Extracting joint weak values with local, single-particle measurements

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure weakly in practice (for instance, in optics -- a common testing ground for this technique -- strong photon-photon interactions would be needed). Here we derive a general, experimentally feasible, method for extracting these values from correlations between single-particle observables.Comment: 6 page

Identification of Decoherence-Free Subspaces Without Quantum Process Tomography

Characterizing a quantum process is the critical first step towards applying such a process in a quantum information protocol. Full process characterization is known to be extremely resource-intensive, motivating the search for more efficient ways to extract salient information about the process. An example is the identification of "decoherence-free subspaces", in which computation or communications may be carried out, immune to the principal sources of decoherence in the system. Here we propose and demonstrate a protocol which enables one to directly identify a DFS without carrying out a full reconstruction. Our protocol offers an up-to-quadratic speedup over standard process tomography. In this paper, we experimentally identify the DFS of a two-qubit process with 32 measurements rather than the usual 256, characterize the robustness and efficiency of the protocol, and discuss its extension to higher-dimensional systems.Comment: 6 pages, 5 figure

The Faraday Quantum Clock and Non-local Photon Pair Correlations

We study the use of the Faraday effect as a quantum clock for measuring traversal times of evanescent photons through magneto-refractive structures. The Faraday effect acts both as a phase-shifter and as a filter for circular polarizations. Only measurements based on the Faraday phase-shift properties are relevant to the traversal time measurements. The Faraday polarization filtering may cause the loss of non-local (Einstein-Podolsky-Rosen) two-photon correlations, but this loss can be avoided without sacrificing the clock accuracy. We show that a mechanism of destructive interference between consecutive paths is responsible for superluminal traversal times measured by the clock.Comment: 6 figure

Sub-femtosecond determination of transmission delay times for a dielectric mirror (photonic bandgap) as a function of angle of incidence

Using a two-photon interference technique, we measure the delay for single-photon wavepackets to be transmitted through a multilayer dielectric mirror, which functions as a ``photonic bandgap'' medium. By varying the angle of incidence, we are able to confirm the behavior predicted by the group delay (stationary phase approximation), including a variation of the delay time from superluminal to subluminal as the band edge is tuned towards to the wavelength of our photons. The agreement with theory is better than 0.5 femtoseconds (less than one quarter of an optical period) except at large angles of incidence. The source of the remaining discrepancy is not yet fully understood.Comment: 5 pages and 5 figure

Conditional probabilities in quantum theory, and the tunneling time controversy

It is argued that there is a sensible way to define conditional probabilities in quantum mechanics, assuming only Bayes's theorem and standard quantum theory. These probabilities are equivalent to the ``weak measurement'' predictions due to Aharonov {\it et al.}, and hence describe the outcomes of real measurements made on subensembles. In particular, this approach is used to address the question of the history of a particle which has tunnelled across a barrier. A {\it gedankenexperiment} is presented to demonstrate the physically testable implications of the results of these calculations, along with graphs of the time-evolution of the conditional probability distribution for a tunneling particle and for one undergoing allowed transmission. Numerical results are also presented for the effects of loss in a bandgap medium on transmission and on reflection, as a function of the position of the lossy region; such loss should provide a feasible, though indirect, test of the present conclusions. It is argued that the effects of loss on the pulse {\it delay time} are related to the imaginary value of the momentum of a tunneling particle, and it is suggested that this might help explain a small discrepancy in an earlier experiment.Comment: 11 pages, latex, 4 postscript figures separate (one w/ 3 parts

Experimental characterization of qutrits using SIC-POVMs

Generalized quantum measurements (also known as POVMs) are of great importance in quantum information and quantum foundations, but often difficult to perform. We present an experimental approach which can in principle be used to perform arbitrary POVMs in a linear-optical context. One of the most interesting POVMs, the SIC-POVM, is the most compact, set of measurements that can be used to fully describe a quantum state. We use our technique to carry out the first experimental characterization of the state of a qutrit using SIC-POVMs. Because of the highly symmetric nature of this measurement, such a representation has the unique property that it permits all other measurement outcomes to be predicted by a simple extension of the classical Bayesian sum rule, making no use of complex amplitudes or Hilbert-space operators. We demonstrate this approach on several qutrit states encoded in single photons.Comment: 4 pages, 4 figures, submitted to PR

Macroscopic Quantum Tunneling Escape of Bose-Einstein Condensates

Recent experiments on macroscopic quantum tunneling reveal a non-exponential decay of the number of atoms trapped in a quasibound state behind a potential barrier. Through both experiment and theory, we demonstrate this non-exponential decay results from interactions between atoms. Quantum tunneling of tens of thousands of 87 Rb atoms in a Bose-Einstein condensate is modeled by a modified Jeffreys-Wentzel-Kramers-Brillouin model, taking into account the effective time-dependent barrier induced by the mean-field. Three-dimensional Gross-Pitaevskii simulations corroborate a mean-field result when compared with experiments. However, with one-dimensional modeling using time-evolving block decimation, we present an effective renormalized mean-field theory that suggests many-body dynamics for which a bare mean-field theory may not apply

Tunneling in graphene-topological insulator hybrid devices

Hybrid graphene-topological insulator (TI) devices were fabricated using a mechanical transfer method and studied via electronic transport. Devices consisting of bilayer graphene (BLG) under the TI Bi$_2$Se$_3$ exhibit differential conductance characteristics which appear to be dominated by tunneling, roughly reproducing the Bi$_2$Se$_3$ density of states. Similar results were obtained for BLG on top of Bi$_2$Se$_3$, with 10-fold greater conductance consistent with a larger contact area due to better surface conformity. The devices further show evidence of inelastic phonon-assisted tunneling processes involving both Bi$_2$Se$_3$ and graphene phonons. These processes favor phonons which compensate for momentum mismatch between the TI $\Gamma$ and graphene $K, K'$ points. Finally, the utility of these tunnel junctions is demonstrated on a density-tunable BLG device, where the charge-neutrality point is traced along the energy-density trajectory. This trajectory is used as a measure of the ground-state density of states

Correlation energy of an electron gas in strong magnetic fields at high densities

The high-density electron gas in a strong magnetic field B and at zero temperature is investigated. The quantum strong-field limit is considered in which only the lowest Landau level is occupied. It is shown that the perturbation series of the ground-state energy can be represented in analogy to the Gell-Mann Brueckner expression of the ground-state energy of the field-free electron gas. The role of the expansion parameter is taken by r_B= (2/3 \pi^2) (B/m^2) (\hbar r_s /e)^3 instead of the field-free Gell-Mann Brueckner parameter r_s. The perturbation series is given exactly up to o(r_B) for the case of a small filling factor for the lowest Landau level.Comment: 10 pages, Accepted for publication in Phys.Rev.

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