Question

Quantum cryptography requires having a photon gun that can, on demand, fire a single photon carrying 1 bit. In this problem, calculate how many photons a bit carries on a 250-Gbps fiber link. Assume that the length of a photon is equal to its wavelength, which for purposes of this problem, is 1 micron. Also, assume that the speed of light in fiber is \(20 \mathrm{~cm} / \mathrm{nsec}\).

Short answer

800 photons per bit.

Step-by-step solution

Understanding the Problem

We need to find out how many photons carry a bit in a 250-Gbps fiber link. We have been provided with the photon's wavelength (1 micron) and the speed of light in the fiber (20 cm/nsec). Let's identify the relationship among the given values to compute the solution.

Calculating Bit Length

First, determine how long a bit takes in terms of spatial length. The speed of light in fiber is 20 cm/nsec, and the link transmits at 250 Gbps, so the bit duration is \( \frac{1}{250 \times 10^9} \) seconds. Convert this to space by multiplying the time taken for a bit by the speed of light: \( \frac{20 \text{ cm/nsec} \times 10^9}{250} \).

Conversion of Units

Convert the speed of light into meters per second: 20 cm/nsec = 2 \( \times 10^8 \) meters/second. Now calculate the length a bit occupies: \( \frac{2 \times 10^8}{250 \times 10^9} = 8 \times 10^{-4} \) meters or 800 microns.

Calculating Number of Photons per Bit

With each photon having a wavelength of 1 micron, and each bit occupying 800 microns, the number of photons per bit is the length of the bit divided by the length of one photon: \( \frac{800 \text{ microns}}{1 \text{ micron}} = 800 \) photons per bit.

Key concepts

Photon Gun

A photon gun is a crucial device in the world of quantum cryptography. It is designed to emit single photons on demand, making it a fundamental tool for secure communication. These photons carry quantum information in the form of bits. This process is vital for establishing a secure quantum channel where information can be transmitted discreetly.

Photon guns help in various applications, including:

• Quantum key distribution
• Ensuring secure communication by mitigating eavesdropping risks
• Research in quantum computing and quantum networks

The essence of the photon gun lies in its ability to release a single photon at a time, a challenging yet critical task. Precision and control are key elements, enabling reliable encryption and decryption processes over quantum channels.

Fiber Optic Communication

Fiber optic communication is the backbone of modern telecommunication, allowing data to be transmitted as light signals through fibers. In the context of quantum cryptography, fiber optic cables serve as the medium that carries individual photons, ensuring fast and efficient data transfer.

Fiber optics offer several advantages:

• High bandwidth capabilities
• Minimal signal loss over long distances
• Resistance to electromagnetic interference

The speed of light within the fiber is crucial, as it influences how quickly data is transferred. In our example, the speed of light in fiber is 20 cm/nsec, highlighting the ultra-fast speed that aids in high-speed data transmission, such as the 250-Gbps link in question.

Bit Length Calculation

Calculating the spatial length of a bit in fiber optic communication involves understanding how fast information is transmitted. Given a speed of 20 cm/nsec for light in the fiber and a 250-Gbps transmission rate, we can determine how far a bit can travel.

First, find the bit duration: \[ \text{Bit duration} = \frac{1}{250 \times 10^9} \text{ seconds} \]Next, use the speed of light to convert this time into spatial length:\[ \text{Bit length} = \frac{20 \times 10^{9}}{250} \text{ cm} = 8 \times 10^{-2} \text{ meters, or } 800 \text{ microns} \]

This calculation reveals that each bit occupies a space of 800 microns in the fiber, which is crucial for understanding the number of photons needed per bit.

Photon Wavelength

Photon wavelength is a key attribute in understanding how light behaves in quantum cryptography. It refers to the distance between successive peaks of a wave. In our problem, the wavelength is given as 1 micron. This distance becomes critical when determining how many photons fit within a given bit length.

Key aspects of photon wavelength include:

• It determines the photon's energy and properties
• In our example, it dictates how many photons can represent a single bit
• Wavelength selection impacts the fiber's performance and the ability to differentiate between signals

Each photon has a defined wavelength, and since our bit length is 800 microns, it means 800 such photons are required to fill the bit length in the fiber optic communication at the wavelength provided.