Strategies for enhancing quantum entanglement by local photon subtraction

Subtracting photons from a two-mode squeezed state is a well-known method to increase entanglement. We analyse different strategies of local photon subtraction from a two-mode squeezed state in terms of entanglement gain and success probability. We develop a general framework that incorporates imperfections and losses in all stages of the process: before, during, and after subtraction. By combining all three effects into a single efficiency parameter, we provide analytical and numerical results for subtraction strategies using photon-number-resolving and threshold detectors. We compare the entanglement gain afforded by symmetric and asymmetric subtraction scenarios across the two modes. For a given amount of loss, we identify an optimised set of parameters, such as initial squeezing and subtraction beam splitter transmissivity, that maximise the entanglement gain rate. We identify regimes for which asymmetric subtraction of different Fock states on the two modes outperforms symmetric strategies. In the lossless limit, subtracting a single photon from one mode always produces the highest entanglement gain rate. In the lossy case, the optimal strategy depends strongly on the losses on each mode individually, such that there is no general optimal strategy. Rather, taking losses on each mode as the only input parameters, we can identify the optimal subtraction strategy and required beam splitter transmissivities and initial squeezing parameter. Finally, we discuss the implications of our results for the distillation of continuous-variable quantum entanglement.Comment: 13 pages, 11 figures. Updated version for publicatio

A tradeoff in simultaneous quantum-limited phase and loss estimation in interferometry

Interferometry with quantum light is known to provide enhanced precision for estimating a single phase. However, depending on the parameters involved, the quantum limit for the simultaneous estimation of multiple parameters may not attainable, leading to trade-offs in the attainable precisions. Here we study the simultaneous estimation of two parameters related to optical interferometry: phase and loss, using a fixed number of photons. We derive a trade-off in the estimation of these two parameters which shows that, in contrast to single-parameter estimation, it is impossible to design a strategy saturating the quantum Cramer-Rao bound for loss and phase estimation in a single setup simultaneously. We design optimal quantum states with a fixed number of photons achieving the best possible simultaneous precisions. Our results reveal general features about concurrently estimating Hamiltonian and dissipative parameters, and has implications for sophisticated sensing scenarios such as quantum imaging.Comment: 9 pages, 6 figure

Molecular ions in L1544. II. The ionization degree

The maps presented in Paper I are here used to infer the variation of the column densities of HCO+, DCO+, N2H+, and N2D+ as a function of distance from the dust peak. These results are interpreted with the aid of a crude chemical model which predicts the abundances of these species as a function of radius in a spherically symmetric model with radial density distribution inferred from the observations of dust emission at millimeter wavelengths and dust absorption in the infrared. Our main observational finding is that the N(N2D+)/N(N2H+) column density ratio is of order 0.2 towards the L1544 dust peak as compared to N(DCO+)/N(HCO+) = 0.04. We conclude that this result as well as the general finding that N2H+ and N2D+ correlate well with the dust is caused by CO being depleted to a much higher degree than molecular nitrogen in the high density core of L1544. Depletion also favors deuterium enhancement and thus N2D+, which traces the dense and highly CO-depleted core nucleus, is much more enhanced than DCO+. Our models do not uniquely define the chemistry in the high density depleted nucleus of L1544 but they do suggest that the ionization degree is a few times 10^{-9} and that the ambipolar diffusion time scale is locally similar to the free fall time. It seems likely that the lower limit which one obtains to ionization degree by summing all observable molecular ions is not a great underestimate of the true ionization degree. We predict that atomic oxygen is abundant in the dense core and, if so, H3O+ may be the main ion in the central highly depleted region of the core

Peoples’ use of, and concerns about, green space networks: A case study of Birchwood, Warrington New Town, UK

Cultural services provided by green space networks and in particular leisure and recreational opportunities are central to the quality of life of those living in urban areas. However, the literature concerned with green space networks has mainly focussed on planning aspects rather than on recreational use. The aim of this study was to evaluate the recreational use of, and concerns about, a naturalistic green space network. The case study location was the naturalistic woodland framework in Birchwood, Warrington, UK, known as Birchwood Forest Park. Non-participant observation and content analysis of local archives were used to collect quantitative and qualitative data. Birchwood Forest Park was used more for leisure activities (52.8%, N = 1,825; i.e. recreation, sports or play) than for utilitarian purposes (47.2%, N = 1,825; i.e. as walking or cycling thoroughfare). However, utilitarian walking (30%, N = 1,825) was the most frequent type of activity observed. The maintenance of the naturalistic woodland framework was the most frequent concern mentioned in the local archives (33.3%, N = 234). This case study suggests that the recreational patterns in, as well as peoples’ concerns about, naturalistic urban landscapes may be a factor of high quality maintenance and associated local aesthetic and cultural perceptions. In developing, planning or managing comprehensive urban green space networks it is important to ensure that natural looking scenes are well maintained and that the local community is culturally connected to such scenes

Inverse correlation between quasiparticle mass and Tc in a cuprate high-Tc superconductor

Close to a zero-temperature transition between ordered and disordered electronic phases, quantum fluctuations can lead to a strong enhancement of electron mass and to the emergence of competing phases such as superconductivity. A correlation between the existence of such a quantum phase transition and superconductivity is quite well established in some heavy fermion and iron-based superconductors, and there have been suggestions that high-temperature superconductivity in copper-oxide materials (cuprates) may also be driven by the same mechanism. Close to optimal doping, where the superconducting transition temperature Tc is maximal in cuprates, two different phases are known to compete with superconductivity: a poorly understood pseudogap phase and a charge-ordered phase. Recent experiments have shown a strong increase in quasiparticle mass m* in the cuprate YBa2Cu3O7-δ as optimal doping is approached, suggesting that quantum fluctuations of the charge-ordered phase may be responsible for the high-Tc superconductivity. We have tested the robustness of this correlation between m* and Tc by performing quantum oscillation studies on the stoichiometric compound YBa2Cu4O8 under hydrostatic pressure. In contrast to the results for YBa2Cu3O7-δ, we find that in YBa2Cu4O8, the mass decreases as Tc increases under pressure. This inverse correlation between m* and Tc suggests that quantum fluctuations of the charge order enhance m* but do not enhance Tc