208 research outputs found
General framework for estimating the ultimate precision limit in noisy quantum-enhanced metrology
The estimation of parameters characterizing dynamical processes is central to
science and technology. The estimation error changes with the number N of
resources employed in the experiment (which could quantify, for instance, the
number of probes or the probing energy). Typically, it scales as 1/N^(1/2).
Quantum strategies may improve the precision, for noiseless processes, by an
extra factor 1/N^(1/2). For noisy processes, it is not known in general if and
when this improvement can be achieved. Here we propose a general framework for
obtaining attainable and useful lower bounds for the ultimate limit of
precision in noisy systems. We apply this bound to lossy optical interferometry
and atomic spectroscopy in the presence of dephasing, showing that it captures
the main features of the transition from the 1/N to the 1/N^(1/2) behaviour as
N increases, independently of the initial state of the probes, and even with
use of adaptive feedback.Comment: Published in Nature Physics. This is the revised submitted version.
The supplementary material can be found at
http://www.nature.com/nphys/journal/v7/n5/extref/nphys1958-s1.pd
Heralded Noiseless Amplification of a Photon Polarization Qubit
Non-deterministic noiseless amplification of a single mode can circumvent the
unique challenges to amplifying a quantum signal, such as the no-cloning
theorem, and the minimum noise cost for deterministic quantum state
amplification. However, existing devices are not suitable for amplifying the
fundamental optical quantum information carrier, a qubit coherently encoded
across two optical modes. Here, we construct a coherent two-mode amplifier, to
demonstrate the first heralded noiseless linear amplification of a qubit
encoded in the polarization state of a single photon. In doing so, we increase
the transmission fidelity of a realistic qubit channel by up to a factor of
five. Qubit amplifiers promise to extend the range of secure quantum
communication and other quantum information science and technology protocols.Comment: 6 pages, 3 figure
Ab-initio Quantum Enhanced Optical Phase Estimation Using Real-time Feedback Control
Optical phase estimation is a vital measurement primitive that is used to
perform accurate measurements of various physical quantities like length,
velocity and displacements. The precision of such measurements can be largely
enhanced by the use of entangled or squeezed states of light as demonstrated in
a variety of different optical systems. Most of these accounts however deal
with the measurement of a very small shift of an already known phase, which is
in stark contrast to ab-initio phase estimation where the initial phase is
unknown. Here we report on the realization of a quantum enhanced and fully
deterministic phase estimation protocol based on real-time feedback control.
Using robust squeezed states of light combined with a real-time Bayesian
estimation feedback algorithm, we demonstrate deterministic phase estimation
with a precision beyond the quantum shot noise limit. The demonstrated protocol
opens up new opportunities for quantum microscopy, quantum metrology and
quantum information processing.Comment: 5 figure
Entanglement-free Heisenberg-limited phase estimation
Measurement underpins all quantitative science. A key example is the
measurement of optical phase, used in length metrology and many other
applications. Advances in precision measurement have consistently led to
important scientific discoveries. At the fundamental level, measurement
precision is limited by the number N of quantum resources (such as photons)
that are used. Standard measurement schemes, using each resource independently,
lead to a phase uncertainty that scales as 1/sqrt(N) - known as the standard
quantum limit. However, it has long been conjectured that it should be possible
to achieve a precision limited only by the Heisenberg uncertainty principle,
dramatically improving the scaling to 1/N. It is commonly thought that
achieving this improvement requires the use of exotic quantum entangled states,
such as the NOON state. These states are extremely difficult to generate.
Measurement schemes with counted photons or ions have been performed with N <=
6, but few have surpassed the standard quantum limit and none have shown
Heisenberg-limited scaling. Here we demonstrate experimentally a
Heisenberg-limited phase estimation procedure. We replace entangled input
states with multiple applications of the phase shift on unentangled
single-photon states. We generalize Kitaev's phase estimation algorithm using
adaptive measurement theory to achieve a standard deviation scaling at the
Heisenberg limit. For the largest number of resources used (N = 378), we
estimate an unknown phase with a variance more than 10 dB below the standard
quantum limit; achieving this variance would require more than 4,000 resources
using standard interferometry. Our results represent a drastic reduction in the
complexity of achieving quantum-enhanced measurement precision.Comment: Published in Nature. This is the final versio
Microwave amplification with nanomechanical resonators
Sensitive measurement of electrical signals is at the heart of modern science
and technology. According to quantum mechanics, any detector or amplifier is
required to add a certain amount of noise to the signal, equaling at best the
energy of quantum fluctuations. The quantum limit of added noise has nearly
been reached with superconducting devices which take advantage of
nonlinearities in Josephson junctions. Here, we introduce a new paradigm of
amplification of microwave signals with the help of a mechanical oscillator. By
relying on the radiation pressure force on a nanomechanical resonator, we
provide an experimental demonstration and an analytical description of how the
injection of microwaves induces coherent stimulated emission and signal
amplification. This scheme, based on two linear oscillators, has the advantage
of being conceptually and practically simpler than the Josephson junction
devices, and, at the same time, has a high potential to reach quantum limited
operation. With a measured signal amplification of 25 decibels and the addition
of 20 quanta of noise, we anticipate near quantum-limited mechanical microwave
amplification is feasible in various applications involving integrated
electrical circuits.Comment: Main text + supplementary information. 14 pages, 3 figures (main
text), 18 pages, 6 figures (supplementary information
An allocation Malmquist index with an application in the China securities industry
This paper proposes an allocation Malmquist index which is inspired by the work on the non-parametric cost Malmquist index. We first show that how to decompose the cost Malmquist index into the input-oriented Malmquist index and the allocation Malmquist index. An application in corporate management of the China securities industry with the panel data set of 40 securities companies during the period 2005–2011 shows the practicality of the propose model
Measuring efficiency and productivity in professional football teams: Evidence from the English Premier League
Professional football clubs are unusual businesses, their performance judged on and off the field of play. This study is concerned with measuring the efficiency of clubs in the English Premier League. Information from clubs’ financial statements is used as a measure of corporate performance. To measure changes in efficiency and productivity the Malmquist non-parametric technique has been used. This is derived from the Data Envelopment Analysis (DEA) linear programming approach, with Canonical Correlation Analysis (CCA) being used to ensure the cohesion of the input-output variables. The study concludes that while clubs operate close to efficient levels for the assessed models, there is limited technological advance in their performance in terms of the displacement of the technological frontier
Debreu’s coefficient of resource utilization, the Solow residual, and TFP: the connection by Leontief preferences
Dissipative and Non-dissipative Single-Qubit Channels: Dynamics and Geometry
Single-qubit channels are studied under two broad classes: amplitude damping
channels and generalized depolarizing channels. A canonical derivation of the
Kraus representation of the former, via the Choi isomorphism is presented for
the general case of a system's interaction with a squeezed thermal bath. This
isomorphism is also used to characterize the difference in the geometry and
rank of these channel classes. Under the isomorphism, the degree of decoherence
is quantified according to the mixedness or separability of the Choi matrix.
Whereas the latter channels form a 3-simplex, the former channels do not form a
convex set as seen from an ab initio perspective. Further, where the rank of
generalized depolarizing channels can be any positive integer upto 4, that of
amplitude damping ones is either 2 or 4. Various channel performance parameters
are used to bring out the different influences of temperature and squeezing in
dissipative channels. In particular, a noise range is identified where the
distinguishability of states improves inspite of increasing decoherence due to
environmental squeezing.Comment: 12 pages, 4 figure
Dynamics of productivity in higher education: cross-european evidence based on bootstrapped Malmquist indices
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