36 research outputs found
Tighter quantum uncertainty relations follow from a general probabilistic bound
Uncertainty relations (URs) like the Heisenberg-Robertson or the time-energy
UR are often considered to be hallmarks of quantum theory. Here, a simple
derivation of these URs is presented based on a single classical inequality
from estimation theory, a Cram\'er-Rao-like bound. The Heisenberg-Robertson UR
is then obtained by using the Born rule and the Schr\"odinger equation. This
allows a clear separtion of the probabilistic nature of quantum mechanics from
the Hilbert space structure and the dynamical law. It also simplifies the
interpretation of the bound. In addition, the Heisenberg-Robertson UR is
tightened for mixed states by replacing one variance by the so-called quantum
Fisher information. Thermal states of Hamiltonians with evenly-gapped energy
levels are shown to saturate the tighter bound for natural choices of the
operators. This example is further extended to Gaussian states of a harmonic
oscillator. For many-qubit systems, we illustrate the interplay between
entanglement and the structure of the operators that saturate the UR with
spin-squeezed states and Dicke states.Comment: 8 pages, 1 figure. v2: improved presentation, references added,
results on the connection between saturated inequality and entanglement
structure for multi-qubit states adde
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
Does a large quantum Fisher information imply Bell correlations?
The quantum Fisher information (QFI) of certain multipartite entangled
quantum states is larger than what is reachable by separable states, providing
a metrological advantage. Are these nonclassical correlations strong enough to
potentially violate a Bell inequality? Here, we present evidence from two
examples. First, we discuss a Bell inequality designed for spin-squeezed states
which is violated only by quantum states with a large QFI. Second, we relax a
well-known lower bound on the QFI to find the Mermin Bell inequality as a
special case. However, a fully general link between QFI and Bell correlations
is still open.Comment: 4 pages, minor edit