By David S. Simon, Visit Amazon's Gregg Jaeger Page, search results, Learn about Author Central, Gregg Jaeger, , Alexander V. Sergienko
This booklet describes the experimental and theoretical bases for the improvement of particularly quantum-mechanical ways to metrology, imaging, and conversation. particularly, it provides novel recommendations constructed over the past twenty years and explicates them either theoretically and via connection with experiments which display their ideas in perform. the actual concepts explored comprise two-photon interferometry, two-photon optical aberration and dispersion cancellation, lithography, microscopy, and cryptography.
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Extra info for Quantum Metrology, Imaging, and Communication
Sample text
Quantum mechanically, there is a nonzero lower limit to the product of the corresponding variances, ΔxΔp, since xˆ and pˆ are conjugate and therefore have nonzero commutators. EPR’s line of thought points out, however, that if Alice measures xˆ and finds value x0 , then its Bob must 36 1 Quantum Optics and Entanglement have value −x0 , while if the Bob measures pˆ and finds value p0 , then its Alice must have value − p0 . Under a local “realist” theory, neither measurement should disturb the values measured at the other, distant location, so that after communicating their results to each other the experimenters should now know the values of both xˆ and p, ˆ to as high an accuracy as their measuring devices can achieve.
K is therefore finite, even for continuous degrees of freedom, as long as the available phase space volume is finite. The quantity log2 K is sometimes called the Schmidt measure. An explicit recipe can be constructed for putting a state into Schmidt form. Consider some pure state | = i j Ci j |u i |v j , so that the density operator is of the form Ci j Ckl∗ |u i u k | ⊗ |v j vl |. 40) ρˆ = i jkl First rotate from the |u i basis to the basis |u i in which ρˆu = Trv ρˆ is diagonal. i j Ci j Ckl∗ = δik |gi |2 in this basis, for some constants gi , and so ρˆu = 2 i |gi | |u i u i |.
In general, entangled states may have positive or negative values of W . 8 Entanglement Witnesses An entanglement witness [45–48] does not provide a quantitative measure of the amount of entanglement, but simply gives (sometimes) a yes or no answer to the question of whether or not a state is entangled. Specifically, an entanglement witness W is any scalar function on the system’s Hilbert space that obeys W > 0 for all separable states. W ≤ 0 is therefore a signal of entanglement. Often, the function W is defined in terms of some operator Wˆ , such that W(ρ) ˆ = Tr ρˆ Wˆ .