How different can pure squeezed states with a given fidelity be?

Minimal Products of Coordinate and Momentum Uncertainties of High Orders: Significant and Weak High-Order Squeezing

“…This is an indication to the insufficiency of the concept of quantum “fidelity” (the scalar product between two states in the case of pure quantum states) as a measure of distinguishability between quantum states in certain physical situations. See, in this connection, e.g., earlier papers [ 69 , 70 , 71 , 72 , 73 , 74 , 75 ].…”

Upper bounds on the relative energy difference of pure and mixed Gaussian states with a fixed fidelity

“…My conjecture is that the upper bounds (22) hold, as a matter of fact, in the most general case, when all three variations (α, β and δ) can be different from zero. Many numerical tests made for different sets of parameters [14] confirm this conjecture: in all the cases the fidelity calculated by formula (2) appeared smaller than the maximal value given by ( 22) with the parameter Y calculated by means of equations ( 5) and (14). But I did not succeed to find an analytical proof, except for the simplest (but, perhaps, the most important) special case when the difference 1 − F = ε is small.…”

Fidelity versus relative energy difference of superpositions of two coherent states

“…min can be found for arbitrary values of the arguments  and . Examples are coherent states [40][41][42], certain subfamilies of Gaussian states (including squeezed vacuum states [40][41][42] and mixed states with a fixed purity [41]), and binomial, negative binomial and coherent phase states [40] max can be found only numerically. The results of such calculations for the even and odd coherent states are given in section 3.…”

“…Here E j is the mean value of the energy in the quantum state ψ | 〉 j . A similar problem for other important families of quantum states, such as coherent, binomial, negative binomial, squeezed and general Gaussian states was considered in recent papers [40][41][42] (see also [43]). The idea is to…”