That remarkable theorem by Bell

Before quantum physics came along, assigning a state to a physical system meant that you can uniquely determine the value of any measurable property using that state. In quantum mechanics, however, we've learned this is not the case: even if you know the quantum state exactly, for most measurements the best you can hope for is to estimate the probabilities for the various possible outcomes.

You might wonder, is the inability to uniquely determine measurement outcomes just a lack of complete knowledge about the system? Or put differently, could you gain some additional information beyond the quantum state that will help you determine outcomes exactly? The answer is "no", quantum phenomena are fundamentally probabilistic in nature and one way to show this is using an argument first made by John Bell in the 1960s.

Bell's theorem, as the result is called, says that there is no hidden mechanism that decides the outcome of a quantum measurement. The way the argument works is that if you assume that there is some  unknown factor that manufactures the statistical results of a measurement, then you can establish a limit on the amount of correlation among certain properties you can measure, which you can state as a Bell inequality. You can then show that there are always some quantum states that can violate the inequality. In this post, we attempt to describe a simple example of Bell's theorem at work.

Understanding quantum entanglement

As mentioned before, a quantum computer exploits the rules of quantum theory for accomplishing feats that are considered impossible with conventional computers. Two features of quantum mechanics are often involved in achieving such feats: superposition, which was discussed in our last post, and entanglement, which is the topic here.

Quantum entanglement is considered to be one of the counterintuitive aspects of quantum mechanics. However it is not a particularly difficult concept to grasp if we start with the notion of correlation. Roughly speaking, entangled quantum systems are objects whose properties so strongly correlated that using a state to describe all of them as a single unit describes them better than assigning a state to individual parts.

A note on quantum superposition

Quantum computing is commonly described as the means of harnessing the laws of quantum mechanics to process information, usually for the purpose of doing certain calculations faster than what you can achieve with conventional computers. 

A typical computer operates on binary digits, or bits, of information, which is a sequence of zeros and ones encoded by electrical signals. A calculation is performed using a circuit of transistors designed to switch the signals on and off in a particular way, so that the final bit values determine the result.  The list of specific steps needed for handling bits in any such calculation is called an algorithm.

In contrast,  a quantum computer encodes information in quantum bits, or qubits. Computation with qubits is different from computation with bits because quantum systems can be prepared and controlled in ways that can not be achieved with signals that represent bits. Quantum algorithms describe ways in which qubits can be manipulated so that the correct measurement yields the desired outcome of a calculation with high probability.

Energy transfer in light-harvesting pigments exhibits non-classical effects

In a previous post, we described the coherent transfer of energy from sunlight in photosynthetic systems. What it shows there is some indication of quantum effects playing a useful role in organic processes. What it does not show is whether there exists a different mechanism for explaining the same effect without using quantum mechanics.

To convince anyone that quantum effects play an important function in biological processes such as photosynthesis, we must show that a classical explanation is not sufficient to account for the efficient transport of energy. In a paper by O'Reilly and Olaya-Castro, they demonstrate this using methods in the quantum theory of light.

Light is a form of electromagnetic radiation, where the term is reserved mainly for radiation that is visible to our eyes. It is composed of electromagnetic waves that vibrate at different frequencies, which we perceive as different shades of colors. Much of how light waves behave can be explained using a classical theory of waves, which describes how waves can be combined to produce various patterns of interference.