On the Optimal Choice of Spin-Squeezed States for Detecting and Characterizing a Quantum Process

Quantum metrology uses quantum states with no classical counterpart to measure a physical quantity with extraordinary sensitivity or precision. Most metrology schemes measure a single parameter of a dynamical process by probing it with a specially designed quantum state. The success of such a scheme usually relies on the process belonging to a particular one-parameter family. If this assumption is violated, or if the goal is to measure more than one parameter, a different quantum state may perform better. In the most extreme case, we know nothing about the process and wish to learn everything. This requires quantum process tomography, which demands an informationally-complete set of probe states. It is very convenient if this set is group-covariant -- i.e., each element is generated by applying an element of the quantum system's natural symmetry group to a single fixed fiducial state. In this paper, we consider metrology with 2-photon ("biphoton") states, and report experimental studies of different states' sensitivity to small, unknown collective SU(2) rotations ("SU(2) jitter"). Maximally entangled N00N states are the most sensitive detectors of such a rotation, yet they are also among the worst at fully characterizing an a-priori unknown process. We identify (and confirm experimentally) the best SU(2)-covariant set for process tomography; these states are all less entangled than the N00N state, and are characterized by the fact that they form a 2-design.Comment: 10 pages, 5 figure

Quantum Darwinism in quantum Brownian motion: the vacuum as a witness

We study quantum Darwinism -- the redundant recording of information about a decohering system by its environment -- in zero-temperature quantum Brownian motion. An initially nonlocal quantum state leaves a record whose redundancy increases rapidly with its spatial extent. Significant delocalization (e.g., a Schroedinger's Cat state) causes high redundancy: many observers can measure the system's position without perturbing it. This explains the objective (i.e. classical) existence of einselected, decoherence-resistant pointer states of macroscopic objects.Comment: 5 page

Adaptive quantum state tomography improves accuracy quadratically

We introduce a simple protocol for adaptive quantum state tomography, which reduces the worst-case infidelity between the estimate and the true state from $O(N^{-1/2})$ to $O(N^{-1})$. It uses a single adaptation step and just one extra measurement setting. In a linear optical qubit experiment, we demonstrate a full order of magnitude reduction in infidelity (from $0.1$ to $0.01$) for a modest number of samples ($N=3\times10^4$).Comment: 8 pages, 7 figure

The structure of preserved information in quantum processes

We introduce a general operational characterization of information-preserving structures (IPS) -- encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes -- by demonstrating that they are isometric to fixed points of unital quantum processes. Using this, we show that every IPS is a matrix algebra. We further establish a structure theorem for the fixed states and observables of an arbitrary process, which unifies the Schrodinger and Heisenberg pictures, places restrictions on physically allowed kinds of information, and provides an efficient algorithm for finding all noiseless and unitarily noiseless subsystems of the process

Hamiltonian Determination with Restricted Access in Transverse Field Ising Chain

We propose a method to evaluate parameters in the Hamiltonian of the Ising chain under site-dependent transverse fields, with a proviso that we can control and measure one of the edge spins only. We evaluate the eigenvalues of the Hamiltonian and the time-evoultion operator exactly for a 3-spin chain, from which we obtain the expectation values of $\sigma_x$ of the first spin. The parameters are found from the peak positions of the Fourier transform of the expectation value. There are four assumptions in our method, which are mild enough to be satisfied in many physical systems.Comment: 15pages, 4 figure

Anisotropy and internal field distribution of MgB2 in the mixed state at low temperatures

Magnetization and muon spin relaxation on MgB2 were measured as a function of field at 2 K. Both indicate an inverse-squared penetration depth strongly decreasing with increasing field H below about 1 T. Magnetization also suggests the anisotropy of the penetration depth to increase with increasing H, interpolating between a low Hc1 and a high Hc2 anisotropy. Torque vs angle measurements are in agreement with this finding, while also ruling out drastic differences between the mixed state anisotropies of the two basic length scales penetration depth and coherence length.Comment: 4 pages, 4 figure

Scalable Noise Estimation with Random Unitary Operators

We describe a scalable stochastic method for the experimental measurement of generalized fidelities characterizing the accuracy of the implementation of a coherent quantum transformation. The method is based on the motion reversal of random unitary operators. In the simplest case our method enables direct estimation of the average gate fidelity. The more general fidelities are characterized by a universal exponential rate of fidelity loss. In all cases the measurable fidelity decrease is directly related to the strength of the noise affecting the implementation -- quantified by the trace of the superoperator describing the non--unitary dynamics. While the scalability of our stochastic protocol makes it most relevant in large Hilbert spaces (when quantum process tomography is infeasible), our method should be immediately useful for evaluating the degree of control that is achievable in any prototype quantum processing device. By varying over different experimental arrangements and error-correction strategies additional information about the noise can be determined.Comment: 8 pages; v2: published version (typos corrected; reference added

Verifying multi-partite mode entanglement of W states

We construct a method for verifying mode entanglement of N-mode W states. The ideal W state contains exactly one excitation symmetrically shared between N modes, but our method takes the existence of higher numbers of excitations into account, as well as the vacuum state and other deviations from the ideal state. Moreover, our method distinguishes between full N-party entanglement and states with M-party entanglement with M<N, including mixtures of the latter. We specialize to the case N=4 for illustrative purposes. In the optical case, where excitations are photons, our method can be implemented using linear optics.Comment: 11 pages, 12 figure

Information preserving structures: A general framework for quantum zero-error information

Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system's ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures to classify all the kinds of information that can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected. We also classify distinct operational criteria for preservation (e.g., "noiseless", "unitarily correctible", etc.) and introduce two new and natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational critera, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel's information-preserving structures.Comment: 29 pages, 19 examples. Contains complete proofs for all the theorems in arXiv:0705.428