Quantum information

The theories of classical physics were predicting absurdities such as the ultraviolet catastrophe, or electrons spiraling into the nucleus.

Von Neumann formulated quantum theory using operator algebra in a way that it described measurement as well as dynamics.

See: Dynamical Pictures In the 1960s, Ruslan Stratonovich, Carl Helstrom and Gordon[20] proposed a formulation of optical communications using quantum mechanics.

[20][21][22] Later, Alexander Holevo obtained an upper bound of communication speed in the transmission of a classical message via a quantum channel.

[23][24] In the 1970s, techniques for manipulating single-atom quantum states, such as the atom trap and the scanning tunneling microscope, began to be developed, making it possible to isolate single atoms and arrange them in arrays.

[2] The development of viable single-state manipulation techniques led to increased interest in the field of quantum information and computation.

In the 1980s, interest arose in whether it might be possible to use quantum effects to disprove Einstein's theory of relativity.

If it were possible to clone an unknown quantum state, it would be possible to use entangled quantum states to transmit information faster than the speed of light, disproving Einstein's theory.

However, around the same time another avenue started dabbling into quantum information and computation: Cryptography.

In a general sense, cryptography is the problem of doing communication or computation involving two or more parties who may not trust one another.

[25] The key idea was the use of the fundamental principle of quantum mechanics that observation disturbs the observed, and the introduction of an eavesdropper in a secure communication line will immediately let the two parties trying to communicate know of the presence of the eavesdropper.

This 'law' is a projective trend that states that the number of transistors in an integrated circuit doubles every two years.

[2] Peter Shor in 1994 came up with a very important and practical problem, one of finding the prime factors of an integer.

Around the time computer science was making a revolution, so was information theory and communication, through Claude Shannon.

Quantum information theory also followed a similar trajectory, Ben Schumacher in 1995 made an analogue to Shannon's noiseless coding theorem using the qubit.

Unlike classical digital states (which are discrete), a qubit is continuous-valued, describable by a direction on the Bloch sphere.

[2] These theorems are proven from unitarity, which according to Leonard Susskind is the technical term for the statement that quantum information within the universe is conserved.

Quantum mechanics is the study of how microscopic physical systems change dynamically in nature.

Regardless of the physical implementation, the limits and features of qubits implied by quantum information theory hold as all these systems are mathematically described by the same apparatus of density matrices over the complex numbers.

[2] Entropy can be studied from the point of view of both the classical and quantum information theories.

[37] Shannon entropy is the quantification of the information gained by measuring the value of a random variable.

This definition of entropy can be used to quantify the physical resources required to store the output of an information source.

The ways of interpreting Shannon entropy discussed above are usually only meaningful when the number of samples of an experiment is large.

The Rényi entropy of order r, written as a function of a discrete probability distribution,

When we want to describe the information or the uncertainty of a quantum state, the probability distributions are simply replaced by density operators

The first quantum key distribution scheme, BB84, was developed by Charles Bennett and Gilles Brassard in 1984.

It is usually explained as a method of securely communicating a private key from a third party to another for use in one-time pad encryption.

These two photons can be created by Alice, Bob, or by a third party including eavesdropper Eve.

If it is not perfectly isolated, for example during a measurement, coherence is shared with the environment and appears to be lost with time; this process is called quantum decoherence.

Many journals publish research in quantum information science, although only a few are dedicated to this area.