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

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

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

Violation of Heisenberg's Measurement-Disturbance Relationship by Weak Measurements

While there is a rigorously proven relationship about uncertainties intrinsic to any quantum system, often referred to as "Heisenberg's Uncertainty Principle," Heisenberg originally formulated his ideas in terms of a relationship between the precision of a measurement and the disturbance it must create. Although this latter relationship is not rigorously proven, it is commonly believed (and taught) as an aspect of the broader uncertainty principle. Here, we experimentally observe a violation of Heisenberg's "measurement-disturbance relationship", using weak measurements to characterize a quantum system before and after it interacts with a measurement apparatus. Our experiment implements a 2010 proposal of Lund and Wiseman to confirm a revised measurement-disturbance relationship derived by Ozawa in 2003. Its results have broad implications for the foundations of quantum mechanics and for practical issues in quantum mechanics.Comment: 5 pages, 4 figure

Shedding light on sporopollenin chemistry, with reference to UV reconstructions

Sporopollenin, which forms the outer wall of pollen and spores, contains a chemical signature of ultraviolet-B flux via concentrations of UV-B absorbing compounds (UACs), providing a proxy for reconstructing UV irradiance through time. Although Fourier transform infrared (FTIR) spectroscopy provides an efficient means of measuring UAC concentrations, nitrogen-containing compounds have the potential to bias the aromatic and hydroxyl bands used to quantify and standardise UAC abundances. Here, we explore the presence and possible influence of nitrogen in UV reconstruction via an FTIR study of Lycopodium spores from a natural shading gradient. We show that the UV-sensitive aromatic peak at 1510 cm− 1 is clearly distinguishable from the amide II peak at 1550 cm− 1, and the decrease in aromatic content with increased shading can be reconstructed using standardisation approaches that do not rely on the 3300 cm− 1 hydroxyl band. Isolation of the sporopollenin results in the loss of nitrogen-related peaks from the FTIR spectra, while the aromatic gradient remains. This confirms the lack of nitrogen in sporopollenin and its limited potential for impacting on palaeo-UV reconstructions. FTIR is therefore an appropriate tool for quantifying UACs in spores and pollen, and information on UV flux should be obtainable from fossil or processed samples

Acid-Labile Traceless Click Linker for Protein Transduction

Intracellular delivery of active proteins presents an interesting approach in research and therapy. We created a protein transduction shuttle based on a new traceless click linker that combines the advantages of click reactions with implementation of reversible pH-sensitive bonds. The azidomethyl-methylmaleic anhydride (AzMMMan) linker was found compatible with different click chemistries, demonstrated in bioreversible protein modification with dyes, polyethylene glycol, or a transduction carrier. Linkages were stable at physiological pH but reversible at the mild acidic pH of endosomes or lysosomes. We show that pH-reversible attachment of a defined endosome-destabilizing three-arm oligo(ethane amino)amide carrier generates an effective shuttle for protein delivery. The cargo protein nlsEGFP, when coupled via the traceless AzMMMan linker, experiences efficient cellular uptake and endosomal escape into the cytosol, followed by import into the nucleus. In contrast, irreversible linkage to the same shuttle hampers nuclear delivery of nlsEGFP which after uptake remains trapped in the cytosol. Successful intracellular delivery of bioactive ß-galactosidase as a model enzyme was also demonstrated using the pH-controlled shuttle system