1,034 research outputs found
Changepoint Problem in Quantumn Setting
In the changepoint problem, we determine when the distribution observed has
changed to another one. We expand this problem to the quantum case where copies
of an unknown pure state are being distributed. We study the fundamental case,
which has only two candidates to choose. This problem is equal to identifying a
given state with one of the two unknown states when multiple copies of the
states are provided. In this paper, we assume that two candidate states are
distributed independently and uniformly in the space of the whole pure states.
The minimum of the averaged error probability is given and the optimal POVM is
defined as to obtain it. Using this POVM, we also compute the error probability
which depends on the inner product. These analytical results allow us to
calculate the value in the asymptotic case, where this problem approaches to
the usual discrimination problem
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
Correlation analysis of stochastic gravitational wave background around 0.1-1Hz
We discuss prospects for direct measurement of stochastic gravitational wave
background around 0.1-1Hz with future space missions. It is assumed to use
correlation analysis technique with the optimal TDI variables for two sets of
LISA-type interferometers. The signal to noise for detection of the background
and the estimation errors for its basic parameters (amplitude, spectral index)
are evaluated for proposed missions.Comment: 11 pages, 7 figures, revised version, to appear in PR
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
Discrimination of the binary coherent signal: Gaussian-operation limit and simple non-Gaussian near-optimal receivers
We address the limit of the Gaussian operations and classical communication
in the problem of quantum state discrimination. We show that the optimal
Gaussian strategy for the discrimination of the binary phase shift keyed (BPSK)
coherent signal is a simple homodyne detection. We also propose practical
near-optimal quantum receivers that beat the BPSK homodyne limit in all areas
of the signal power. Our scheme is simple and does not require realtime
electrical feedback.Comment: 7 pages, 4 figures, published versio
Quantum criticality as a resource for quantum estimation
We address quantum critical systems as a resource in quantum estimation and
derive the ultimate quantum limits to the precision of any estimator of the
coupling parameters. In particular, if L denotes the size of a system and
\lambda is the relevant coupling parameters driving a quantum phase transition,
we show that a precision improvement of order 1/L may be achieved in the
estimation of \lambda at the critical point compared to the non-critical case.
We show that analogue results hold for temperature estimation in classical
phase transitions. Results are illustrated by means of a specific example
involving a fermion tight-binding model with pair creation (BCS model).Comment: 7 pages. Revised and extended version. Gained one author and a
specific exampl
Optimal minimum-cost quantum measurements for imperfect detection
Knowledge of optimal quantum measurements is important for a wide range of
situations, including quantum communication and quantum metrology. Quantum
measurements are usually optimised with an ideal experimental realisation in
mind. Real devices and detectors are, however, imperfect. This has to be taken
into account when optimising quantum measurements. In this paper, we derive the
optimal minimum-cost and minimum-error measurements for a general model of
imperfect detection.Comment: 5 page
Optimum unambiguous discrimination of two mixed states and application to a class of similar states
We study the measurement for the unambiguous discrimination of two mixed
quantum states that are described by density operators and of
rank d, the supports of which jointly span a 2d-dimensional Hilbert space.
Based on two conditions for the optimum measurement operators, and on a
canonical representation for the density operators of the states, two equations
are derived that allow the explicit construction of the optimum measurement,
provided that the expression for the fidelity of the states has a specific
simple form. For this case the problem is mathematically equivalent to
distinguishing pairs of pure states, even when the density operators are not
diagonal in the canonical representation. The equations are applied to the
optimum unambiguous discrimination of two mixed states that are similar states,
given by , and that belong to the class where the
unitary operator U can be decomposed into multiple rotations in the d mutually
orthogonal two-dimensional subspaces determined by the canonical
representation.Comment: 8 pages, changes in title and presentatio
Discrimination of two mixed quantum states with maximum confidence and minimum probability of inconclusive results
We study an optimized measurement that discriminates two mixed quantum states
with maximum confidence for each conclusive result, thereby keeping the overall
probability of inconclusive results as small as possible. When the rank of the
detection operators associated with the two different conclusive outcomes does
not exceed unity we obtain a general solution. As an application, we consider
the discrimination of two mixed qubit states. Moreover, for the case of
higher-rank detection operators we give a solution for particular states. The
relation of the optimized measurement to other discrimination schemes is also
discussed.Comment: 7 pages, 1 figure, accepted for publication in Phys. Rev.
Optimal estimation of entanglement
Entanglement does not correspond to any observable and its evaluation always
corresponds to an estimation procedure where the amount of entanglement is
inferred from the measurements of one or more proper observables. Here we
address optimal estimation of entanglement in the framework of local quantum
estimation theory and derive the optimal observable in terms of the symmetric
logarithmic derivative. We evaluate the quantum Fisher information and, in
turn, the ultimate bound to precision for several families of bipartite states,
either for qubits or continuous variable systems, and for different measures of
entanglement. We found that for discrete variables, entanglement may be
efficiently estimated when it is large, whereas the estimation of weakly
entangled states is an inherently inefficient procedure. For continuous
variable Gaussian systems the effectiveness of entanglement estimation strongly
depends on the chosen entanglement measure. Our analysis makes an important
point of principle and may be relevant in the design of quantum information
protocols based on the entanglement content of quantum states.Comment: 9 pages, 2 figures, v2: minor correction
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