There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

On September 14, 2015 at 09:50:45 UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal. The signal sweeps upwards in frequency from 35 to 250 Hz with a peak gravitational-wave strain of 1.0×10(-21). It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole. The signal was observed with a matched-filter signal-to-noise ratio of 24 and a false alarm rate estimated to be less than 1 event per 203,000 years, equivalent to a significance greater than 5.1σ. The source lies at a luminosity distance of 410(-180)(+160)  Mpc corresponding to a redshift z=0.09(-0.04)(+0.03). In the source frame, the initial black hole masses are 36(-4)(+5)M⊙ and 29(-4)(+4)M⊙, and the final black hole mass is 62(-4)(+4)M⊙, with 3.0(-0.5)(+0.5)M⊙c(2) radiated in gravitational waves. All uncertainties define 90% credible intervals. These observations demonstrate the existence of binary stellar-mass black hole systems. This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.

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The Observation of Gravitational Waves from a Binary Black Hole Merger

We review the field of cavity optomechanics, which explores the interaction between electromagnetic radiation and nano- or micromechanical motion This review covers the basics of optical cavities and mechanical resonators, their mutual optomechanical interaction mediated by the radiation pressure force, the large variety of experimental systems which exhibit this interaction, optical measurements of mechanical motion, dynamical backaction amplification and cooling, nonlinear dynamics, multimode optomechanics, and proposals for future cavity quantum optomechanics experiments In addition, we describe the perspectives for fundamental quantum physics and for possible applications of optomechanical devices

Cavity Optomechanics

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on an eavesdropper's power. This article provides a concise up-to-date review of QKD, biased toward the practical side. Essential theoretical tools that have been developed to assess the security of the main experimental platforms are presented (discrete-variable, continuous-variable, and distributed-phase-reference protocols).

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The security of practical quantum key distribution

The security of prepare-and-measure satellite-based quantum key distribution (QKD), under restricted eavesdropping scenarios, is addressed. We particularly consider cases where the eavesdropper, Eve, has limited access to the transmitted signal by Alice, and/or Bob’s receiver station. This restriction is modeled by lossy channels between Alice/Bob and Eve, where the transmissivity of such channels can, in principle, be bounded by monitoring techniques. An artefact of such lossy channels is the possibility of having bypass channels, those which are not accessible to Eve, but may not necessarily be characterized by the users either. This creates interesting, unexplored , scenarios for analyzing QKD security. In this paper, we obtain generic bounds on the key rate in the presence of bypass channels and apply them to continuous-variable QKD protocols with Gaussian encoding with direct and reverse reconciliation. We ﬁnd regimes of operation in which the above restrictions on Eve can considerably improve system performance. We also develop customised bounds for several protocols in the BB84 family and show that, in certain regimes, even the simple protocol of BB84 with weak coherent pulses is able to offer positive key rates at high channel losses, which would otherwise be impossible under an unrestricted Eve. In this case the limitation on Eve would allow Alice to send signals with larger intensities than the optimal value under an ideal Eve, which effectively reduces the effective channel loss. In all these cases, the part of the transmitted signal that does not reach Eve can play a non-trivial role in specifying the achievable key rate. Our work opens up new security frameworks for spaceborne quantum communications systems.

Realistic Threat Models for Satellite-Based Quantum Key Distribution

Protocols for discriminating between a pair of channels or for estimating a channel parameter can often be aided by adaptivity or by entanglement between the probe states. For large numbers of channel uses, this can make it diﬃcult to bound the best possible performance for such protocols. In this paper, we introduce a quantity that we call the relative ﬁdelity of a given pair of channels and a pair of input states to those channels. Constraining the allowed input states to all pairs of states whose ﬁdelity is greater than some minimum “input ﬁdelity” and minimising this quantity over the valid pairs of states, we get the minimum relative ﬁdelity for that input ﬁdelity constraint. We are then able to lower bound the ﬁdelity between the possible output states of any protocol acting on one of two possible channels in terms of the minimum relative ﬁdelity. This allows us to bound the performance of discrimination and parameter estimation protocols, as well as to rule out perfect discrimination for certain pairs of channels, even using the most general, adaptive protocols. By ﬁnding a continuity bound for the relative ﬁdelity, we are also able to provide a simple proof that the quantum Fisher information (QFI) of the output of an N -use protocol is no more than N 2 times the one-shot QFI.

Bounding the beneﬁt of adaptivity in quantum metrology using the relative ﬁdelity

We consider a quantum relay that is used by two parties to perform several continuous-variable protocols of quantum communication, from entanglement distribution (swapping and distillation) to quantum teleportation, and quantum key distribution. The theory of these protocols is suitably extended to a non-Markovian model of decoherence characterized by correlated Gaussian noise in the bosonic environment. In the worst-case scenario where bipartite entanglement is completely lost at the relay, we show that the various protocols can be reactivated by the assistance of classical (separable) correlations in the environment. In fact, above a critical amount, these correlations are able to guarantee the distribution of a weaker form of entanglement (quadripartite), which can be localized by the relay into a stronger form (bipartite) that is exploitable by the parties. Our findings are confirmed by a proof-of-principle experiment where we show, for the first time, that memory effects in the environment can drastically enhance the performance of a quantum relay, well beyond the single-repeater bound for quantum and private communications.

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Environment-assisted bosonic quantum communications

Gaussian networks are fundamental objects in network information theory. Here many senders and receivers are connected by physically motivated Gaussian channels while auxiliary Gaussian components, such as Gaussian relays, are entailed. Whilst the theoretical backbone of classical Gaussian networks is well established, the quantum analogue is yet immature. Here, we theoretically tackle composable security of arbitrary Gaussian quantum networks (quantum networks), with generally untrusted nodes, in the finite-size regime. We put forward a general methodology for parameter estimation, which is only based on the data shared by the remote end-users. Taking a chain of identical quantum links as an example, we further demonstrate our study. Additionally, we find that the key rate of a quantum amplifier-assisted chain can ideally beat the fundamental repeaterless limit with practical block sizes. However, this objective is practically questioned leading the way to new network/chain designs. 

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Composable end-to-end security of Gaussian quantum networks with untrusted relays

Since the invention of the laser in the 60s, one of the most fundamental communication channels has been the free-space optical channel. For this type of channel, a number of effects generally need to be considered, including diffraction, refraction, atmospheric extinction, pointing errors and, most importantly, turbulence. Because of all these adverse features, the free-space channel is more difficult to study than a stable fiber-based link. For the same reasons, only recently it has been possible to establish the ultimate performances achievable in quantum communications via free-space channels, together with practical rates for continuous variable (CV) quantum key distribution (QKD). Differently from previous literature, mainly focused on the regime of weak turbulence, this work considers the free-space optical channel in the more challenging regime of moderate-to-strong turbulence, where effects of beam widening and breaking are more important than beam wandering. This regime may occur in long-distance free-space links on the ground, in uplink to high-altitude platform systems (HAPS) and, more interestingly, in downlink from near-horizon satellites. In such a regime we rigorously investigate ultimate limits for quantum communications and show that composable keys can be extracted using CV-QKD. In particular, we apply our results to downlink from satellites at large zenith angles, for which not only turbulence is strong but also refraction causes non-trivial effects in terms of trajectory elongation.

Stefano Pirandola

Papers

Realistic Threat Models for Satellite-Based Quantum Key Distribution

Bounding the beneﬁt of adaptivity in quantum metrology using the relative ﬁdelity

Environment-assisted bosonic quantum communications

Composable end-to-end security of Gaussian quantum networks with untrusted relays

Quantum communications in a moderate-to-strong turbulent space