Quantifying entanglement in two-mode Gaussian states

Entangled two-mode Gaussian states are a key resource for quantum information technologies such as teleportation, quantum cryptography and quantum computation, so quantification of Gaussian entanglement is an important problem. Entanglement of formation is unanimously considered a proper measure of quantum correlations, but for arbitrary two-mode Gaussian states no analytical form is currently known. In contrast, logarithmic negativity is a measure straightforward to calculate and so has been adopted by most researchers, even though it is a less faithful quantifier. In this work, we derive an analytical lower bound for entanglement of formation of generic two-mode Gaussian states, which becomes tight for symmetric states and for states with balanced correlations. We define simple expressions for entanglement of formation in physically relevant situations and use these to illustrate the problematic behavior of logarithmic negativity, which can lead to spurious conclusions.Comment: 8 pages,3 figs; The original submission gave an analytical formula that was claimed to give the entanglement of formation for arbitrary two-mode Gaussian states - this was incorrect. The formula gives a lower bound of EoF which saturates for symmetric states and for states with balanced correlations, and is a good approximation for most other states. This error is corrected in the revised versio

Frequency and temporal effects in linear optical quantum computing

Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be non-idealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a non-deterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing non-ideal photon counters, which have finite bandwidth and time response.Comment: 10 pages, 9 figures, replaced with published versio

Estimating space-time parameters with a quantum probe in a lossy environment

We study the problem of estimating the Schwarzschild radius of a massive body using Gaussian quantum probe states. Previous calculations assumed that the probe state remained pure after propagating a large distance. In a realistic scenario, there would be inevitable losses. Here we introduce a practical approach to calculate the Quantum Fisher Informations (QFIs) for a quantum probe that has passed through a lossy channel. Whilst for many situations loss means coherent states are optimal, we identify certain situations for which squeezed states have an advantage. We also study the effect of the frequency profile of the wavepacket propagating from Alice to Bob. There exists an optimal operating point for a chosen mode profile. In particular, employing a smooth rectangular frequency profile significantly improves the error bound on the Schwarzschild radius compared to a Gaussian frequency profile.Comment: 14 pages, 18 figure

Modeling photo-detectors in quantum optics

Photo-detection plays a fundamental role in experimental quantum optics and is of particular importance in the emerging field of linear optics quantum computing. Present theoretical treatment of photo-detectors is highly idealized and fails to consider many important physical effects. We present a physically motivated model for photo-detectors which accommodates for the effects of finite resolution, bandwidth and efficiency, as well as dark-counts and dead-time. We apply our model to two simple well known applications, which illustrates the significance of these characteristics.Comment: 8 pages, 7 figure

Quantum Metrology in the Kerr Metric

A surprising feature of the Kerr metric is the anisotropy of the speed of light. The angular momentum of a rotating massive object causes co- and counter-propagating light paths to move at faster and slower velocities, respectively as determined by a far-away clock. Based on this effect we derive ultimate quantum limits for the measurement of the Kerr rotation parameter $a$ using a interferometric set up. As a possible implementation, we propose a Mach-Zehnder interferometer to measure the "one-way height differential" time effect. We isolate the effect by calibrating to a dark port and rotating the interferometer such that only the direction dependent Kerr-metric induced phase term remains. We transform to the Zero Angular Momentum Observer (ZAMO) flat metric where the observer see $c=1$. We use this metric and the Lorentz transformations to calculate the same Kerr phase shift. We then consider non-stationary observers moving with the planet's rotation, and find a method for cancelling the additional phase from the classical relative motion, thus leaving only the curvature induced phase.Comment: 9 pages, 7 figures, closest to published versio

Quantifying entanglement of formation for two-mode Gaussian states: Analytical expressions for upper and lower bounds and numerical estimation of its exact value

Entanglement of formation quantifies the entanglement of a state in terms of the entropy of entanglement of the least entangled pure state needed to prepare it. An analytical expression for this measure exists only for special cases, and finding a closed formula for an arbitrary state still remains an open problem. In this work we focus on two-mode Gaussian states, and we derive narrow upper and lower bounds for the measure that get tight for several special cases. Further, we show that the problem of calculating the actual value of the entanglement of formation for arbitrary two-mode Gaussian states reduces to a trivial single parameter optimization process, and we provide an efficient algorithm for the numerical calculation of the measure.Comment: 5 pages, 2 figures In this third version a few typos of the first and second versions have been correcte

Simulation of Gaussian channels via teleportation and error correction of Gaussian states

Gaussian channels are the typical way to model the decoherence introduced by the environment in continuous-variable quantum states. It is known that those channels can be simulated by a teleportation protocol using as a resource state either a maximally entangled state passing through the same channel, i.e., the Choi-state, or a state that is entangled at least as much as the Choi-state. Since the construction of the Choi-state requires infinite mean energy and entanglement, i.e. it is unphysical, we derive instead every physical state able to simulate a given channel through teleportation with finite resources, and we further find the optimal ones, i.e., the resource states that require the minimum energy and entanglement. We show that the optimal resource states are pure and equally entangled to the Choi-state as measured by the entanglement of formation. We also show that the same amount of entanglement is enough to simulate an equally decohering channel, while even more entanglement can simulate less decohering channels. We, finally, use that fact to generalize a previously known error correction protocol by making it able to correct noise coming not only from pure loss but from thermal loss channels as well.Comment: 12 pages, 8 figure

Noiseless phase quadrature amplification via electro-optic feed-forward

Theoretical results are presented which show that noiseless phase quadrature amplification is possible, and limited experimentally only by the efficiency of the phase detection system. Experimental results obtained using a Nd:YAG laser show a signal gain of 10dB and a signal transfer ratio of T_s=0.9. This result easily exceeds the standard quantum limit for signal transfer. The results also explicitly demonstrate the phase sensitive nature of the amplification process.Comment: 8 pages, 4 figure

Quantum Correlations in Nonlocal BosonSampling

Determination of the quantum nature of correlations between two spatially separated systems plays a crucial role in quantum information science. Of particular interest is the questions of if and how these correlations enable quantum information protocols to be more powerful. Here, we report on a distributed quantum computation protocol in which the input and output quantum states are considered to be classically correlated in quantum informatics. Nevertheless, we show that the correlations between the outcomes of the measurements on the output state cannot be efficiently simulated using classical algorithms. Crucially, at the same time, local measurement outcomes can be efficiently simulated on classical computers. We show that the only known classicality criterion violated by the input and output states in our protocol is the one used in quantum optics, namely, phase-space nonclassicality. As a result, we argue that the global phase-space nonclassicality inherent within the output state of our protocol represents true quantum correlations.Comment: 5 pages, 1 figure, comments are very welcome