Quantum Gaussian Channels with Weak Measurements

In this paper we perform a novel analysis of quantum Gaussian channels in the context of weak measurements. Suppose Alice sends classical information to Bob using a quantum channel. Suppose Bob is allowed to use only weak measurements, what would be the channel capacity? We formulate weak measurement theory in these terms and discuss the above question.Comment: 9 pages, 1 figure. Accepted for publication in QI

Dense Wavelength Division Multiplexed Quantum Key Distribution Using Entangled Photons

Quantum key distribution (QKD) enables two parties to establish a secret key over a potentially hostile channel by exchanging photonic quantum states, relying on the fact that it is impossible for an eavesdropper to tap the quantum channel without disturbing these photons in a way that can be detected [1]. Here we introduce a large-alphabet QKD protocol that makes optimal use of temporal and spectral correlations of entangled photons, reaching the maximum number of inde- pendent basis states (the Schmidt number) and enabling extremely high information content per photon together with an optimal rate of secret key generation. This protocol, which we call 'Dense Wavelength Division Multiplexed Quantum Key Distribution' (DWDM-QKD), derives its security by the conjugate nature of the temporal and spectral entanglement of photon pairs generated by spontaneous parametric down conversion. By using a combination of spectral and temporal bases, we can adjust the protocol to be resource efficient. We show that DWDM-QKD is well suited to approach the optimal key generation rate using present-day sources, detectors, and DWDM opti- cal networks from classical communications, as well as emerging optical interconnect and photonic integrated chip (PIC) systems.Comment: 9 pages, 4 figure

Classical capacity per unit cost for quantum channels

In most communication scenarios, sending a symbol encoded in a quantum state requires spending resources such as energy, which can be quantified by a cost of communication. A standard approach in this context is to quantify the performance of communication protocol by classical capacity, quantifying the maximal amount of information that can be transmitted through a quantum channel per single use of the channel. However, different figures of merit are also possible, and a particularly well-suited one is the classical capacity per unit cost, which quantifies the maximal amount of information that can be transmitted per unit cost. I generalize this concept to account for the quantum nature of the information carriers and communication channels and show that if there exists a state with cost equal to zero, e.g. a vacuum state, the capacity per unit cost can be expressed by a simple formula containing maximization of the relative entropy between two quantum states. This enables me to analyze the behavior of photon information efficiency for general communication tasks and show simple bounds on the capacity per unit cost in terms of quantities familiar from quantum estimation theory. I calculate also the capacity per unit cost for general Gaussian quantum channels.Comment: 11 pages, 2 figures, final version, updated reference

Process tomography of quantum channels using classical light

High-dimensional entanglement with spatial modes of light promises increased security and information capacity over quantum channels. Unfortunately, entanglement decays due to perturbations, corrupting quantum links which cannot be repaired without a tomography of the channel. Paradoxically, the channel tomography itself is not possible without a working link. Here we overcome this problem with a robust approach to characterising quantum channels by means of classical light. Using free-space communication in a turbulent atmosphere as an example, we show that the state evolution of classically entangled degrees of freedom is equivalent to that of quantum entangled pho- tons, thus providing new physical insights into the notion of classical entanglement. The analysis of quantum channels by means of classical light in real time unravels stochastic dynamics in terms of pure state trajectories and thus enables precise quantum error-correction in short and long haul optical communication, in both free-space and fibre

Quantum information with Gaussian states

Quantum optical Gaussian states are a type of important robust quantum states which are manipulatable by the existing technologies. So far, most of the important quantum information experiments are done with such states, including bright Gaussian light and weak Gaussian light. Extending the existing results of quantum information with discrete quantum states to the case of continuous variable quantum states is an interesting theoretical job. The quantum Gaussian states play a central role in such a case. We review the properties and applications of Gaussian states in quantum information with emphasis on the fundamental concepts, the calculation techniques and the effects of imperfections of the real-life experimental setups. Topics here include the elementary properties of Gaussian states and relevant quantum information device, entanglement-based quantum tasks such as quantum teleportation, quantum cryptography with weak and strong Gaussian states and the quantum channel capacity, mathematical theory of quantum entanglement and state estimation for Gaussian states.Comment: 170 pages. Minors of the published version are corrected and listed in the Acknowledgement part of this versio

Quantum statistics of polariton parametric interactions

Using a high-quality GaAs planar microcavity, we optically generate polariton pairs, and verify their correlations by means of time-resolved single-photon detection. We find that correlations between the different modes are consistently lower than identical mode correlations, which is attributed to the presence of uncorrelated background. We discuss a model to quantify the effects of such a background on the observed correlations. Using spectral and temporal filtering, the background can be suppressed and a change in photon statistics towards non-classical correlations is observed. These results improve our understanding of the statistics of polariton-polariton scattering and background mechanisms, and pave the way to the generation of entangled polariton pairs

Theory of atmospheric quantum channels based on the law of total probability

The atmospheric turbulence is the main factor that influences quantum properties of propagating optical signals and may sufficiently degrade the performance of quantum communication protocols. The probability distribution of transmittance (PDT) for free-space channels is the main characteristics of the atmospheric links. Applying the law of total probability, we derive the PDT by separating the contributions from turbulence-induced beam wandering and beam-spot distortions. As a result, the obtained PDT varies from log-negative Weibull to truncated log-normal distributions depending on the channel characteristics. Moreover, we show that the method allows one to consistently describe beam tracking, a procedure which is typically used in practical long-distance free-space quantum communication. We analyze the security of decoy-state quantum key exchange through the turbulent atmosphere and show that beam tracking does not always improves quantum communication.Comment: 15 pages, 6 figure

Smoothing of Gaussian quantum dynamics for force detection

Building on recent work by Gammelmark et al. [Phys. Rev. Lett. 111, 160401 (2013)] we develop a formalism for prediction and retrodiction of Gaussian quantum systems undergoing continuous measurements. We apply the resulting formalism to study the advantage of incorporating a full measurement record and retrodiction for impulse-like force detection and accelerometry

Gaussian benchmark for optical communication aiming towards ultimate capacity

We establish the fundamental limit of communication capacity within Gaussian schemes under phase-insensitive Gaussian channels, which employ multimode Gaussian states for encoding and collective Gaussian operations and measurements for decoding. We prove that this Gaussian capacity is additive, i.e., its upper bound occurs with separable encoding and separable receivers so that a single-mode communication suffices to achieve the largest capacity under Gaussian schemes. This rigorously characterizes the gap between the ultimate Holevo capacity and the capacity within Gaussian communication, showing that Gaussian regime is not sufficient to achieve the Holevo bound particularly in the low-photon regime. Furthermore the Gaussian benchmark established here can be used to critically assess the performance of non-Gaussian protocols for optical communication. We move on to identify non-Gaussian schemes to beat the Gaussian capacity and show that a non-Gaussian receiver recently implemented by Becerra et al. [Nat. Photon. 7, 147 (2013)] can achieve this aim with an appropriately chosen encoding strategy.Comment: 9 pages, 6 figures, with supplemental materia

Demonstration of Weak Measurement Based on Atomic Spontaneous Emission

We demonstrate a new type of weak measurement based on the dynamics of spontaneous emission. The pointer in our scheme is given by the Lorentzian distribution characterizing atomic exponential decay via emission of a single photon. We thus introduce weak measurement, so far demonstrated nearly exclusively with laser beams and Gaussian statistics, into the quantum regime of single emitters and single quanta, enabling the exploitation of a wide class of sources that are abundant in nature. We describe a complete analogy between our scheme and weak measurement with conventional Gaussian pointers. Instead of a shift in the mean of a Gaussian distribution, an imaginary weak value is exhibited in our scheme by a significantly slower-than-natural exponential distribution of emitted photons at the postselected polarization, leading to a large shift in their mean arrival time. The dynamics of spontaneous emission offer a broader view of the measurement process than is usually considered within the weak measurement formalism. Our scheme opens the path for the use of atoms and atomlike systems as sensitive probes in weak measurements, one example being optical magnetometry.Comment: Final version as appears in Physical Review Letter