C. Allen Bishop

Nonperturbative dynamical decoupling with random control

Jun Jing, C. Allen Bishop, and Lian-Ao Wu Institute of Theoretical Physics and Department of Physics, Shanghai University, Shanghai 200444, China Department of Theoretical Physics and History of Science, The Basque Country University (EHU/UPV), PO Box 644, 48080 Bilbao Spain GridCOM Technologies, Inc., San Diego, CA 92081, USA Ikerbasque, Basque Foundation for Science, 48011 Bilbao Spain (Dated: July 4, 2014)Parametric fluctuations or stochastic signals are introduced into the rectangular pulse sequence to investigate the feasibility of random dynamical decoupling. In a large parameter region, we find that the out-of-order control pulses work as well as the regular pulses for dynamical decoupling and dissipation suppression. Calculations and analysis are enabled by and based on a nonperturbative dynamical decoupling approach allowed by an exact quantum-state-diffusion equation. When the average frequency and duration of the pulse sequence take proper values, the random control sequence is robust, fault-tolerant, and insensitive to pulse strength deviations and interpulse temporal separation in the quasi-periodic sequence. This relaxes the operational requirements placed on quantum control devices to a great deal.

General open-system quantum evolution in terms of affine maps of the polarization vector

The operator-sum decomposition (OS) of a mapping from one density matrix to another has many applications in quantum information science. To this mapping there corresponds an affine map which provides a geometric description of the density matrix in terms of the polarization vector representation. This has been thoroughly explored for qubits since the components of the polarization vector are measurable quantities (corresponding to expectation values of Hermitian operators) and also because it enables the description of map domains geometrically. Here we extend the OS-affine map correspondence to qudits, briefly discuss general properties of the map, the form for particular important cases, and provide several explicit results for qutrit maps. We use the affine map and a singular-value-like decomposition, to find positivity constraints that provide a symmetry for small polarization vector magnitudes (states which are closer to the maximally mixed state) which is broken as the polarization vector increases in magnitude (a state becomes more pure). The dependence of this symmetry on the magnitude of the polarization vector implies the polar decomposition of the map can not be used as it can for the qubit case. However, it still leads us to a connection between positivity and purity for general d-state systems.

High-fidelity state transfer over an unmodulated linear XY spin chain

We provide a class of initial encodings that can be sent with a high fidelity over an unmodulated, linear,

Compatible transformations for a qudit decoherence-free/noiseless encoding

\mathit{XY}

Methods for producing decoherence-free states and noiseless subsystems using photonic qutrits

spin chain. As an example, an average fidelity of

Quantum gates and their coexisting geometric phases

96%

Robust and reliable transfer of a qubit state through an XY spin chain

can be obtained using an 11-spin encoding to transmit a state over a chain containing 10 000 spins. An analysis of the magnetic-field dependence is given, and conditions for field optimization are provided.

Casimir invariants for systems undergoing collective motion

The interest in decoherence-free, or noiseless subsystems (DFS/NSs) of quantum systems is both of fundamental and of practical interest. Understanding the invariance of a set of states under certain transformations is mutually associated with a better understanding of some fundamental aspects of quantum mechanics as well as the practical utility of invariant subsystems. For example, DFS/NSs are potentially useful for protecting quantum information in quantum cryptography and quantum computing as well as enabling universal computation. Here we discuss transformations which are compatible with a DFS/NS that is composed of d-state systems which protect against collective noise. They are compatible in the sense that they do not take the logical (encoded) states outside of the DFS/NS during the transformation. Furthermore, it is shown that the Hamiltonian evolutions derived here can be used to perform universal quantum computation on a three qudit DFS/NS. Many of the methods used in our derivations are directly applicable to a large variety of DFS/NSs. More generally, we may also state that these transformations are compatible with collective motions.

Shortcut to nonadiabatic quantum state transmission

We outline a proposal for a method of preparing an encoded two-state system (logical qubit) that is immune to collective noise acting on the Hilbert space of the states supporting it. The logical qubit is comprised of three photonic three-state systems (qutrits) and is generated by the process of spontaneous parametric down conversion. The states are constructed using linear optical elements along with three down-conversion sources, and are deemed successful by the simultaneous detection of six events. We also show how to select a maximally entangled state of two qutrits by similar methods. For this maximally entangled state we describe conditions for the state to be decoherence-free which do not correspond to collective errors.

Quantum-Secured Surveillance Based on Mach-Zehnder Interferometry

Lian-Ao Wu,1, 2 C. Allen Bishop,3 and Mark S. Byrd3, 4 Ikerbasque, Basque Foundation for Science, 48011 Bilbao, Spain Department of Theoretical Physics and History of Science, The Basque Country University (EHU/UPV), PO Box 644, 48080 Bilbao, Spain Physics Department, Southern Illinois University, Carbondale, Illinois 62901-4401 Computer Science Department, Southern Illinois University, Carbondale, Illinois 62901 (Dated: January 20, 2013)