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

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

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

Experimental Entanglement of Temporal Orders

The study of causal relations has recently been applied to the quantum realm, leading to the discovery that not all quantum processes have a definite causal structure. While such processes have previously been experimentally demonstrated, these demonstrations relied on the assumption that quantum theory can be applied to causal structures and laboratory operations. Here, we present the first demonstration of entangled temporal orders beyond the quantum formalism. We do so by proving the incompatibility of our experimental outcomes with a class of generalized probabilistic theories which satisfy the assumptions of locality and definite temporal orders. To this end, we derive physical constraints (in the form of a Bell-like inequality) on experimental outcomes within such a class of theories. We then experimentally invalidate these theories by violating the inequality, thus providing an experimental proof, outside the quantum formalism, that nature is incompatible with the assumption that the temporal order between events is definite locally.Comment: 20 pages, 8 figures. Thoroughly revised manuscript. Updated theory-independent proofs including new experimental dat

Scalable Spatial Super-Resolution using Entangled Photons

N00N states -- maximally path-entangled states of N photons -- exhibit spatial interference patterns sharper than any classical interference pattern. This is known as super-resolution. However, even with perfectly efficient number-resolving detectors, the detection efficiency of all previously demonstrated methods to measure such interference decreases exponentially with the number of photons in the N00N state, often leading to the conclusion that N00N states are unsuitable for spatial measurements. Here, we create spatial super-resolution fringes with two-, three-, and four-photon N00N states, and demonstrate a scalable implementation of the so-called ``optical centroid measurement'' which provides an in-principle perfect detection efficiency. Moreover, we compare the N00N-state interference to the corresponding classical super-resolution interference. Although both provide the same increase in spatial frequency, the visibility of the classical fringes decreases exponentially with the number of detected photons, while the visibility of our experimentally measured N00N-state super-resolution fringes remains approximately constant with N. Our implementation of the optical centroid measurement is a scalable method to measure high photon-number quantum interference, an essential step forward for quantum-enhanced measurements, overcoming what was believed to be a fundamental challenge to quantum metrology

Detection of subclinical keratoconus with a validated alternative method to corneal densitometry

Purpose: To enhance the current standards of subclinical keratoconus screening based on the statistical modeling of the pixel intensity distribution of Scheimpflug images. Methods: Scheimpflug corneal tomographies corresponding to 25 corneal meridians of 60 participants were retrospectively collected and divided into three groups: controls (20 eyes), subclinical keratoconus (20 eyes), and clinical keratoconus (20 eyes). Only right eyes were selected. After corneal segmentation, pixel intensities of the stromal tissue were statistically modeled using a Weibull probability density function from which parameter a (pixel brightness) was derived. Further, data were transformed to polar coordinates, smoothed, and interpolated to build a map of the corneal a parameter. The discriminative power of the method was analyzed using receiver operating characteristic curves. Results: The proposed platform-independent method achieved a higher performance in discriminating subclinical keratoconus from control eyes (90.0% sensitivity, 95.0% specificity, 0.97 area under the curve [AUC]) than the standard method (Belin–Ambrósio enhanced ectasia display), which uses only corneal morphometry (85.0% sensitivity, 85.0% specificity, 0.80 AUC). Conclusions: Analysis of light backscatter at the cornea successfully discriminates subclinical keratoconus from control eyes, upgrading the results previously reported in the literature. Translational Relevance: The proposed methodology has the potential to support clinicians in the detection of keratoconus before showing clinical signs. © 2021 The Authors