Creating Superposition: The Beam Splitter

Now that we have explored qubits and the phenomenon of superposition, we can ask the question: how do we know that superposition actually happens? is the evidence that shows that a quantum particle really does exist in two different locations at this same time while in a quantum superposition? The nature of science means that experiments are constantly updating previous results, so are there other interpretations of the experimental results that can explain the data without the need for superposition? In this chapter we’ll explore the experimental evidence interpretations other than quantum superposition. Further, while a flipping coin is a simple model of a qubit, it is not very useful for building a quantum computer because it does not exhibit all of the properties of a true quantum superposition. For example, we cannot manipulate the superposition amplitudes. In this chapter, we will study some real physical examples of quantum particles in a superposition containing two states. These examples include a photon in a beam splitter and the Mach–Zehnder interferometer.

Worksheets

Apply the idea of basis changing to explain the correlation that is observed.

Entanglement

So far, we have discussed the manipulation and measurement of a single qubit. However, quantum entanglement is a physical phenomenon that occurs when multiple qubits are correlated with each other. Entanglement can have strange and useful consequences that could make quantum computers faster than classical computers. Qubits can be “entangled,” providing hidden quantum information that does not exist in the classical world. It is this entanglement that is one of the main advantages of the quantum world!

Creating Superposition: Stern–Gerlach

In the previous chapter, we have seen that a photon in an interferometer can be a prototype for a qubit. Might there be any other prototypes for a qubit arising from other particles that we might know? In fact, an electron is another prototype for a qubit. An electron has many measurable properties such as energy, mass, momentum. But, for the purposes of creating a qubit, we want to focus on a property with only two measurable values. An electron has a two-state property which is called spin.

Quantum Algorithms

We have come a long way from Chap. 10.1007/978-3-030-61601-4_1 To recap on what we have learnt, we have understood important quantum mechanical phenomena such as superposition and measurement (through the Stern-Gerlach and Mach-Zehnder experiments). We have also learnt that while quantum computers can in principle break classical encryption protocols, they can also be used to make new secure channels of communication. Furthermore, we have applied quantum logic gates to qubits to perform quantum computations. With entanglement, we teleported the information in an unknown qubit to another qubit. This is quite a substantial achievement.

Quantum Cryptography

The Internet can be thought of as a channel of information being sent from you to everyone else connected to the Internet. If you wanted to transmit your sensitive information (such as bank account numbers or military secrets) over the Internet, then you have to ensure that only the persons you intend to read your information have access to your sensitive data. Otherwise, everyone would be able to read your information, e.g., access to your bank account details and transfer money out of your account. Therefore, one needs to encrypt any data sent over the Internet. Encryption, in this context, ensures that only the intended sender and receiver can understand any message being sent over an Internet channel.

Quantum Teleportation

One interesting application of entanglement is quantum teleportation, which is a technique for transferring an unknown quantum state from one place to another. In science fiction, teleportation generally involves a machine scanning a person and another machine reassembling the person on the other end. The original body disintegrates and no longer exists. Similarly, quantum teleportation works by “scanning” the original qubit, sending a recipe, and reconstructing the qubit elsewhere. The original qubit is not physically destroyed in the science fiction sense, but it is no longer in the same state. Otherwise, the previously mentioned no-cloning theorem—which states that a qubit cannot be exactly copied onto another qubit—would be violated.1 As we will see, the “scanning” part poses a problem which can only be solved by leveraging quantum entanglement.

Quantum Gates

As discussed in Chap. 10.1007/978-3-030-61601-4_2, information in classical computers is represented by bits. However, if the bits did not change, then the computer would remain the same forever and would not be very useful! Therefore, it is necessary to change the values of bits depending on what you want the computer to do. For example, if you want a computer to multiply the number 2 and the number 3 together to produce the number 6, then you need to put each of the numbers 2 and 3 into an 8-bit binary representation, and then have a computational operation to multiply the two 8-bit values together to produce 6. The operation of changing bits in a classical computer is performed by classical logic gates.

What Is a Qubit?

In classical computers, information is represented as the binary digits 0 or 1. These are called bits. For example, the number 1 in an 8-bit binary representation is written as 00000001. The number 2 is represented as 00000010. We place extra zeros in front to write every number with 8-bits total, which is called one byte. In fact, every classical computer translates these bits into the human readable information on your electronic device. The document you read or video you watch is encoded in the computer binary language in terms of these 1’s and 0’s. Computer hardware understands the 1-bit as an electrical current flowing through a wire (in a transistor) while the 0-bit is the absence of an electrical current in a wire. These electrical signals can be thought of as “on” (the 1-bit) or “off” (the 0-bit). Your computer then decodes the classical 1 or 0 bits into words or videos, etc.

Introduction to Superposition

In this section, we review the concepts of classical and quantum superposition. Quantum superposition is the framework for understanding all quantum phenomena. As we do not observe quantum phenomena in our everyday lives, it may seem confusing at first. However, as unintuitive as the quantum world may appear, there are a vast number of experiments which conclusively show that the universe really does operate according to the law of quantum superposition at the smallest distances accessible today. Before going into specific details on quantum superposition, it is useful to explain how the term “superposition” is used in different contexts in both classical and quantum physics. At the end of the chapter, we present the related activities and questions. After gaining experience with quantum superposition from working through these problems, it will become more intuitive. The more experience you gain by advancing through this book, the more quantum superposition will make sense.