The amount of information that can be transmitted using a single photon's wavelength property is determined by the number of distinguishable wavelengths that can be reliably detected and distinguished by the perfect wavelength detector.
In classical communication systems, information is typically encoded using binary digits, or bits, which can take on two values: 0 or 1. Each bit represents one unit of information. However, in quantum communication, information can be encoded in quantum states, such as the different wavelengths of a single photon.
To calculate the amount of information that can be transmitted, we can use the concept of "quantum bits" or qubits. While a single qubit can represent more than one classical bit, the exact amount depends on the encoding scheme used.
Assuming that the perfect wavelength detector can reliably distinguish between n different wavelengths, each corresponding to a different qubit state, the number of bits that can be encoded using a single photon would be log2(n). This means that each photon could carry log2(n) bits of information.
For example, if the perfect detector can reliably distinguish between 8 different wavelengths, then each photon could carry log2(8) = 3 bits of information.
It's important to note that this calculation assumes ideal conditions, including perfect detectors and no noise or loss in the communication channel. In practical scenarios, various factors can limit the actual information transmission rate in quantum communication systems.