124 research outputs found
State estimation: direct state measurement vs. tomography
We compare direct state measurement (DST or weak state tomography) to
conventional state reconstruction (tomography) through accurate Monte-Carlo
simulations. We show that DST is surprisingly robust to its inherent bias. We
propose a method to estimate such bias (which introduces an unavoidable error
in the reconstruction) from the experimental data. As expected we find that DST
is much less precise than tomography. We consider both finite and
infinite-dimensional states of the DST pointer, showing that they provide
comparable reconstructions.Comment: 4 pages, 4 figure
Information-disturbance tradeoff in quantum measurements
We present a simple information-disturbance tradeoff relation valid for any
general measurement apparatus: The disturbance between input and output states
is lower bounded by the information the apparatus provides in distinguishing
these two states.Comment: 4 Pages, 1 Figure. Published version (reference added and minor
changes performed
Sub-Heisenberg estimation strategies are ineffective
In interferometry, sub-Heisenberg strategies claim to achieve a phase
estimation error smaller than the inverse of the mean number of photons
employed (Heisenberg bound). Here we show that one can achieve a comparable
precision without performing any measurement, just using the large prior
information that sub-Heisenberg strategies require. For uniform prior (i.e. no
prior information), we prove that these strategies cannot achieve more than a
fixed gain of about 1.73 over Heisenberg-limited interferometry. Analogous
results hold for arbitrary single-mode prior distributions. These results
extend also beyond interferometry: the effective error in estimating any
parameter is lower bounded by a quantity proportional to the inverse
expectation value (above a ground state) of the generator of translations of
the parameter.Comment: 4 pages, 2 figures, revised version that was publishe
State-independent preparation uncertainty relations
The standard state-dependent Heisenberg-Robertson uncertainly-relation lower
bound fails to capture the quintessential incompatibility of observables as the
bound can be zero for some states. To remedy this problem, we establish a class
of tight (i.e., inequalities are saturated)variance-based sum-uncertainty
relations derived from the Lie algebraic properties of observables and show
that our lower bounds depend only on the irreducible representation assumed
carried by the Hilbert space of state of the system. We illustrate our result
for the cases of the Weyl-Heisenberg algebra, special unitary algebras up to
rank 4, and any semisimple compact algebra. We also prove the usefulness of our
results by extending a known variance-based entanglement detection criterion.Comment: 7 pages, 1 figur
Robust strategies for lossy quantum interferometry
We give a simple multiround strategy that permits to beat the shot noise
limit when performing interferometric measurements even in the presence of
loss. In terms of the average photon number employed, our procedure can achieve
twice the sensitivity of conventional interferometric ones in the noiseless
case. In addition, it is more precise than the (recently proposed) optimal
two-mode strategy even in the presence of loss.Comment: 4 pages, 3 figure
Noise, errors and information in quantum amplification
We analyze and compare the characterization of a quantum device in terms of noise, transmitted bit-error-rate (BER) and mutual information, showing how the noise description is meaningful only for Gaussian channels. After reviewing the description of a quantum communication channel, we study the insertion of an amplifier. We focus attention on the case of direct detection, where the linear amplifier has a 3 decibels noise figure, which is usually considered an unsurpassable limit, referred to as the standard quantum limit (SQL). Both noise and BER could be reduced using an ideal amplifier, which is feasible in principle. However, just a reduction of noise beyond the SQL does not generally correspond to an improvement of the BER or of the mutual information. This is the case of a laser amplifier, where saturation can greatly reduce the noise figure, although there is no corresponding improvement of the BER. Such mechanism is illustrated on the basis of Monte Carlo simulations
Ancilla-assisted schemes are beneficial for Gaussian state phase estimation
We study interferometry with Gaussian states and show that an ancilla-assisted scheme outperforms coherent state interferometry for all levels of loss. We also compare the ancilla-assisted scheme to other interferometric schemes involving squeezing, and show that it has the most advantage in the high-loss, high photon-number regime. In fact, in the presence of high loss, it outperforms many other strategies proposed to date. We find the optimal measurement observable for each scheme discussed. We also find that, with the appropriate measurement, the achievable precision of the proposal by Caves [Phys. Rev. D 23, 1693 (1981)] can be improved upon, and is less vulnerable to losses than previously thought
Phase estimation via quantum interferometry for noisy detectors
The sensitivity in optical interferometry is strongly affected by losses
during the signal propagation or at the detection stage. The optimal quantum
states of the probing signals in the presence of loss were recently found.
However, in many cases of practical interest, their associated accuracy is
worse than the one obtainable without employing quantum resources (e.g.
entanglement and squeezing) but neglecting the detector's loss. Here we detail
an experiment that can reach the latter even in the presence of imperfect
detectors: it employs a phase-sensitive amplification of the signals after the
phase sensing, before the detection. We experimentally demonstrated the
feasibility of a phase estimation experiment able to reach its optimal working
regime. Since our method uses coherent states as input signals, it is a
practical technique that can be used for high-sensitivity interferometry and,
in contrast to the optimal strategies, does not require one to have an exact
characterization of the loss beforehand.Comment: 4 pages + supplementary information (10 pages), 3 + 4 figure
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