- Nov 23 2017 quant-ph cond-mat.str-el arXiv:1711.07982v1We study symmetry-enriched topological order in two-dimensional tensor network states by using graded matrix product operator algebras to represent symmetry induced domain walls. A close connection to the theory of graded unitary fusion categories is established. Tensor network representations of the topological defect superselection sectors are constructed for all domain walls. The emergent symmetry-enriched topological order is extracted from these representations, including the symmetry action on the underlying anyons. Dual phase transitions, induced by gauging a global symmetry, and condensation of a bosonic subtheory, are analyzed and the relationship between topological orders on either side of the transition is derived. Several examples are worked through explicitly.
- Nov 23 2017 quant-ph arXiv:1711.08112v1We theoretically and experimentally investigate a strong uncertainty relation valid for any $n$ unitary operators, which implies the standard uncertainty relation as a special case, and which can be written in terms of geometric phases. It is saturated by every pure state of any $n$-dimensional quantum system, generates a tight overlap uncertainty relation for the transition probabilities of any $n+1$ pure states, and gives an upper bound for the out-of-time-order correlation function. We test these uncertainty relations experimentally for photonic polarisation qubits, including the minimum uncertainty states of the overlap uncertainty relation, via interferometric measurements of generalised geometric phases.
- Nov 23 2017 quant-ph arXiv:1711.08066v1Contextuality is a necessary resource for universal quantum computation and non-contextual quantum mechanics can be simulated efficiently by classical computers in many cases. Orders of Planck's constant, $\hbar$, can also be used to characterize the classical-quantum divide by expanding quantities of interest in powers of $\hbar$---all orders higher than $\hbar^0$ can be interpreted as quantum corrections to the order $\hbar^0$ term. We show that contextual measurements in finite-dimensional systems have formulations within the Wigner-Weyl-Moyal (WWM) formalism that require higher than order $\hbar^0$ terms to be included in order to violate the classical bounds on their expectation values. As a result, we show that contextuality as a resource is equivalent to orders of $\hbar$ as a resource within the WWM formalism. This explains why qubits can only exhibit state-independent contextuality under Pauli observables as in the Peres-Mermin square while odd-dimensional qudits can also exhibit state-dependent contextuality. In particular, we find that qubit Pauli observables lack an order $\hbar^0$ contribution in their Weyl symbol and so exhibit contextuality regardless of the state being measured. On the other hand, odd-dimensional qudit observables generally possess non-zero order $\hbar^0$ terms, and higher, in their WWM formulation, and so exhibit contextuality depending on the state measured: odd-dimensional qudit states that exhibit measurement contextuality have an order $\hbar^1$ contribution that allows for the violation of classical bounds while states that do not exhibit measurement contextuality have insufficiently large order $\hbar^1$ contributions.
- We show that quantum expander codes, a constant-rate family of quantum LDPC codes, with the quasi-linear time decoding algorithm of Leverrier, Tillich and Zémor can correct a constant fraction of random errors with very high probability. This is the first construction of a constant-rate quantum LDPC code with an efficient decoding algorithm that can correct a linear number of random errors with a negligible failure probability. Finding codes with these properties is also motivated by Gottesman's construction of fault tolerant schemes with constant space overhead. In order to obtain this result, we study a notion of $\alpha$-percolation: for a random subset $W$ of vertices of a given graph, we consider the size of the largest connected $\alpha$-subset of $W$, where $X$ is an $\alpha$-subset of $W$ if $|X \cap W| \geq \alpha |X|$.
- Nov 23 2017 cond-mat.str-el cond-mat.stat-mech arXiv:1711.08455v1This review article is devoted to the interplay between frustrated magnetism and quantum critical phenomena, covering both theoretical concepts and ideas as well as recent experimental developments in correlated-electron materials. The first part deals with local-moment magnetism in Mott insulators and the second part with frustration in metallic systems. In both cases, frustration can either induce exotic phases accompanied by exotic quantum critical points or lead to conventional ordering with unconventional crossover phenomena. In addition, the competition of multiple phases inherent to frustrated systems can lead to multi-criticality.
- Nov 23 2017 cs.NA arXiv:1711.08453v1
- Nov 23 2017 stat.ML arXiv:1711.08451v1
- Nov 23 2017 cs.CV arXiv:1711.08447v1
- Nov 23 2017 cs.DS arXiv:1711.08446v1
- Nov 23 2017 math.DG arXiv:1711.08443v1
- Nov 23 2017 astro-ph.CO gr-qc arXiv:1711.08441v1
- Nov 23 2017 physics.optics nlin.CD arXiv:1711.08440v1
- Nov 23 2017 math.SP arXiv:1711.08439v1
- Nov 23 2017 hep-ph arXiv:1711.08437v1
- Nov 23 2017 hep-th arXiv:1711.08435v1
- Nov 23 2017 astro-ph.CO hep-ph arXiv:1711.08434v1
- Nov 23 2017 astro-ph.EP arXiv:1711.08433v1
- Nov 23 2017 physics.optics arXiv:1711.08429v1
- Nov 23 2017 quant-ph arXiv:1711.08427v1
- Nov 23 2017 math.AP arXiv:1711.08423v1
- Nov 23 2017 hep-th arXiv:1711.08422v1
- Nov 23 2017 eess.SP arXiv:1711.08420v1
- Nov 23 2017 math.OC arXiv:1711.08418v1
- Nov 23 2017 cs.LG arXiv:1711.08416v1
- Nov 23 2017 math.AG arXiv:1711.08414v1
- Nov 23 2017 math.GR arXiv:1711.08410v1
- Nov 23 2017 math.LO arXiv:1711.08409v1
- Nov 23 2017 nucl-th arXiv:1711.08404v1