Fundamental limits of information transfer

Communication technologies are concerned with transferring information between two points in space, where a message is encoded onto a physical carrier, sent through a channel that degrades it, and recovered at the far end. In an earlier post, we gave each domain of technologies a dominant bound, and communications got the Holevo limit. Here we will look at where that bound comes from and what it turns out to buy.

The throughput gap

The size of the gap is set by two numbers, both normalized to 1 W and 1 km. An ultimate communication link is bounded at ~10¹⁶ bits per second (Giovannetti et al., 2004), while a fiber-optic communication link built in 2025 carries ~10¹⁰ bits per second (Optical Internetworking Forum, 2025). Latency is a different story, since propagation is bounded by the speed of light and a deployed link is already close to it (Giovannetti et al., 2004; Optical Internetworking Forum, 2025). Therefore the throughput gap is the one worth attacking, and it is ~6 orders of magnitude wide.

Most of those 6 orders are ordinary engineering, coming from bandwidth we don’t use, power we don’t launch, and electronics that add noise. The quantum step, from the Shannon limit to the Holevo limit, is a small part of the total in a conventional link. It is still worth understanding, because it behaves unlike any of the classical terms.

Where the Shannon limit comes from

Throughput is bounded by the channel capacity, which depends on what we allow the receiver to do. Why can’t we close the gap by building a cleaner receiver? Take one mode per symbol and write its mean photon number as N. For coherent-state inputs, measuring both field quadratures at once turns the link into a complex additive white Gaussian noise channel with per-quadrature signal-to-noise ratio N, and its capacity is the Shannon limit,

C_Sh = log₂(1 + N) bits per mode (Shannon, 1948).

The extra vacuum unit in that noise floor is the price of measuring two non-commuting quadratures simultaneously, and quantum mechanics doesn’t require us to measure that way. If the receiver performs one joint measurement across many uses of the channel instead of one symbol at a time, the bound becomes the Holevo limit (Holevo, 1973; Schumacher & Westmoreland, 1997),

C_Hol = (N+1)log₂(N+1) − N log₂N bits per mode.

The difference comes out in one line, since C_Hol − C_Sh = N log₂(1 + 1/N), positive for every N > 0. So the distinction is about the measurement at the receiver rather than the channel or what we transmit, since coherent states with Gaussian modulation, read out by a joint measurement, already saturate the Holevo limit for the lossy bosonic channel (Giovannetti et al., 2004).

There is a third bound above both of these. If the transmitter and receiver share entanglement ahead of time, the limit becomes the entanglement-assisted classical capacity (Bennett et al., 1999; Bennett et al., 2002), which doubles the Holevo capacity in the noiseless limit and recovers the two bits per channel use of superdense coding (Bennett & Wiesner, 1992). So C_EA ≥ C_Hol ≥ C_Sh, the first gap bought with pre-shared entanglement and the second with joint measurement.

What the quantum step actually buys

How big is that second gap? At large N the two bounds converge in relative terms as the field starts behaving classically, with the additive difference saturating at log₂e bits per mode. A fraction of a bit per mode is not 6 orders of magnitude, which is why nobody worries about Holevo in a conventional high-power link.

At small N the picture inverts. The ratio of the two capacities grows like 1 − ln N without bound (Banaszek et al., 2020), so joint detection becomes arbitrarily better than quadrature measurement as the photon number per mode falls. The same asymmetry shows up in energy, where the Shannon limit bottoms out at a floor of ħω ln2, about the energy of a single photon per bit, while the corresponding Holevo energy per bit falls toward zero (Verdu, 1990; Giovannetti et al., 2004). Under joint detection each photon can carry ~log₂(1/N) bits, so thinning the signal across more modes raises the bits per photon with no floor underneath it. That ħω ln2 figure turns out to be a property of symbol-by-symbol measurement rather than a property of the channel.

So the quantum step is an energy-efficiency result before a throughput result, since the rate per mode falls as N does and aggregate throughput then takes many multiplexed low-power channels. Both capacities should also be evaluated at the photon number reaching the detector, so channel loss and detector inefficiency push the improvement factor down.

Latency, blocklength, and error rate

Capacity on its own says nothing about error rate. Shannon’s theorem says we can push the error probability arbitrarily low by coding over longer blocks at any rate below capacity (Shannon, 1948), and the cost is latency. For blocklength n over a bandwidth B, the decoding latency is bounded below by n/B, which is separate from the propagation delay above.

How far below capacity do we back off at a finite blocklength? The back-off scales as the square root of V/n, where V is the channel dispersion, the conditional variance of the information density for the capacity-achieving input (Polyanskiy et al., 2010). Each capacity carries its own dispersion, and the pair sets the latency-reliability trade-off of that limit.

The interesting case is the photon-starved one again. At small N the ratio C_Hol/C_Sh diverges, so rates between the two are reachable with vanishing error probability under joint detection and unreachable under symbol-by-symbol two-quadrature reception at any blocklength. Therefore at low signal power the payoff comes from a better receiver instead of a longer code, which is an unusual situation in communications engineering.

Quantum-limited receivers

Collective decoding is out of reach for now. However, there are two things we can build that move a real communication link closer to the Shannon limit, and in one case past it:

1. We can change how we measure, by making the receiver quantum-limited, so that the noise floor is set by the quantum fluctuations of the light rather than by the electronics behind the photodiodes. This doesn’t pass the Shannon limit, but it puts a link on the ideal Shannon curve rather than one degraded by electronic noise, and it is what let us detect squeezed light at all (Gurses et al., 2026).
2. We can change what we send, by encoding information in nonclassical states of light, such as squeezed light. At low photon number this can beat the rate of a two-quadrature coherent receiver (Gurses et al., 2026; Banaszek et al., 2020), though it still doesn’t reach the Holevo limit.

We worked on the first one. We demonstrated an integrated photonic-electronic quantum-limited coherent receiver with 14.0 dB of shot noise clearance, 520 μW knee power, 2.57 GHz 3-dB bandwidth, and 90.2 dB of common-mode rejection ratio (Gurses et al., 2026). Scaling the corresponding design to a 32-channel array gives a median 26.6 dB of clearance, and automatic common-mode rejection correction yields a median 76.8 dB of rejection at minimum (Gurses et al., 2026). Running this receiver against a fiber-optic transmitter, we measured 0.15 ± 0.01 dB of squeezing below the shot noise limit, which turns out to be limited by off-chip losses (Gurses et al., 2026). This receiver came together over several iterations (Gurses & Hajimiri, 2022; Gurses et al., 2023; Gurses et al., 2024). Pablo Backer-Peral led the work that transmitted and received squeezed light over a fiber-optic link (Backer-Peral et al., 2025), and the corresponding free-space system is an on-chip phased array that images squeezed light over free space across 32 pixels (Gurses et al., 2025).

We also propose a squeezed light communication scheme that can surpass the Shannon limit (Gurses et al., 2026). However, we haven’t demonstrated it on a link yet, so the receiver above is so far a measurement device.

Remaining obstacles

That squeezing figure is small, and off-chip coupling loss capped it (Gurses et al., 2026). That is a packaging problem rather than a channel problem, however loss hurts in both places, since the classical capacity of the lossy bosonic channel falls as the transmissivity falls (Giovannetti et al., 2004). Loss also doesn’t treat the two kinds of light the same way. A coherent state comes out of a lossy channel as a weaker coherent state, while a squeezed state comes out with less squeezing and in a mixed state, so squeezing is the property that degrades first.

The second obstacle is the joint-detection receiver itself. Structured designs exist, such as Hadamard-coded coherent-state sequences decoded through a mesh of order n log n elements followed by photon counting (Guha, 2011). Superadditive gains have been seen in small experiments, though not at the blocklengths or rates a deployed link needs, so joint detection is still a design target. We are working through this for interconnects in high-performance computing, where the distances are short and the power budgets are tight (Gurses & others, 2026). That work is in preparation, so treat it as provisional.