42 research outputs found
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
True precision limits in quantum metrology
We show that quantification of the performance of quantum-enhanced
measurement schemes based on the concept of quantum Fisher information yields
asymptotically equivalent results as the rigorous Bayesian approach, provided
generic uncorrelated noise is present in the setup. At the same time, we show
that for the problem of decoherence-free phase estimation this equivalence
breaks down and the achievable estimation uncertainty calculated within the
Bayesian approach is by a factor larger than that predicted by the QFI
even in the large prior knowledge (small parameter fluctuation) regime, where
QFI is conventionally regarded as a reliable figure of merit. We conjecture
that the analogous discrepancy is present in arbitrary decoherence-free unitary
parameter estimation scheme and propose a general formula for the
asymptotically achievable precision limit. We also discuss protocols utilizing
states with indefinite number of particles and show that within the Bayesian
approach it is legitimate to replace the number of particles with the mean
number of particles in the formulas for the asymptotic precision, which as a
consequence provides another argument that proposals based on the properties of
the QFI of indefinite particle number states leading to sub-Heisenberg
precisions are not practically feasible.Comment: 20 pages, 4 figure
Matrix product states for quantum metrology
We demonstrate that the optimal states in lossy quantum interferometry may be
efficiently simulated using low rank matrix product states. We argue that this
should be expected in all realistic quantum metrological protocols with
uncorrelated noise and is related to the elusive nature of the Heisenberg
precision scaling in presence of decoherence.Comment: 5 pages, 2 figure
On quantum interferometric measurements of temperature
We provide a detailed description of the quantum interferometric thermometer,
which is a device that estimates the temperature of a sample from the
measurements of the optical phase. For the first time, we rigorously analyze
the operation of such a device by studying the interaction of the optical probe
system prepared in a single-mode Gaussian state with a heated sample modeled as
a dissipative thermal reservoir. We find that this approach to thermometry is
capable of measuring the temperature of a sample in the nanokelvin regime.
Furthermore, we compare the fundamental precision of quantum interferometric
thermometers with the theoretical precision offered by the classical idealized
pyrometers, which infer the temperature from a measurement of the total thermal
radiation emitted by the sample. We find that the interferometric thermometer
provides a superior performance in temperature sensing even when compared with
this idealized pyrometer. We predict that interferometric thermometers will
prove useful for ultraprecise temperature sensing and stabilization of quantum
optical experiments based on the nonlinear crystals and atomic vapors.Comment: 13 pages, 3 figures, final versio
Dephasing in coherent communication with weak signal states
We analyze the ultimate quantum limit on the accessible information for an
optical communication scheme when time bins carry coherent light pulses
prepared in one of several orthogonal modes and the phase undergoes diffusion
after each channel use. This scheme, an example of a quantum memory channel,
can be viewed as noisy pulse position modulation (PPM) keying with phase
fluctuations occurring between consecutive PPM symbols. We derive a general
expression for the output states in the Fock basis and implement a numerical
procedure to calculate the Holevo quantity. Using asymptotic properties of
Toeplitz matrices, we also present an analytic expression for the Holevo
quantity valid for very weak signals and sufficiently strong dephasing when the
dominant contribution comes from the single-photon sector in the Hilbert space
of signal states. Based on numerical results we conjecture an inequality for
contributions to the Holevo quantity from multiphoton sectors which implies
that in the asymptotic limit of weak signals, for arbitrarily small dephasing
the accessible information scales linearly with the average number of photons
contained in the pulse. Such behaviour presents a qualitative departure from
the fully coherent case.Comment: 20 pages, final versio
Attaining classical capacity per unit cost of noisy bosonic Gaussian channels
I show that classical capacity per unit cost of noisy bosonic Gaussian
channels can be attained by employing generalized on-off keying modulation
format and a projective measurement of individual output states. This means
that neither complicated collective measurements nor phase-sensitive detection
is required to communicate over optical channels at the ultimate limit imposed
by laws of quantum mechanics in the limit of low average cost.Comment: 6 pages, 2 figure
Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
We point out a contrasting role the entanglement plays in communication and
estimation scenarios. In the first case it brings noticeable benefits at the
measurement stage (output super-additivity), whereas in the latter it is the
entanglement of the input probes that enables significant performance
enhancement (input super-additivity). We identify a weak estimation regime
where a strong connection between concepts crucial to the two fields is
demonstrated; the accessible information and the Holevo quantity on one side
and the quantum Fisher information related quantities on the other. This allows
us to shed new light on the problem of super-additivity in communication using
the concepts of quantum estimation theory.Comment: 31 pages, 3 figures, published versio
Optimal lossy quantum interferometry in phase space
We analyse the phase space representation of the optimal measurement of a
phase shift in an interferometer with equal photon loss in both its arms. In
the local phase estimation scenario with a fixed number of photons, we identify
features of the spin Wigner function that warrant sub-shot noise precision, and
discuss their sensitivity to losses. We derive the asymptotic form of an
integral kernel describing the process of photon loss in the phase space in the
limit of large photon numbers. The analytic form of this kernel allows one to
assess the ultimate precision limit for a lossy interferometer. We also provide
a general lower bound on the quantum Fisher information in terms of spin Wigner
functions.Comment: 20 pages, 6 figures, published versio
Quantum fingerprinting using two-photon interference
We present a quantum fingerprinting protocol relying on two-photon
interference which does not require a shared phase reference between the
parties preparing optical signals carrying data fingerprints. We show that the
scaling of the protocol, in terms of transmittable classical information, is
analogous to the recently proposed and demonstrated scheme based on coherent
pulses and first-order interference, offering comparable advantage over
classical fingerprinting protocols without access to shared prior randomness.
We analyze the protocol taking into account non-Poissonian photon statistics of
optical signals and a variety of imperfections, such as transmission losses,
dark counts, and residual distinguishability. The impact of these effects on
the protocol performance is quantified with the help of Chernoff information.Comment: manuscript accepted to Optics Express journa
Quantum Limits in Optical Communications
This tutorial reviews the Holevo capacity limit as a universal tool to
analyze the ultimate transmission rates in a variety of optical communication
scenarios, ranging from conventional optically amplified fiber links to
free-space communication with power-limited optical signals. The canonical
additive white Gaussian noise model is used to describe the propagation of the
optical signal. The Holevo limit exceeds substantially the standard Shannon
limit when the power spectral density of noise acquired in the course of
propagation is small compared to the energy of a single photon at the carrier
frequency per unit time-bandwidth area. General results are illustrated with a
discussion of efficient communication strategies in the photon-starved regime.Comment: 14 pages, 10 figures. This tutorial is to be published in the Special
Issue of Journal of Lightwave Technology on the European Conference on
Optical Communication (ECOC) 201