Quantum information theory is the study ofhow to integrate information theory withquantum mechanics, by studying howinformation can be stored with (andretrieved from) a quantum mechanicalsystem.
QUANTUM INFORMATION TECHNOLOGY IS NOTHING BUT DEALING WITH COMPUTERS USING QUANTUM PHYSICS…AND HENCE ITS ALSO CALLED QUANTUM COMPUTING…
Computation with coherent atomic-scale dynamics. The behavior of a quantum computer is governed by the laws of quantum mechanics.
In quantum systems possibilities count, even if they never happen! -like particle theory. Eachof exponentially many possibilities can be used to perform a part of a computation at the same time.
Moore’s Law: We hit the quantum level 2010~2020. Quantum computation is more powerfulthan classical computation. More can be computed in less time—thecomplexity classes are different!
Digital systems have – bit Quantum systems have – qubit The primary piece of information in quantum information theory is the qubit, an analog to the bit (1 or 0) in classical information theory. The two position states of a photon in a Mach-Zehnder apparatus is just one example of a quantum bit or qubit
Theparticle can exist in a linear combination or superposition of the two paths This concept is applied here using qubits for computations.
Quantum Gates are similar to classical gates, but do not have a degenerate output. i.e. their original input state can be derived from their output state, uniquely. They must be reversible. This means that a deterministic computation can be performed on a quantum computer only if it is reversible.
The following quantum physics concepts are used in Quantum Computing. superposition Interference(constructive & destructive) Coherence Entanglement
Superposition is a principle of quantum theory Theprinciple of superposition claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously. Mathematically, it refers to a property of solutions to the Schrödinger equation
In physics, interference is the phenomenon in which two waves superpose each other to form a resultant wave of greater or lower amplitude.
In physics, coherence is a property of waves that enables stationary (i.e. temporally and spatially constant) interference.
Entanglement is a term used in quantumtheory to describe the way that particles ofenergy/matter can become correlated topredictably interact with each otherregardless of how far apart they are.
CRYPTOGRAPHY:- Transmitting information with access restricted to the intended recipient even if the message is intercepted by others.
The process• Sender Plaintext KeyEncryption Secure Cryptotext transmission DecryptionRecipient Plaintext Key ready for use Message encryption Secure key distribution Hard Problem for conventional encryption
Encryption algorithm and related key are kept secret. Breaking the system is hard due to large numbers of possible keys. For example: for a key 128 bits long there 128 38 2 10 are keys to check using brute force. The fundamental difficulty is key distribution to parties who want to exchange messages.
In 1970s the Public Key Cryptography emerged. Each user has two mutually inverse keys. The encryption key is published; The decryption key is kept secret. Eg:- Anybody can send a message to Bob but only Bob can read it.
The most widely used PKC is the RSA algorithm based on the difficulty of factoring a product of two large primes. EASY PROBLEM:- Given two large primes p and q and compute n p q HARD PROBLEM:- Given n compute p and q.
The best known conventional algorithm requires the solution time proportional to: 1/ 3 2/3T (n) exp[ c (ln n ) (ln ln n ) ] For p & q 65 digits long T(n) is approximately one month using cluster of workstations and For p&q 200 digits long T(n) is astronomical.
In 1994 Peter Shor from the AT&T Bell Laboratory showed that in principle a quantum computer could factor a very long product of primes in seconds.Shor’s algorithm time computational complexity is 3 T (n) O [(ln n ) ]
It solved THE KEY DISTRIBUTION problem. It unconditionally secured the key distribution method proposed by Charles Bennett and Gilles Brassard in 1984. The method is called BB84.
This makes impossible to intercept message without being detected.
Potential (benign) applications - Faster combinatorial search - Simulating quantum systems ‘Spinoff’in quantum optics, chemistry, etc. Makes QM accessible to non-physicists Surprising connections between physics and CS New insight into mysteries of the quantum
Key technical challenge: prevent decoherence , or unwanted interaction with environment. Approaches: NMR, ion trap, quantum dot, Josephson junction, opticals,etc….