Probably the most shocking feature of quantum mechanics arises in the fact that the same theory that characterizes the physical entities with stochastic variables, also describes the evolution of systems with deterministic equations.
The scientific basis of this self-contradiction, brought with it one of the most important revolutions in physics, and at the same time, changed the fundamentals in the fields of information theory and computation.
The main theoretical achievements in the quantum information theory that could be materialised in real applications in the coming years are embodied in the following three topics: Super Dense Coding, Quantum Teleportation and Quantum Computation.
Super Dense Coding
In quantum information theory, Shanon entropy is reformulated in a new expression known as ‘Neuman entropy’. In this new paradigm, codification of messages using quantum systems allows to achieve lower values of entropy beyond the limitation given by the classical picture. This feature allows the possibility of sending classical information equivalent to two classical bits (for example 00), using a single quantum bit or qubit. The following imaginary example illustrates contraction of classical bits in to qubits by entanglement of quantum systems.
Suppose Alice would like to send classical information to Bob using qubits, instead of classical bits. Alice would encode the classical information in a qubit and send it to Bob. After receiving the qubit, Bob recovers the classical information via measurement.
The question is: how much classical information can be transmitted per qubit? If Alice and Bob share an entangled state, two classical bits per qubit can be achieved. The term ‘superdense’ refers to this doubling of efficiency. Also, it can be proved that the maximum amount of classical information that can be sent (even while using entangled state) using one qubit is two bits.
Quantum teleportation provides a mechanism of moving a qubit from one location to another, without having to physically transport the underlying particle that a qubit is normally attached to. Much like the invention of the telegraph allowed classical bits to be transported at high speed across continents, quantum teleportation holds the promise that one day, qubits could be moved likewise. However, as of 2013, only photons and single atoms have been employed as information bearers.
The movement of qubits does require the movement of “things”; in particular, the actual teleportation protocol requires that an entangled quantum state or Bell state be created, and its two parts shared between two locations (the source and destination, or Alice and Bob). In essence, a certain kind of “quantum channel” between two sites must be established first, before a qubit can be moved. Teleportation also requires a classical information link to be established, as two classical bits must be transmitted to accompany each qubit. The reason for this is that the results of the measurements must be communicated, and this must be done over ordinary classical communication channels.
The need for such links may, at first, seem disappointing; however, this is not unlike ordinary communications, which requires wires, radios or lasers. What’s more, Bell states are most easily shared using photons from lasers, and so teleportation could be done, in principle, through open space.
In this scheme, hacking, or intercepting messages turns an impossible task without modification the quantum system, and thus, allowing the receptor to know if the message has been hacked during the pad. For this reason, applications of this technologies in the field of cryptology could change in a definitive way the concept of network security.
The incorporation of quantum systems, and specially the application of the measurement axiom, to logic gates and operations, brings astonishing results in terms of computations complexity. Quantum way of facing problems offer totally anti-intuitive tools that may seems impossible and unreal, but that actually works in real systems with quantum gates. A famous example, is the solution of the problem of finding an unknown straight line just having one of its points.
One of the most important theoretical applications of quantum computing, that concerns the global security, is known as the Shor Algorithm. Most of the security systems nowadays, are based on the impossibility of the of solving the problem of factorising prime numbers with many digits.
The security system gives one prime number to the sender, another to the receptor, and the product of the two numbers turns the codification of the message.
If a malware was able to decompose this number in to its two prime factors, it would be possible to intercept bank operations of the majority of the companies with the current security systems.
The computational complexity of this problem for a classical computer, grows exponentially with the number of digits of this number. So, at the end, no algorithm in classical computation would be able to factorise the number in less than almost 4 years. However, using quantum gates operation, the computational complexity of the problem turns polynomial with the number of digits, so in principle a quantum computer would be able to solve the problem in the order of minutes.
Quantum physics violates the most fundamental principles of our perception of reality, and moreover, of our logic intuition. For this reason, this field represent and endless source of concepts to be understood, and therefore, an endless source of technological applications.
Joaquin, Consultant, Leyton Spain