Entanglement-Assisted Absorption Spectroscopy

Spectroscopy is an important tool for probing the properties of materials, chemicals, and biological samples. We design a practical transmitter-receiver system that exploits entanglement to achieve a provable quantum advantage over all spectroscopic schemes based on classical sources. To probe the absorption spectra, modeled as a pattern of transmissivities among different frequency modes, we employ broadband signal-idler pairs in two-mode squeezed vacuum states. At the receiver side, we apply photodetection after optical parametric amplification. Finally, we perform a maximum likelihood decision test on the measurement results, achieving an error probability orders of magnitude lower than the optimum classical systems in various examples, including “wine tasting” and “drug testing” where real molecules are considered. In detecting the presence of an absorption line, our quantum scheme achieves the optimum performance allowed by quantum mechanics. The quantum advantage in our system is robust against noise and loss, which makes near-term experimental demonstration possible.

Figure 1

Diagram of the entanglement-assisted absorption spectroscopy. The source generates multichromatic entangled signal-idler pairs via a nonlinear process. The signals interact with the sample and then go through another nonlinear process jointly with the idlers at the quantum receiver. Photodetection extracts the absorption coefficients at different frequencies.

Figure 2

Schematic of receiver. Signal beams are irradiated over the sample, modeled by frequency-dependent transmissivities ${\mathbf{\kappa }}^{(h)}=\{{\kappa }_{\ell }^{(h)}{\}}_{\ell =1}^m$. The modulated beams go through a single optical parametric amplifier. Finally spectrally resolving photodetection offers a $2mM$-dimensional count based on which the maximum likelihood decision $\tilde{h}$ is made.

Figure 3

Error rate versus number of probing modes with practical parameters $N_S=1$, ${\kappa }_T=0.75$, and ${\kappa }_B=0.95$. (a) Absorption detection. EA nulling receiver (solid orange) is compared to classical lower bound of Eq. (3) (dot-dashed black), QCB (dashed black), and the EA homodyne receiver (solid purple). (b) Peak positioning. Single-peak positioning (solid green) and double-peak positioning (solid blue) with $m=10$ frequency slots. Single-peak positioning with $m=100$ (solid red) provided as a reference. Classical lower bounds given by Eq. (4) (dashed, accordingly colored).

Figure 4

(a),(b) Error probability of EAAS $P_{E,m}$ versus transmissivities ${\kappa }_B$ and ${\kappa }_T$. (c),(d) ${\log }_{10}{P}_{E,m}$ versus idler loss $1-{\kappa }_I$ and thermal noise $N_B$ at fixed ${\kappa }_T=0.75$ and ${\kappa }_B=0.95$. Absorption detection ($m=1$) in (a),(c) compared with single-peak positioning ($m=100$) in (b),(d). $M$ is chosen to fixed the classical lower bounds to 0.01 [42]. $N_S=1$ is assumed. Red-crossed diagonal region in (a),(b) represents the degenerate case ${\kappa }_B={\kappa }_T$.

Figure 5

Identification of $H=3$ molecules with $m=4$ frequency slots for wine tasting in (a),(b),(c) and drug testing in (d),(e),(f). (a),(d) are $m=4$ sampled discrete spectra on the fourier-transform infrared spectra in (b),(e). (c),(f) show the logarithmic error rate of EAAS, with $N_S=1$. “EAAS” assumes a uniform distribution of photons at the input modes (solid orange), while numerically optimized energy distribution is presented in “${\mathrm{EAAS}}^{\star }$” (solid purple). The classical lower bound (dot-dashed black) and homodyne detection (solid black). Insets of (c),(f): Error probability ratio of EAAS with gain optimization after energy-distribution optimization and EAAS with merely energy-distribution optimization.