549 research outputs found
Optimal phase measurements with pure Gaussian states
We analyze the Heisenberg limit on phase estimation for Gaussian states. In
the analysis, no reference to a phase operator is made. We prove that the
squeezed vacuum state is the most sensitive for a given average photon number.
We provide two adaptive local measurement schemes that attain the Heisenberg
limit asymptotically. One of them is described by a positive operator-valued
measure and its efficiency is exhaustively explored. We also study Gaussian
measurement schemes based on phase quadrature measurements. We show that
homodyne tomography of the appropriate quadrature attains the Heisenberg limit
for large samples. This proves that this limit can be attained with local
projective Von Neuman measurements.Comment: 9 pages. Revised version: two new sections added, revised
conclusions. Corrected prose. Corrected reference
Iterative procedure for computing accessible information in quantum communication
We present an iterative algorithm that finds the optimal measurement for
extracting the accessible information in any quantum communication scenario.
The maximization is achieved by a steepest-ascent approach toward the extremal
point, following the gradient uphill in sufficiently small steps. We apply it
to a simple ad-hoc example, as well as to a problem with a bearing on the
security of a tomographic protocol for quantum key distribution.Comment: REVTeX, 4 pages, 1 figure, 1 tabl
Mixed state Pauli channel parameter estimation
The accuracy of any physical scheme used to estimate the parameter describing
the strength of a single qubit Pauli channel can be quantified using standard
techniques from quantum estimation theory. It is known that the optimal
estimation scheme, with m channel invocations, uses initial states for the
systems which are pure and unentangled and provides an uncertainty of
O[1/m^(1/2)]. This protocol is analogous to a classical repetition and
averaging scheme. We consider estimation schemes where the initial states
available are not pure and compare a protocol involving quantum correlated
states to independent state protocols analogous to classical repetition
schemes. We show, that unlike the pure state case, the quantum correlated state
protocol can yield greater estimation accuracy than any independent state
protocol. We show that these gains persist even when the system states are
separable and, in some cases, when quantum discord is absent after channel
invocation. We describe the relevance of these protocols to nuclear magnetic
resonance measurements
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 measurement precision of a nonlinear interferometer
We study the best attainable measurement precision when a double-well trap
with bosons inside acts as an interferometer to measure the energy difference
of the atoms on the two sides of the trap. We introduce time independent
perturbation theory as the main tool in both analytical arguments and numerical
computations. Nonlinearity from atom-atom interactions will not indirectly
allow the interferometer to beat the Heisenberg limit, but in many regimes of
the operation the Heisenberg limit scaling of measurement precision is
preserved in spite of added tunneling of the atoms and atom-atom interactions,
often even with the optimal prefactor.Comment: very close to published versio
Ziv-Zakai Error Bounds for Quantum Parameter Estimation
I propose quantum versions of the Ziv-Zakai bounds as alternatives to the
widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From
a simple form of the proposed bounds, I derive both a "Heisenberg" error limit
that scales with the average energy and a limit similar to the quantum
Cram\'er-Rao bound that scales with the energy variance. These results are
further illustrated by applying the bound to a few examples of optical phase
estimation, which show that a quantum Ziv-Zakai bound can be much higher and
thus tighter than a quantum Cram\'er-Rao bound for states with highly
non-Gaussian photon-number statistics in certain regimes and also stay close to
the latter where the latter is expected to be tight.Comment: v1: preliminary result, 3 pages; v2: major update, 4 pages +
supplementary calculations, v3: another major update, added proof of
"Heisenberg" limit, v4: accepted by PR
Quantum bit commitment under Gaussian constraints
Quantum bit commitment has long been known to be impossible. Nevertheless,
just as in the classical case, imposing certain constraints on the power of the
parties may enable the construction of asymptotically secure protocols. Here,
we introduce a quantum bit commitment protocol and prove that it is
asymptotically secure if cheating is restricted to Gaussian operations. This
protocol exploits continuous-variable quantum optical carriers, for which such
a Gaussian constraint is experimentally relevant as the high optical
nonlinearity needed to effect deterministic non-Gaussian cheating is
inaccessible.Comment: 9 pages, 6 figure
Complete solution for unambiguous discrimination of three pure states with real inner products
Complete solutions are given in a closed analytic form for unambiguous
discrimination of three general pure states with real mutual inner products.
For this purpose, we first establish some general results on unambiguous
discrimination of n linearly independent pure states. The uniqueness of
solution is proved. The condition under which the problem is reduced to an
(n-1)-state problem is clarified. After giving the solution for three pure
states with real mutual inner products, we examine some difficulties in
extending our method to the case of complex inner products. There is a class of
set of three pure states with complex inner products for which we obtain an
analytical solution.Comment: 13 pages, 3 figures, presentation improved, reference adde
Probabilistic quantum multimeters
We propose quantum devices that can realize probabilistically different
projective measurements on a qubit. The desired measurement basis is selected
by the quantum state of a program register. First we analyze the
phase-covariant multimeters for a large class of program states, then the
universal multimeters for a special choice of program. In both cases we start
with deterministic but erroneous devices and then proceed to devices that never
make a mistake but from time to time they give an inconclusive result. These
multimeters are optimized (for a given type of a program) with respect to the
minimum probability of inconclusive result. This concept is further generalized
to the multimeters that minimize the error rate for a given probability of an
inconclusive result (or vice versa). Finally, we propose a generalization for
qudits.Comment: 12 pages, 3 figure
Discriminating quantum-optical beam-splitter channels with number-diagonal signal states: Applications to quantum reading and target detection
We consider the problem of distinguishing, with minimum probability of error,
two optical beam-splitter channels with unequal complex-valued reflectivities
using general quantum probe states entangled over M signal and M' idler mode
pairs of which the signal modes are bounced off the beam splitter while the
idler modes are retained losslessly. We obtain a lower bound on the output
state fidelity valid for any pure input state. We define number-diagonal signal
(NDS) states to be input states whose density operator in the signal modes is
diagonal in the multimode number basis. For such input states, we derive series
formulas for the optimal error probability, the output state fidelity, and the
Chernoff-type upper bounds on the error probability. For the special cases of
quantum reading of a classical digital memory and target detection (for which
the reflectivities are real valued), we show that for a given input signal
photon probability distribution, the fidelity is minimized by the NDS states
with that distribution and that for a given average total signal energy N_s,
the fidelity is minimized by any multimode Fock state with N_s total signal
photons. For reading of an ideal memory, it is shown that Fock state inputs
minimize the Chernoff bound. For target detection under high-loss conditions, a
no-go result showing the lack of appreciable quantum advantage over coherent
state transmitters is derived. A comparison of the error probability
performance for quantum reading of number state and two-mode squeezed vacuum
state (or EPR state) transmitters relative to coherent state transmitters is
presented for various values of the reflectances. While the nonclassical states
in general perform better than the coherent state, the quantitative performance
gains differ depending on the values of the reflectances.Comment: 12 pages, 7 figures. This closely approximates the published version.
The major change from v2 is that Section IV has been re-organized, with a
no-go result for target detection under high loss conditions highlighted. The
last sentence of the abstract has been deleted to conform to the arXiv word
limit. Please see the PDF for the full abstrac
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