36 research outputs found
Parameters estimation in quantum optics
We address several estimation problems in quantum optics by means of the
maximum-likelihood principle. We consider Gaussian state estimation and the
determination of the coupling parameters of quadratic Hamiltonians. Moreover,
we analyze different schemes of phase-shift estimation. Finally, the absolute
estimation of the quantum efficiency of both linear and avalanche
photodetectors is studied. In all the considered applications, the Gaussian
bound on statistical errors is attained with a few thousand data.Comment: 11 pages. 6 figures. Accepted on Phys. Rev.
Protocols for entanglement transformations of bipartite pure states
We present a general theoretical framework for both deterministic and
probabilistic entanglement transformations of bipartite pure states achieved
via local operations and classical communication. This framework unifies and
greatly simplifies previous works. A necessary condition for ``pure
contraction'' transformations is given. Finally, constructive protocols to
achieve both probabilistic and deterministic entanglement transformations are
presented.Comment: 7 pages, no figures. Version slightly modified on Physical Review A
reques
Local observables for entanglement witnesses
We present an explicit construction of entanglement witnesses for depolarized
states in arbitrary finite dimension. For infinite dimension we generalize the
construction to twin-beams perturbed by Gaussian noises in the phase and in the
amplitude of the field. We show that entanglement detection for all these
families of states requires only three local measurements. The explicit form of
the corresponding set of local observables (quorom) needed for entanglement
witness is derived.Comment: minor corrections, title change
Physical realizations of quantum operations
Quantum operations (QO) describe any state change allowed in quantum
mechanics, such as the evolution of an open system or the state change due to a
measurement. We address the problem of which unitary transformations and which
observables can be used to achieve a QO with generally different input and
output Hilbert spaces. We classify all unitary extensions of a QO, and give
explicit realizations in terms of free-evolution direct-sum dilations and
interacting tensor-product dilations. In terms of Hilbert space dimensionality
the free-evolution dilations minimize the physical resources needed to realize
the QO, and for this case we provide bounds for the dimension of the ancilla
space versus the rank of the QO. The interacting dilations, on the other hand,
correspond to the customary ancilla-system interaction realization, and for
these we derive a majorization relation which selects the allowed unitary
interactions between system and ancilla.Comment: 8 pages, no figures. Accepted for publication on Phys. Rev.
Universal homodyne tomography with a single local oscillator
We propose a general method for measuring an arbitrary observable of a
multimode electromagnetic field using homodyne detection with a single local
oscillator. In this method the local oscillator scans over all possible linear
combinations of the modes. The case of two modes is analyzed in detail and the
feasibility of the measurement is studied on the basis of Monte-Carlo
simulations. We also provide an application of this method in tomographic
testing of the GHZ state.Comment: 12 pages, 5 figures (8 eps files
Optimal cloning of unitary transformations
After proving a general no-cloning theorem for black boxes, we derive the
optimal universal cloning of unitary transformations, from one to two copies.
The optimal cloner is realized by quantum channels with memory, and greately
outperforms the optimal measure-and-reprepare cloning strategy. Applications
are outlined, including two-way quantum cryptographic protocols.Comment: 4 pages, 1 figure, published versio
Operational distance and fidelity for quantum channels
We define and study a fidelity criterion for quantum channels, which we term
the minimax fidelity, through a noncommutative generalization of maximal
Hellinger distance between two positive kernels in classical probability
theory. Like other known fidelities for quantum channels, the minimax fidelity
is well-defined for channels between finite-dimensional algebras, but it also
applies to a certain class of channels between infinite-dimensional algebras
(explicitly, those channels that possess an operator-valued Radon--Nikodym
density with respect to the trace in the sense of Belavkin--Staszewski) and
induces a metric on the set of quantum channels which is topologically
equivalent to the CB-norm distance between channels, precisely in the same way
as the Bures metric on the density operators associated with statistical states
of quantum-mechanical systems, derived from the well-known fidelity
(`generalized transition probability') of Uhlmann, is topologically equivalent
to the trace-norm distance.Comment: 26 pages, amsart.cls; improved intro, fixed typos, added a reference;
accepted by J. Math. Phy
Covariant quantum measurements which maximize the likelihood
We derive the class of covariant measurements which are optimal according to
the maximum likelihood criterion. The optimization problem is fully resolved in
the case of pure input states, under the physically meaningful hypotheses of
unimodularity of the covariance group and measurability of the stability
subgroup. The general result is applied to the case of covariant state
estimation for finite dimension, and to the Weyl-Heisenberg displacement
estimation in infinite dimension. We also consider estimation with multiple
copies, and compare collective measurements on identical copies with the scheme
of independent measurements on each copy. A "continuous-variables" analogue of
the measurement of direction of the angular momentum with two anti-parallel
spins by Gisin and Popescu is given.Comment: 8 pages, RevTex style, submitted to Phys. Rev.
Optimal quantum circuits for general phase estimation
We address the problem of estimating the phase phi given N copies of the
phase rotation gate u(phi). We consider, for the first time, the optimization
of the general case where the circuit consists of an arbitrary input state,
followed by any arrangement of the N phase rotations interspersed with
arbitrary quantum operations, and ending with a POVM. Using the polynomial
method, we show that, in all cases where the measure of quality of the estimate
phi' for phi depends only on the difference phi'-phi, the optimal scheme has a
very simple fixed form. This implies that an optimal general phase estimation
procedure can be found by just optimizing the amplitudes of the initial state.Comment: 4 pages, 3 figure
Testing axioms for Quantum Mechanics on Probabilistic toy-theories
In Ref. [1] one of the authors proposed postulates for axiomatizing Quantum
Mechanics as a "fair operational framework", namely regarding the theory as a
set of rules that allow the experimenter to predict future events on the basis
of suitable tests, having local control and low experimental complexity. In
addition to causality, the following postulates have been considered: PFAITH
(existence of a pure preparationally faithful state), and FAITHE (existence of
a faithful effect). These postulates have exhibited an unexpected theoretical
power, excluding all known nonquantum probabilistic theories. Later in Ref. [2]
in addition to causality and PFAITH, postulate LDISCR (local discriminability)
and PURIFY (purifiability of all states) have been considered, narrowing the
probabilistic theory to something very close to Quantum Mechanics. In the
present paper we test the above postulates on some nonquantum probabilistic
models. The first model, "the two-box world" is an extension of the
Popescu-Rohrlich model, which achieves the greatest violation of the CHSH
inequality compatible with the no-signaling principle. The second model "the
two-clock world" is actually a full class of models, all having a disk as
convex set of states for the local system. One of them corresponds to the "the
two-rebit world", namely qubits with real Hilbert space. The third model--"the
spin-factor"--is a sort of n-dimensional generalization of the clock. Finally
the last model is "the classical probabilistic theory". We see how each model
violates some of the proposed postulates, when and how teleportation can be
achieved, and we analyze other interesting connections between these postulate
violations, along with deep relations between the local and the non-local
structures of the probabilistic theory.Comment: Submitted to QIP Special Issue on Foundations of Quantum Informatio