74 research outputs found
All macroscopic quantum states are fragile and hard to prepare
We study the effect of local decoherence on arbitrary quantum states.
Adapting techniques developed in quantum metrology, we show that the action of
generic local noise processes -- though arbitrarily small -- always yields a
state whose Quantum Fisher Information (QFI) with respect to local observables
is linear in system size N, independent of the initial state. This implies that
all macroscopic quantum states, which are characterized by a QFI that is
quadratic in N, are fragile under decoherence, and cannot be maintained if the
system is not perfectly isolated. We also provide analytical bounds on the
effective system size, and show that the effective system size scales as the
inverse of the noise parameter p for small p for all the noise channels
considered, making it increasingly difficult to generate macroscopic or even
mesoscopic quantum states. In turn, we also show that the preparation of a
macroscopic quantum state, with respect to a conserved quantity, requires a
device whose QFI is already at least as large as the one of the desired state.
Given that the preparation device itself is classical and not a perfectly
isolated macroscopic quantum state, the preparation device needs to be
quadratically bigger than the macroscopic target state
Certifiability criterion for large-scale quantum systems
Can one certify the preparation of a coherent, many-body quantum state by
measurements with bounded accuracy in the presence of noise and decoherence?
Here, we introduce a criterion to assess the fragility of large-scale quantum
states which is based on the distinguishability of orthogonal states after the
action of very small amounts of noise. States which do not pass this criterion
are called asymptotically incertifiable. We show that, if a coherent quantum
state is asymptotically incertifiable, there exists an incoherent mixture (with
entropy at least log 2) which is experimentally indistinguishable from the
initial state. The Greenberger-Horne-Zeilinger states are examples of such
asymptotically incertifiable states. More generally, we prove that any
so-called macroscopic superposition state is asymptotically incertifiable. We
also provide examples of quantum states that are experimentally
indistinguishable from highly incoherent mixtures, i.e., with an almost-linear
entropy in the number of qubits. Finally we show that all unique ground states
of local gapped Hamiltonians (in any dimension) are certifiable.Comment: 21 pages, 1 figure; V2: title changed plus minor changes in the text
and some additional reference
Heisenberg scaling in Gaussian quantum metrology
We address the issue of precisely estimating small parameters encoded in a
general linear transformation of the modes of a bosonic quantum field. Such
Bogoliubov transformations frequently appear in the context of quantum optics.
We provide a set of instructions for computing the quantum Fisher information
for arbitrary pure initial states. We show that the maximally achievable
precision of estimation is inversely proportional to the squared average
particle number and that such Heisenberg scaling requires non-classical, but
not necessarily entangled states. Our method further allows us to quantify
losses in precision arising from being able to monitor only finitely many
modes, for which we identify a lower bound.Comment: v2: 8 pages, 1 figure, additional examples and extended appendices
w.r.t. v
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