18,996 research outputs found
Tomography from collective measurements
We discuss the tomography of N-qubit states using collective measurements. The method is exact for symmetric states, whereas for not completely symmetric states the information accessible can be arranged as a mixture of irreducible SU(2) blocks. For the fully symmetric sector, the reconstruction protocol can be reduced to projections onto a canonically chosen set of pure states
Optimal verification of entangled states with local measurements
Consider the task of verifying that a given quantum device, designed to
produce a particular entangled state, does indeed produce that state. One
natural approach would be to characterise the output state by quantum state
tomography; or alternatively to perform some kind of Bell test, tailored to the
state of interest. We show here that neither approach is optimal amongst local
verification strategies for two qubit states. We find the optimal strategy in
this case and show that quadratically fewer total measurements are needed to
verify to within a given fidelity than in published results for quantum state
tomography, Bell test, or fidelity estimation protocols. We also give efficient
verification protocols for any stabilizer state. Additionally, we show that
requiring that the strategy be constructed from local, non-adaptive and
non-collective measurements only incurs a constant-factor penalty over a
strategy without these restrictions.Comment: Document includes supplemental material. Main paper: 5 pages, 2 figs;
supplemental material: 16 pages, 2 fig
Decoherence-Free Quantum Information Processing with Four-Photon Entangled States
Decoherence-free states protect quantum information from collective noise,
the predominant cause of decoherence in current implementations of quantum
communication and computation. Here we demonstrate that spontaneous parametric
down-conversion can be used to generate four-photon states which enable the
encoding of one qubit in a decoherence-free subspace. The immunity against
noise is verified by quantum state tomography of the encoded qubit. We show
that particular states of the encoded qubit can be distinguished by local
measurements on the four photons only.Comment: 4 pages, 4 eps figures, revtex
Deterministic realization of collective measurements via photonic quantum walks
Collective measurements on identically prepared quantum systems can extract
more information than local measurements, thereby enhancing
information-processing efficiency. Although this nonclassical phenomenon has
been known for two decades, it has remained a challenging task to demonstrate
the advantage of collective measurements in experiments. Here we introduce a
general recipe for performing deterministic collective measurements on two
identically prepared qubits based on quantum walks. Using photonic quantum
walks, we realize experimentally an optimized collective measurement with
fidelity 0.9946 without post selection. As an application, we achieve the
highest tomographic efficiency in qubit state tomography to date. Our work
offers an effective recipe for beating the precision limit of local
measurements in quantum state tomography and metrology. In addition, our study
opens an avenue for harvesting the power of collective measurements in quantum
information processing and for exploring the intriguing physics behind this
power.Comment: Close to the published versio
Choice of Measurement Sets in Qubit Tomography
Optimal generalized measurements for state estimation are well understood.
However, practical quantum state tomography is typically performed using a
fixed set of projective measurements and the question of how to choose these
measurements has been largely unexplored in the literature. In this work we
develop theoretical asymptotic bounds for the average fidelity of pure qubit
tomography using measurement sets whose axes correspond to vertices of Platonic
solids. We also present complete simulations of maximum likelihood tomography
for mixed qubit states using the Platonic solid measurements. We show that
overcomplete measurement sets can be used to improve the accuracy of
tomographic reconstructions.Comment: 13 Pages, 6 figure
Separable Measurement Estimation of Density Matrices and its Fidelity Gap with Collective Protocols
We show that there exists a gap between the performance of separable and
collective measurements in qubit mixed-state estimation that persists in the
large sample limit. We characterize such gap in terms of the corresponding
bounds on the mean fidelity. We present an adaptive protocol that attains the
separable-measurement bound. This (optimal separable) protocol uses von Neumann
measurements and can be easily implemented with current technology.Comment: version published in PR
Collective vs local measurements in qubit mixed state estimation
We discuss the problem of estimating a general (mixed) qubit state. We give
the optimal guess that can be inferred from any given set of measurements. For
collective measurements and for a large number of copies, we show that the
error in the estimation goes as 1/N. For local measurements we focus on the
simpler case of states lying on the equatorial plane of the Bloch sphere. We
show that standard tomographic techniques lead to an error proportional to
, while with our optimal data processing it is proportional to
.Comment: 4 pages, 1 figure, minor style changes, refs. adde
Measurement schemes for the spin quadratures on an ensemble of atoms
We consider how to measure collective spin states of an atomic ensemble based
on the recent multi-pass approaches for quantum interface between light and
atoms. We find that a scheme with two passages of a light pulse through the
atomic ensemble is efficient to implement the homodyne tomography of the spin
state. Thereby, we propose to utilize optical pulses as a phase-shifter that
rotates the quadrature of the spins. This method substantially simplifies the
geometry of experimental schemes.Comment: 4pages 2 figure
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