Table III.

Experimentally attained performance of quantum receivers with different encodings. The best energy sensitivity improvement over classical detection is given by the smallest ratio of experimentally measured SER (P_E) to the classical theoretical SNL adjusted for receiver’s system efficiency η (P_SNL(η)) and to the ideal SNL (P_SNL). The input energy in average number of photons per bit (photons/bit) when this minimum occurs is given in adjacent columns. The energy required to experimentally achieve 10% SER (P_E = 0:1) is compared to energy requirements to achieve the same with classical measurements, shown as energy efficiency improvement relative to ideal (〈n〉_SNL/〈n〉_E) and adjusted (〈n〉_SNL(η)/〈n〉_E) SNLs.

Encoding protocol	$\frac{P_{\text{E}}}{P_{\text{SNL}(\eta )}}@\frac{{\langle n\rangle }_{\text{E}}}{{\log }_{2}M}$		η	$\frac{P_{\text{E}}}{P_{\text{SNL}}}@\frac{{\langle n\rangle }_{\text{E}}}{{\log }_{2}M}$		⟨n⟩E/log2M @PE = 0.1	⟨n⟩SNL/⟨n⟩E @PE = 0.1	⟨n⟩SNL(η)/⟨n⟩E @PE = 0.1	References
	dB	photons/bit		dB	photons/bit	photons/bit
OOK	−2.2	2	0.35	−0.31	0.29	a	a	a	57
	−0.5	0.2	−0.75	0.2	0.7	a	a	a	20
BPSK	−0.77	0.44	0.55	b		0.73	0.56	1.03	54
	−0.42	0.21	0.91	−0.15	0.21	0.41	1	1.1	22
	−6	7	0.72	b		0.5	0.82	1.14	60
	−4	2.2	0.58	b		0.78	0.53	0.91	55 c
4-PPM	−2.3	1.6	0.4	b		a	a	a	51
4-PSK	−0.22	1.51	0.53	b		a	a	a	59
	−13	4.5	0.72	−6.7	5.5	1.25	1.07	1.48	67
	−27	10	0.72	−14	10	1.25	1.07	1.48	69
	−6.8	2	0.7	−3.7	2	1.02	1.31	1.87	73
	−8.9	4.7	0.65	−1.7	4.2	1.3	1	1.58	68 c
	−6.3	2	0.75	−3.7	2	1	1.33	1.79	75
4-CFSK	−11	2.7	0.75	−7.1	2.7	0.84	1.49	1.98	49
8-CFSK	−7.1	2	0.75	−3.1	2	1	1.25	1.67	49
16-CFSK	−2.6	1	0.75	−0.30	1	1.28	0.95	1.27	49
8-PSK	−3.8	3.1	0.75	−1.86	3.1	2.42	1.27	1.69	75
16-PSK	−2.7	7.4	0.75	−1.2	6.3	7.75	1.15	1.33	75

^aExperimentally measured SER is above P_E = 0.1.

^bExperimental SER does not surpass absolute SNL.

^cMark experiments at the telecom wavelength (1550 nm).