Session F26: Quantum Crytography, Quantum Communication, and Quantum Measurement

Quantum to classical randomness extractors

The goal of randomness extraction is to distill (almost) perfect randomness from a weak source of randomness. When the source yields a classical string X, many extractor constructions are known. Yet, when considering a physical randomness source, X is itself ultimately the result of a measurement on an underlying quantum system. When characterizing the power of a source to supply randomness it is hence a natural question to ask, how much classical randomness we can extract from a quantum system. To tackle this question we here introduce the notion of quantum-to-classical randomness extractors (QC-extractors). We identify an entropic quantity that determines exactly how much randomness can be obtained. Furthermore, we provide constructions of QC-extractors based on measurements in a full set of mutually unbiased bases (MUBs), and certain single qubit measurements. As the first application, we show that any QC-extractor gives rise to entropic uncertainty relations with respect to quantum side information. Such relations were previously only known for two measurements. As the second application, we resolve the central open question in the noisy-storage model [Wehner et al., PRL 100, 220502 (2008)] by linking security to the quantum capacity of the adversary's storage device.   

Quantum secret sharing with minimized quantum communication

Standard techniques for sharing a quantum secret among multiple players (such that certain subsets of the players can recover the secret while others are denied all knowledge of the secret) require a large amount of quantum communication to distribute the secret, which is likely to be the most costly resource in any practical scheme. Two known methods for reducing this cost are the use of imperfect ``ramp'' secret sharing (in which security is sacrificed for efficiency) and classical encryption (in which certain elements of the players' shares consist of classical information only). We demonstrate how one may combine these methods to reduce the required quantum communication below what has been previously achieved, in some cases to a provable minimum, without any loss of security. The techniques involved are closely-related to the properties of stabilizer codes, and thus have strong potential for being adapted to a wide range of quantum secret sharing schemes.   

Quantum teleportation over 143 kilometres using active feed-forward

Quantum teleportation is a quintessential prerequisite of many quantum information processing protocols. By using quantum teleportation, one can circumvent the no-cloning theorem and faithfully transfer unknown quantum states to a party whose location is even unknown over arbitrary distances. Ever since the first experimental demonstrations of quantum teleportation of independent qubits and of squeezed states, researchers have progressively extended the communication distance in teleportation. Here we report the first long-distance quantum teleportation experiment with active feed-forward in real time. The experiment employed two optical links, quantum and classical, over 143 km free space between the two Canary Islands of La Palma and Tenerife. To achieve this, the experiment had to employ a combination of advanced techniques such as a frequency-uncorrelated polarization-entangled photon pair source, ultra-low-noise single-photon detectors, and entanglement-assisted clock synchronization. The average teleported state fidelity was well beyond the classical limit of 2/3.   

Ultrafast quantum communications over long distances using quantum encoding

Quantum repeaters provide a way of enabling long distance quantum communication by establishing entangled qubits between remote locations. The first generation quantum repeater protocols involve time consuming entanglement purification steps that demand a long lived quantum memory and two-way classical communication that makes them slow. This problem can be circumvented by the new generation quantum repeater protocols that use quantum encoding, one-way classical communication and classical error correction techniques. Furthermore, each quantum repeater station only needs short lived quantum memory bits, the number of which has favorable poly-logarithmic scaling with the distance. We investigate the tolerance of these schemes against photon losses and depolarizing errors, and discuss the possibility of realizing these schemes in physical systems with the current state of art.   

Generating and verifying entanglement of itinerant microwave modes

Entanglement is a critical resource for quantum information science. In particular, shared entanglement between pairs of electromagnetic fields propagating on two physically separate channels is required for quantum communication protocols with continuous variables. Moreover, the ability to entangle propagating microwave fields provides possible schemes to create quantum communication channels between localized superconducting qubits. In this talk, we will present an experimental demonstration of this type of entanglement. We generate the entangled state by combining a squeezed state and vacuum on a balanced beam splitter. The entanglement is then revealed by strong correlations between the quadrature amplitudes of the two output modes of the beam splitter. Crucial for an eventual teleportation demonstration, the two modes are measured efficiently and with independent choice of measured quadratures.   

Microwave Photon Counter Based on Josephson Junctions

We describe progress in the development of a microwave photon counter based on the current biased Josephson junction; absorption of a single photon causes the junction to switch to the voltage state, producing a large and easily measured classical signal. We discuss a self-resetting bias scheme based on a superconducting kinetic inductor that causes the junction to reset automatically to the active state following photon absorption. We investigate detector quantum efficiency and dark rate, and discuss applications to mesoscopic noise and circuit quantum electrodynamics.   

Utilization of an Electron Multiplying CCD camera for applications in quantum information processing

Electron Multiplying Charge-Coupled Device (EMCCD) cameras utilize an on-chip amplification process which boosts low-light signals above the readout noise floor. Although traditionally used for biological imaging, they have recently attracted interest for single-photon counting and entangled state characterization in quantum information processing applications. In addition, they exhibit some photon number-resolving capacity, which is attractive from the point-of-view of several applications in optical continous-variable computing, such as building a cubic phase gate. We characterize the Andor Luca-R EMCCD camera as an affordable tool for applications in optical quantum information. We present measurements of single-photon detection efficiency, dark count probability as well as photon-number resolving capacity and place quantitative bounds on the noise performance and detection efficiency of the EMCCD detector array. We find that the readout noise floor is a Gaussian distribution centered at 500 counts/pixel/frame at high EM gain setting. We also characterize the trade-off between quantum efficiency and detector dark-count probability.   

High-efficiency Cooper pair splitting demonstrated by two-particle conductance resonance and positive noise cross-correlation

Entanglement is at the heart of the Einstein-Podolsky-Rosen paradox, where the non-locality is a necessary ingredient. Cooper pairs in superconductors can be split adiabatically, thus forming entangled electrons. Here, we fabricate such an electron splitter by contacting an~aluminum superconductor strip at the centre of a suspended~InAs~nanowire. The nanowire is terminated at both ends with two normal metallic drains. Dividing each half of the nanowire by a gate-induced Coulomb blockaded quantum dot strongly impeds the flow of Cooper pairs due to the large charging energy, while still permitting passage of single electrons. We provide conclusive evidence of extremely high efficiency Cooper pair splitting via observing positive two-particle correlations of the conductance and the shot noise of the split electrons in the two opposite drains of the nanowire. Moreover, the actual charge of the injected quasiparticles is verified by shot noise measurements.   

An operational approach to indirectly measuring tunneling time

The tunneling time through an arbitrary one-dimensional barrier is investigated using the dwell time operator approach Since the tunneling time contains a natural post-selection ( we only average over particles that successfully tunnel), the tunneling time can ve related to the weak value of the dwell time operator. We analyze the situation by considering a specific measurement context containing experimentally observable quantities, since measuring the dwell time operator directly is not strictly achievable in the laboratory. Therefore, we reconstruct the average value of the dwell time operator applying the contextual values formalism [J. Dressel and A. N. Jordan, Phys. Rev. A \textbf{85}, 022123 (2012)] for generalized measurements based on the Larmor clock [ M. B\"{u}ttiker, Phys. Rev. B \textbf{27}, 6178 (1983)].   

A Stochastic Path Integral Formulation for Continuous Quantum Measurement

We consider the continuous quantum measurement of a two-level system, for example, a double-quantum dot weakly measured by a quantum point contact. In a weak measurement regime, the measurement outcome at each time step is non-deterministic and fluctuates around its mean value. While the stochastic master/Schr\"{o}dinger equations are commonly used to study the state of the qubit, we propose an alternative formalism -- the stochastic path integral -- which can compute moments and correlation functions of the measurement outcomes, and the distributions of possible qubit states. By constructing a probability functional of the measurement outcomes in a path integral form, the moments can be computed from perturbative expansions, which can be resumed to exact solutions in some cases. We show that this approach reproduces and extends existing solutions derived using different methods, and introduces a new way to compute conditioned moments and correlation functions. We also show how real-time feedback can be naturally included in this approach.   

Weak values are universal in von Neumann measurements

We refute the widely held belief that the quantum weak value necessarily pertains to weak measurements. To accomplish this, we use the transverse position of a free particle as the detector for the conditioned von Neumann measurement of a system observable. For any coupling strength, any initial states, and any choice of conditioning, the averages of the detector position and momentum are completely described by the real parts of three generalized weak values in the joint Hilbert space. Higher-order detector moments also have similar weak value expansions. Using the Wigner distribution of the initial detector state, we find compact expressions for these weak values within the reduced system Hilbert space, demonstrating that the effective preselection for a measured system weak value is decohered by the detector. As an optical application of the approach, we consider an arbitrary Hermite-Gauss mode for a paraxial beam-like detector. For non-Gaussian modes the momentum shift involves the imaginary part of the system weak value plus an additional weak-value-like correction.   

Implementing general quantum measurements on linear optical and solid-state qubits

We show a systematic construction for implementing general measurements on a single qubit, including both strong (or projection) and weak measurements. We mainly focus on linear optical qubits. The present approach is composed of simple and feasible elements, i.e., beam splitters, wave plates, and polarizing beam splitters. We show how the parameters characterizing the measurement operators are controlled by the linear optical elements. We also propose a method for the implementation of general measurements in solid-state qubits. Furthermore, we show an interesting application of the general measurements, i.e., entanglement amplification.   

Embedded SIC-POVMs

Symmetric informationally complete (SIC) sets of quantum states have applications in foundational studies of quantum mechanics, quantum tomography, quantum communication, quantum cryptography, and classical signal processing. However, their existence in every dimension has not been proven, and no general construction has been known. During our study of linear dependencies in Weyl-Heisenberg orbits [1], we discovered 2-dimensional SICs embedded in a 6-dimensional Hilbert space. This offers a robust construction for 2-dimensional SICs, and may potentially impact the SIC existence problem. In this talk, I will explain how this construction works, and present numerical results for some other dimensions. References: [1] Hoan Bui Dang, Kate Blanchfield, Ingemar Bengtsson, D. M. Appleby, ``Linear Dependencies in Weyl-Heisenberg Orbits,'' arXiv:1211.0215.   

A multiport scheme for performing SIC-POVMs

SIC-POVMs comprise a family of generalized quantum measurements known to be optimal for linear quantum tomography, according to fairly standard Hilbert-Schmidt measures of statistical efficiency [1]. Because of the practical significance of state estimation in quantum information processing, it should prove useful to develop experimental methods for implementing SIC-POVMs directly. Based on the idea of Naimark extensions for POVMs, I propose the design for a SIC-POVM experiment using multiport devices with path-encoded qudits and demonstrate how it can be realized with integrated linear optics for qubits and qutrits [2]. References: [1] A. J. Scott, J. Phys. A 39, 13507 (2006). [2] G. N. M. Tabia, arXiv:1207.6035 (2012).