Theory of entanglement and measurement in high-order harmonic generation

Quantum information science and intense laser-matter interaction are two apparently unrelated fields. Here, we introduce the notion of quantum information theory to intense laser-driven processes by providing the quantum mechanical description of measurement protocols for high-order harmonic generation in atoms. This allows one to conceive new protocols for quantum state engineering of light. We explicitly evaluate conditioning experiments on individual optical field modes and provide the corresponding quantum operation for coherent states. The associated positive-operator-valued measures are obtained and give rise to the quantum theory of measurement for the generation of high-dimensional entangled states and coherent-state superposition with controllable nonclassical features on the attosecond timescale. This establishes the use of intense laser-driven processes as an alternative platform for quantum information processing.

Figure 1

Schematic illustration of the conditioning experiment in HHG. The initial product state $|\alpha \rangle \otimes |\left\{0_{q\ge 2}\right\}\rangle$ of the optical field mode is shifted via $K_{\mathrm{HHG}}\simeq {\prod }_{q}D\left({\chi }_q\right)$ and correlated (via the wave-packet mode $|\tilde{n}\rangle$). Performing a conditioning measurement on the harmonic modes $\left|\right\{{\chi }_q\}\rangle$ leads to the quantum operation ${\mathrm{\Phi }}_{\tilde{n}\ne 0}^{\chi }[·]$ on the initial coherent state of the driving laser.