Dolinar receiver

The ability to discriminate signals encoded in coherent light has applications in communications where losses are unavoidable,[3] such as transmission along fiber optics cable, through the atmosphere, or across deep space.

In a similar way that digital information can be transmitted by modulating the frequency or amplitude of electromagnetic waves, digital information can be encoded within the phase of coherent light.

is a complex vector within the phase space of a quantum harmonic oscillator such that

is the average number of photons in the state and is related to the intensity of the light.

Binary digital communication can be achieved by sending, for instance, state

A simple example of a device that could transmit the binary coherent states is a switchable laser and an electo-optic modulator (EOM) that applies either a 0 or

If a 0 is required to be transmitted with that pulse, the EOM does nothing and applies no phase shift.

However, for low photon numbers, the two states become less distinguishable and the error closer approaches the maximum of 50%.

This inherent, fundamental source of error due to the quantum nature of the coherent state poses limits to the discrimination of low-intensity coherent states.

The Kennedy receiver [2] is a device that can distinguish between binary coherent states.

and the resulting state is sent to a single-photon detector (SPD), such as a photomultiplier tube or an avalanche photodiode.

The displacement can be performed by interference at a beam splitter with another coherent light source of the state

The Dolinar receiver also makes use of an adaptive displacement mechanism, one that can quickly change from either

The unique feature of the Dolinar receiver is the feedback from the detector and the displacement mechanism in between arrivals of the input state copies.

, and depending on which displacement is used and if a photon is counted or not, a best hypothesis as to the nature of the input state can be put forth.

If no photons are counted, it is most likely that the hypothesis was correct and that the input state was displaced to vacuum.

If one or more photons are counted, it is known that the guess was wrong as the input state was not displaced to vacuum.

The feedback of the Dolinar receiver works by switching the displacement if there was a photon counted but before the next copy of the input state arrives.

If no photons are detected, the displacement remains unchanged for the next arrival of a copy.

For each no count result, it becomes more and more likely that the state copies are being displaced to vacuum and the certainty of the hypothesis increases.

[1] On the whole, the history of the detection results in conjunction with their corresponding displacements can give more and more complete information about the most likely identity of the input state.

As an example, suppose before the first copy of the input state arrives, the receiver is set to test for

At this point, any hypothesis is limited by a 50% chance of guessing the input state on sheer luck alone, and thus the choice is arbitrary.

As before, each lack of counted photons after a displacement switch reinforces the hypothesis that the original guess was incorrect.

While more complex than the Kennedy receiver and requiring multiple copies of the input state, the Dolinar receiver's adaptive feedback offers a mechanism to reduce the chances of a hypothesis being wrong.

If the detector counts a photon even when the hypothesis is correct and the input state copy was displaced to vacuum, the displacement will switch and there is a likely chance another photon will be detected on the next pass, switching the displacement back, where there will be a less likely chance to detect photons for future detection.

As long as the rate of dark counts is not too high, the overall history of detection results can give a likely picture as to the nature of the original input state.

Two bits of information is encoded into each state using a method known as quadrature phase-shift keying.

Rather, after a displacement and detection result, a deliberate decision is made on the new hypothesis given the total history of displacements and detection results using Bayesian inference.

This awareness of the history of detection results provides robustness against dark counts inherent in the feedback technique of the Dolinar receiver.