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| related topics |
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| {measurement, state, measurements} |
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| {qubit, qubits, gate} |
| {states, state, optimal} |
| {state, states, entangled} |
| {bell, inequality, local} |
| {spin, pulse, spins} |
| {classical, space, random} |
| {energy, gaussian, time} |
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|
Optimal estimation of qubit states with continuous time measurements
Madalin Guta, Bas Janssens, Jonas Kahn
abstract: We propose an adaptive, two steps strategy, for the estimation of mixed qubit
states. We show that the strategy is optimal in a local minimax sense for the
trace norm distance as well as other locally quadratic figures of merit. Local
minimax optimality means that given $n$ identical qubits, there exists no
estimator which can perform better than the proposed estimator on a
neighborhood of size $n^{-1/2}$ of an arbitrary state. In particular, it is
asymptotically Bayesian optimal for a large class of prior distributions.
We present a physical implementation of the optimal estimation strategy based
on continuous time measurements in a field that couples with the qubits.
The crucial ingredient of the result is the concept of local asymptotic
normality (or LAN) for qubits. This means that, for large $n$, the statistical
model described by $n$ identically prepared qubits is locally equivalent to a
model with only a classical Gaussian distribution and a Gaussian state of a
quantum harmonic oscillator.
The term `local' refers to a shrinking neighborhood around a fixed state
$\rho_{0}$. An essential result is that the neighborhood radius can be chosen
arbitrarily close to $n^{-1/4}$. This allows us to use a two steps procedure by
which we first localize the state within a smaller neighborhood of radius
$n^{-1/2+\epsilon}$, and then use LAN to perform optimal estimation.
- oai_identifier:
- oai:arXiv.org:quant-ph/0608074
- categories:
- quant-ph
- comments:
- 32 pages, 3 figures, to appear in Commun. Math. Phys
- arxiv_id:
- quant-ph/0608074
- created:
- 2006-08-08
- updated:
- 2007-05-24
Full article ▸
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