Anyway, I have not said much to persuade you that the Quantum Bloch Sphere is like a tennis ball. It is all about spin. A one-handed top spin backhand is one of my favourite shots. When hit correctly, the power and curve on the shot are beautiful. Sometimes I do this and my friends call this shot ‘Mr. Whippy’. Of course, you have other spins such as backspin and slice with their differing curves as well as just the regular flat shot. These spins and shots remind me of Quantum algorithms. Quantum algorithms are functions that try to change the wave of the electron so that it has a greater probability of being in a certain position when measured. The algorithms remind me of applying a spin to a tennis ball to influence its flight and bounce. Unfortunately, nowadays my friends recognise when I set up to use ‘Mr. Whippy’ so well, that they are waiting at the net to volley and the probability of me winning a point is low.
The basics of Quantum theory is that an electron is spinning around in a three dimensional space like tossed coins. Just like tossed coins, which usually only land on one side or the other, when the electron is stopped, it can only have a state of 0 or 1.
The Pilot Wave Quantum theory is that the electron follows a predictable path. However we do not know where it is until it is measured. The Dynamical Collapse theory believes the path is random. Of course the best theory for science fiction writers is the Many Worlds theory where the electron is everywhere at the same time. Schroedinger came up with the story of the cat in the box with the piece of radium in a vial that could break at any time and kill the cat. The Many Worlds theory allowed the cat to be both alive and dead at the same time. Schroedinger came up with this story in order to point out that the theory was extremely unlikely. Ironically, this story is often used to support the Many Worlds theory. Schroedinger himself ended up a bit like his cat, as he was both an Irish and Austrian citizen at the same time.
This three dimensional space the electron spins in is represented by a sphere called the Bloch Sphere – or as I like to think of it as my tennis ball. The electron can be anywhere in the tennis–ball. As it is in 3D, there are three axes, x, y, z. One way to describe the location of the electron is to use the coordinates of the axes based on the Cartesian co-ordinate system. A second way is to describe the location of the electron based on a mix of the quantum states |0> and |1>. This mix of quantum states defines the Qubit. If the electron is at the North Pole, its Quantum state is |0>. When it is at the South Pole its Quantum state is |1>.
Quantum theory is a bit crazy. Is the electron a wave or a particle? Well it is both. The electron is a particle whose location is determined by the equation for a wave. The equation gives the probability of the particle being in a particular place when measured. It does not follow a fixed orbit or a wave pattern around the nucleus. If it did, it would end up sinking into the nucleus. An electron is just an electron, and you can’t actually say whether it’s a wave or a particle.
The North Pole is on the z-axis and has a Quantum state of |0>. It is at Z+ = 0, 0, 1 on my tennis ball. The South Pole it on the z-axis and has a Quantum state of |1>. It is at Z- + 0, 0, -1 on my tennis ball.
The x-axis is the axis going from the front of the sphere to the back through the centre. I call these poles the Near and Far poles. The Near Pole is on the x-axis and has a quantum state of (|0> + |1>)/√2. It is at X+ = 1, 0, 0 on my tennis ball. The Far Pole is on the x-axis and has a quantum state of (|0> – |1>)/√2. It is at X- = -1, 0, 0 on my tennis ball. This now introduces negativity to Quantum states.
The y-axis goes from the West pole through the centre to the East pole. It gives the third dimension. A qubit is a Quantum bit and its state is described as a mixture of the states |0> and |1> which are orthogonal. With only two orthogonal bases, you can only describe two dimensions. So what is the solution? The third dimension is described by introducing i, which is orthogonal or perpendicular to the plane created by the x and z-axes. The East Pole is on the y-axis and has a Quantum state of (|0> + i|1>)/√2. It is at Y+ = 0, 1, 0 on my tennis ball. The Far Pole is on the y-axis and has a Quantum state of (|0> – i|1>)/√2. It is at Y- = 0, -1, 0 on my tennis ball.
Quantum is difficult enough to understand without introducing negative states when negative does not exist in reality.
