Physics:Quantum methods/information theory
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Information theory in quantum physics studies how information is represented, processed, transmitted, and measured when encoded in the quantum states of physical systems. It is the basic entity of study in quantum information science.[1][2]
Quantum information differs fundamentally from classical information because quantum states may exist in quantum superposition, may exhibit entanglement, and cannot generally be copied or measured without disturbance. The elementary unit of quantum information is the qubit, which generalizes the classical bit.[3]
The field combines ideas from quantum mechanics, information theory, computer science, cryptography, mathematics, and communication theory.[4]
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Quantum information
Quantum information is information encoded in the state of a quantum system.[5]
In classical systems, information is stored in bits that take values 0 or 1. In quantum systems, a qubit may exist in a superposition of basis states, allowing a richer mathematical structure and enabling computational and communication techniques not available in classical physics.
A quantum state may contain correlations between separated systems through entanglement. Because measurements generally disturb quantum states, information extraction is fundamentally constrained by the uncertainty principle and the non-commuting nature of quantum observables.[6]
Qubits
The qubit is the elementary unit of quantum information. Physically, qubits may be realized using photons, trapped ions, superconducting circuits, neutral atoms, or nuclear spins.[7]
Unlike a classical bit, which can only occupy one of two states, a qubit can exist in a linear combination of basis states. A pure qubit state can be represented geometrically on the Bloch sphere.
Although qubits are continuously parameterized, measurement outcomes are discrete and probabilistic.
Entropy and information
Classical information theory uses Shannon entropy to quantify uncertainty in a probability distribution.[8]
Quantum information theory generalizes this concept using the von Neumann entropy, defined for a density matrix as:
S(\rho)=-\mathrm{Tr}(\rho\log_2\rho)
Von Neumann entropy measures the uncertainty or mixedness of a quantum state and plays an important role in quantum communication, entanglement theory, quantum compression, and error correction.[9]
Limits on quantum information
Several important theorems distinguish quantum information from classical information.
The no-cloning theorem states that an arbitrary unknown quantum state cannot be copied.[10]
Related results include no-deleting, no-broadcasting, and no-hiding theorems.
The impossibility of perfectly copying quantum states is essential for quantum cryptography and secure communication.
Quantum communication
Quantum communication studies how quantum states and classical messages encoded in quantum systems are transmitted through quantum channels.[11]
Applications include:
- quantum teleportation
- dense coding
- quantum key distribution
- entanglement distribution
- quantum networks
Quantum teleportation transfers a quantum state between distant systems using entanglement and classical communication.
Quantum cryptography
One of the best known applications of quantum information theory is quantum cryptography. The BB84 protocol, introduced by Bennett and Brassard in 1984, allows secure key distribution using quantum states.[12]
Security arises because measurement disturbs quantum systems. Any eavesdropping attempt changes the transmitted states and can therefore be detected.
Quantum computation
Quantum information processing forms the basis of quantum computing. Quantum algorithms manipulate qubits using quantum gates and unitary transformations.[13]
Important quantum algorithms include:
- Shor's factoring algorithm
- Grover's search algorithm
- quantum simulation algorithms
Quantum computation also requires methods for decoherence control and fault-tolerant error correction.
Quantum error correction
Quantum systems are highly sensitive to interactions with their environment. Such interactions lead to quantum decoherence, which destroys coherent quantum behavior.
Quantum error correction protects quantum information against noise and imperfect operations. Error correction is essential for scalable fault-tolerant quantum computers.
History
The origins of quantum information theory lie in the development of quantum mechanics during the early twentieth century.[14]
During the 1960s and 1970s, researchers developed quantum communication theory and established limits on information transmission in quantum channels.[15]
In the 1980s and 1990s, rapid developments in cryptography and computer science led to the emergence of quantum computation and quantum information science as major research fields.
Applications
Applications of quantum information theory include:
- quantum computing
- quantum communication
- quantum cryptography
- quantum sensing
- quantum networking
- quantum error correction
The field is considered one of the foundations of modern quantum technologies.
See also
Table of contents (49 articles)
Index
Full contents
References
- ↑ Vedral, Vlatko (2006). Introduction to Quantum Information Science. Oxford: Oxford University Press. ISBN 9780199215706.
- ↑ Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information (10th anniversary ed.). Cambridge: Cambridge University Press. ISBN 9780511976667.
- ↑ Bennett, Charles H.; Shor, Peter (1998). "Quantum information theory". IEEE Transactions on Information Theory 44 (6): 2724–2742. doi:10.1109/18.720553.
- ↑ Bokulich, Alisa; Jaeger, Gregg (2010). Philosophy of Quantum Information and Entanglement. Cambridge: Cambridge University Press. ISBN 9780511676550.
- ↑ Preskill, John (2018). Quantum Computation. Pasadena: California Institute of Technology.
- ↑ Hayashi, Masahito (2017). Quantum Information Theory: Mathematical Foundation. Berlin: Springer. ISBN 978-3-662-49725-8.
- ↑ Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. ISBN 9780511976667.
- ↑ Shannon, Claude E. (1948). "A mathematical theory of communication". Bell System Technical Journal 27 (3): 379–423.
- ↑ Watrous, John (2018). The Theory of Quantum Information. Cambridge: Cambridge University Press. ISBN 9781316848142.
- ↑ Nielsen, Michael A.; Chuang, Isaac L. (2010). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. ISBN 9780511976667.
- ↑ Gordon, J. P. (1962). "Quantum effects in communications systems". Proceedings of the IRE 50 (9): 1898–1908.
- ↑ Bennett, Charles H.; Brassard, Gilles (2014). "Quantum cryptography: public key distribution and coin tossing". Theoretical Computer Science 560: 7–11.
- ↑ Deutsch, David (1985). "Quantum theory, the Church–Turing principle and the universal quantum computer". Proceedings of the Royal Society A 400 (1818): 97–117.
- ↑ Mahan, Gerald D. (2009). Quantum Mechanics in a Nutshell. Princeton: Princeton University Press. ISBN 978-1-4008-3338-2.
- ↑ Holevo, Alexander S. (1973). "Bounds for the quantity of information transmitted by a quantum communication channel". Problems of Information Transmission 9 (3): 177–183.
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