Extended comment supplementing @MarkAdler's oft-cited "13 bits per photon" answer
Is it possible to extend high speed data transmission with lasers to the distance Earth to Mars?
Yes, it seems so!
Wikipedia's Psyche (spacecraft); Laser communications experiment or Deep Space Optical Communications (DSOC) unit:
The Discovery program solicitation offered mission projects an extra $30 M if they would host and test the 25 kg DSOC unit which needs about 75 Watts. It is hoped to advance DSOC to TRL 6. DSOC tests should begin about 60 days after launch. The test-runs of the laser equipment will occur over distances of 0.1 to 2.5 astronomical units (AU) on the outward-bound probe.
That probably qualifies as "...to the distance Earth to Mars" since although that could be as much as 2.7 AU (as opposed to 2.5) that's at opposition when you'd be pointing your telescopes in the general direction of the Sun. Of course with narrow band optical interference filters for the laser wavelengths, careful baffling, spatial filtering, "coronographing" and other stray light management techniques, you really could point close to the Sun if you really wanted or needed to.
JPL's Aug. 7, 2023 NASA’s Deep Space Communications to Get a Laser Boost shows the dripping-with-new-technology optical communications system attached to the side of the Psyche deep space spacecraft and discusses how it will operate in great detail.
It also importantly links JPL's (older but undated) Superconducting Nanowire Single Photon Detectors for DSOC
The Deep Space Optical Communications (DSOC) flight transceiver is inside a large tube-like sunshade and telescope on the Psyche spacecraft, as seen here inside a clean room at JPL. An earlier photo, inset, shows the transceiver assembly before it was... Credit: NASA/JPL-Caltech
Groundbreaking Technologies
The transceiver riding on Psyche features several new technologies, including a never-before-flown photon-counting camera attached to an 8.6-inch (22-centimeter) aperture telescope that protrudes from the side of the spacecraft. The transceiver will autonomously scan for, and “lock” onto, the high-power near-infrared laser uplink transmitted by the Optical Communication Telescope Laboratory at JPL’s Table Mountain Facility near Wrightwood, California. The laser uplink will also demonstrate sending commands to the transceiver.
“The powerful uplink laser is a critical part of this tech demo for higher rates to spacecraft, and upgrades to our ground systems will enable optical communications for future deep space missions,” said Jason Mitchell, program executive for NASA’s Space Communications and Navigation (SCaN) program at NASA Headquarters.
Once locked onto the uplink laser, the transceiver will locate the 200-inch (5.1-meter) Hale Telescope at Caltech’s Palomar Observatory in San Diego County, California, about 100 miles (130 kilometers) south of Table Mountain. The transceiver will then use its near-infrared laser to transmit high-rate data down to Palomar. Spacecraft vibrations that might otherwise nudge the laser off target will be dampened by state-of-the-art struts attaching the transceiver to Psyche.
To receive the high-rate downlink laser from the DSOC transceiver, the Hale Telescope has been fitted with a novel superconducting nanowire single photon detector assembly. The assembly is cryogenically cooled so that a single incident laser photon (a quantum particle of light) can be detected and its arrival time recorded. Transmitted as a train of pulses, the laser light must travel more than 200 million miles (300 million kilometers) – the farthest the spacecraft will be during this tech demo – before the faint signals can be detected and processed to extract the information.
“Every component of DSOC exhibits new technology, from the high-power uplink lasers to the pointing system on the transceiver’s telescope and down to the exquisitely sensitive detectors that can count the single photons as they arrive,” said JPL’s Bill Klipstein, the DSOC project manager. “The team even needed to develop new signal-processing techniques to squeeze information out of such weak signals transmitted over vast distances.”
The distances involved pose another challenge for the tech demo: The farther Psyche journeys, the longer the photons will take to reach their destination, creating a lag of up to tens of minutes. The positions of Earth and the spacecraft will be constantly changing while the laser photons travel, so this lag will need to be compensated for.
“Pointing the laser and locking on over millions of miles while dealing with the relative motion of Earth and Psyche poses an exciting challenge for our project,” said Biswas.
Notably, the superconducting nanowire detector was not included on the spacecraft as well (for this demonstration) so the ground station needs to have a particularly high power laser and significantly large aperture so that a conventional photodetector can be used as the receiver on the spacecraft.
While conventional radio communications (to date, used for every deep space mission critical communications) signal to noise ratio S/N scales as the familiar
$$\frac{1}{r^{ \ 2}} \frac{1}{k_B \ T}$$
where $T$ is the temperature of the radio receiver's front-end amplifier and $r$ is the distance between transmitter and receiver, the S/N of deep space optical communications systems based on conventional photodetectors scales as
$$\frac{1}{r^{ \ 4}} f(k_B \ T)$$
i.e. an inverse fourth power of distance and a more complicated function of front-end temperature, because the front end involves a two step process - photons are (generally) first converted to electron-hole pairs in a conventional semiconductor photodiode, then the charge is collected and amplified by a charge or transimpedance. That double conversion results in the much faster drop in S/N as the signal gets weaker with distance. For more on that see
Because the superconducting nanowire receiver technology is not robustly deep-space friendly at this point in time, it seems the designers have leveraged it's extra benefits when used as both a photon counter and timer in the Mt. Palormar receiving ground station since the transmitting laser aboard Psyche will likely be only a few up to a dozen watts and the aperture is only 0.22 meters.
If I understand correctly, we can still expect a roughly $~1/r^2$ S/N scaling for both uplink and downlink because even though it's not of the superconducting nanowire variety, the optical receiver aboard Psyche is still a photon counter, rather than an analog light intensity to current converter followed by a current amplifier. So we've got on the uplink a powerful laser coupled to a large aperture telescope received by a small mirror and photon-counting photodetector (probably some kind of avalanche photodiode or other electron multiplier), and a downlink using the fancy superconducting nanowire detector and yes, the 200-inch Hale telescope atop Mt. Palomar, both hopefully providing circa $~1/r^2$ S/N scaling deep space optical links.
And in the future?
An image in this answer indicates an operation temperature for the superconducting nanowire array of "<3 Kelvin", so below that of liquid helium and perhaps even below the cosmic microwave background, so a small but very special kind of refrigerator is needed.
A system like that robust against vibrations associated with launch and conditions in deep space over long periods of time is something that will require a separate development and demonstration program before it can be used routinely for uplink as well.
It's also important to note that you can push the distance even further if you know exactly when to expect the individual photons to arrive or not arrive (again hats off to @MarkAdler's 13 bits per photon answer) and to that end it is possible that deep space atomic clock technology may be of use.
