dimensions.We study how universality classes of O(N)-symmetric models depend continuously on the dimension d and the number of field components N. We observe, from a renormalization group perspective, how the implications of the Mermin-Wagner-Hohenberg theorem set in as we gradually deform theory space towards d = 2. For a fractal dimension in the range 2 < d < 3, we find, for any N ≥ 1, a finite family of multicritical effective potentials of increasing order. Apart from the N = 1 case, these disappear in d = 2 consistently with the Mermin-Wagner-Hohenberg theorem. Finally, we study O(N = 0)-universality classes and find an infinite family of these in two dimensions.

arXiv:1210.4037Physical Review LettersApr 5, 201377 citations

Directions in the Theory of Quantum Control

Domenico D’Alessandro

Springer eBooksAug 10, 20077 citations

Generalized SWAP and iSWAP and Solutions to the Yang-Baxter Equation in All Dimensions

Arash Pourkia

We introduce an infinite family of universal quantum logic gates that includes not only higher-dimensional versions of the usual SWAP and $\mathbf{i}$ SWAP gates, but also their previously known extensions. This family consists of permutation-like matrices with nonzero entries of the form $e^{\mathbf{i}\alpha_i}$ , where the $\alpha_i$ are arbitrary real numbers. Moreover, we show that these gates, which we refer to as $\alpha SWAP$ , provide unitary solutions to the constant Yang--Baxter equation in all dimensions.We introduce an infinite family of universal quantum logic gates that includes not only higher-dimensional versions of the usual SWAP and $\mathbf{i}$SWAP gates, but also their previously known extensions. This family consists of permutation-like matrices with nonzero entries of the form $e^{\mathbf{i}\alpha_i}$, where the $\alpha_i$ are arbitrary real numbers. Moreover, we show that these gates, which we refer to as $\alpha SWAP$, provide unitary solutions to the constant Yang--Baxter equation in all dimensions.

European Journal of Pure and Applied MathematicsAug 1, 20251 citation

Advances in Quantum Control Theory

Jeffrey L. Krause

APSMar 1, 20010 citations

We introduce an infinite family of universal quantum logic gates that includes not only higher-dimensional versions of the usual SWAP and

\mathbf{i}

SWAP gates, but also their previously known extensions. This family consists of permutation-like matrices with nonzero entries of the form

e^{\mathbf{i}\alpha_i}

, where the

\alpha_i

are arbitrary real numbers. Moreover, we show that these gates, which we refer to as

\alpha SWAP

, provide unitary solutions to the constant Yang--Baxter equation in all dimensions.