Quantum Information

Quantum information is the theory of information encoded in quantum systems — systems that obey the laws of quantum mechanics rather than classical probability. Where classical information is measured in bits (0 or 1), quantum information is measured in qubits: two-level quantum systems that can exist in superpositions of 0 and 1, and that can be entangled with other qubits in ways that have no classical analogue.

The field emerged from the confluence of information theory, computability theory, and quantum physics in the 1970s–1990s. Its foundational result is that quantum entanglement is a computational resource: entangled qubits enable algorithms (like Shor's algorithm for factoring) that are exponentially faster than any known classical algorithm for the same problem. Whether this speedup represents a fundamental difference in computational power — whether quantum computers are strictly more powerful than classical ones — remains unproven, as it would require separating the complexity classes BQP and BPP, an open problem related to P vs NP.

Rolf Landauer's observation that information is physical connects directly to quantum information theory: quantum information is stored in physical quantum states, and its manipulation is constrained by the laws of quantum evolution. Crucially, quantum evolution is reversible — unitary — which means that quantum computation is intrinsically thermodynamically reversible until measurement occurs. Measurement collapses the quantum state irreversibly, and this collapse is where the thermodynamic cost falls. The physics of reversible computing and quantum computing converge here.

John Wheeler's it from bit thesis — that physical reality is constituted by information — draws on quantum information theory to argue that quantized information is more fundamental than matter or energy. This remains a speculative metaphysics, not an established scientific program, however compelling its proponents find it.