By finding measurements that optimally resolve neighboring quantum states, we use statistical distinguishability to define a natural Riemannian metric on the space of quantum-mechanical density operators and to formulate uncertainty principles that are more general and more stringent than standard uncertainty principles.
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[Show abstract][Hide abstract] ABSTRACT: An unknown quantum state cannot be copied on demand and broadcast freely due
to the famous no-cloning theorem. Approximate cloning schemes have been
proposed to achieve the optimal cloning characterized by the maximal fidelity
between the original and its copies. Here, from the perspective of quantum
Fisher information (QFI), we investigate the distribution of QFI in asymmetric
cloning machines which produce two nonidentical copies. As one might expect,
improving the QFI of one copy results in decreasing the QFI of the other copy,
roughly the same as that of fidelity. It is perhaps also unsurprising that
asymmetric phase-covariant cloning machine outperforms universal cloning
machine in distributing QFI since a priori information of the input state has
been utilized. However, interesting results appear when we compare the
distributabilities of fidelity (which quantifies the full information of
quantum states), and QFI (which only captures the information of relevant
parameters) in asymmetric cloning machines. In contrast to the results of
fidelity, where the distributability of symmetric cloning is always optimal for
any d-dimensional cloning, we find that asymmetric cloning performs always
better than symmetric cloning on the distribution of QFI for $d\leq18$, but
this conclusion becomes invalid when $d>18$.
"The closeness of two pure quantum states ψ | 〉 1 and ψ | 〉 2 can be quantified in many different ways. One of the simplest and therefore most popular measures of the closeness is the absolute value of the scalar product between these states or some function of this quantity   . Following , we use the name fidelity for the square of the absolute value of this scalar product: "
[Show abstract][Hide abstract] ABSTRACT: We give analytical and numerical upper bounds for the relative energy difference of different superpositions of two coherent states ('cat' states) with a fixed fidelity between them.
Journal of Physics A Mathematical and Theoretical 07/2014; 47(31):315301. DOI:10.1088/1751-8113/47/31/315301 · 1.58 Impact Factor
"where A is found from solving the symmetric logarithmic derivative ∂ρ/∂φ = 1/2 [Aρ + ρA]. The precision in the phase measurement (more specifically the lower bound on the standard deviation) is given by the quantum Cramér-Rao bound (Braunstein and Caves, 1994): "
[Show abstract][Hide abstract] ABSTRACT: Quantum entanglement offers the possibility of making measurements beyond the
classical limit, however some issues still need to be overcome before it can be
applied in realistic lossy systems. Recent work has used the quantum Fisher
information (QFI) to show that entangled coherent states (ECSs) may be useful
for this purpose as they combine sub-classical phase precision capabilities
with robustness (Joo et al., 2011). However, to date no effective scheme for
measuring a phase in lossy systems using an ECS has been devised. Here we
present a scheme that does just this. We show how one could measure a phase to
a precision significantly better than that attainable by both unentangled
"classical" states and highly-entangled NOON states over a wide range of
different losses. This brings quantum metrology closer to being a realistic and