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Quantum information is the study of how information is encoded, transformed, transmitted, and measured when the physical systems that carry it obey the laws of quantum mechanics. It sits at the intersection of physics, computer science, and mathematics, and its central concern is not merely that quantum systems are small or strange, but that their behavior offers resources—and imposes constraints—that have no classical counterpart. The field asks what information theoretic tasks are possible, how they can be performed reliably, and what fundamental limits govern them.
To understand quantum information, one must first understand the quantum state. A quantum system is described by a state vector in a complex vector space, and the most distinctive feature of such a state is superposition: a system can be in a combination of multiple definite states at once. For example, a quantum bit, or qubit, can be in a state that is neither simply 0 nor simply 1, but a coherent blend of both. When measured, the qubit yields either 0 or 1 with probabilities determined by the state, and the act of measurement irreversibly collapses the superposition.
The second foundational concept is entanglement. When two or more quantum systems interact, their states can become correlated in a way that cannot be described by assigning independent states to each system. Entangled systems exhibit correlations that violate the constraints of any local hidden-variable theory, a fact first highlighted by the Einstein–Podolsky–Rosen argument and later formalized in Bell's theorem. Entanglement is not merely a curiosity; it is a resource. It enables tasks such as quantum teleportation, where an unknown quantum state is transferred from one location to another using shared entanglement and classical communication, and it underpins the security of quantum key distribution.
The third concept is the no-cloning theorem, which states that an unknown quantum state cannot be perfectly duplicated. This is a direct consequence of the linearity of quantum mechanics, and it has profound consequences: it prevents the kind of copying that classical information routinely allows, but it also provides the basis for quantum cryptography, since an eavesdropper cannot copy a quantum signal without disturbing it.
These concepts together define the field's central questions. What information can be extracted from a quantum system, and at what cost? How can quantum states be protected from the inevitable noise of the environment? What computational problems can be solved more efficiently using quantum resources? And what are the ultimate limits on communication, measurement, and computation imposed by quantum mechanics?
The intellectual roots of quantum information lie in the debates of the 1920s and 1930s about the interpretation of quantum mechanics. The Einstein–Podolsky–Rosen paper of 1935 raised the question of whether quantum mechanics could be considered complete, and Schrödinger's response introduced the term "entanglement" and recognized its significance. However, these were philosophical and foundational concerns, not yet a research program in information processing.
The modern field began to take shape in the 1970s and 1980s, when physicists and computer scientists started asking concrete information-theoretic questions. In the early 1970s, Stephen Wiesner proposed conjugate coding, a scheme for using quantum states to create money that could not be counterfeited. Although unpublished for a decade, this idea influenced later work. In 1982, Richard Feynman suggested that a computer built from quantum components might be able to simulate quantum systems efficiently, a task that appears intractable for classical computers. Around the same time, David Deutsch formalized the notion of a universal quantum computer and showed that quantum computation could outperform classical computation for certain abstract problems.
The 1990s brought the field to maturity. Peter Shor's discovery in 1994 that a quantum computer could factor large integers efficiently—a problem believed to be hard classically and the basis of much of modern cryptography—dramatically raised the stakes. Lov Grover's 1996 algorithm for unstructured search showed a more modest but general speedup. On the communication side, Charles Bennett and Gilles Brassard had proposed a quantum key distribution protocol in 1984, and in 1993 Bennett and collaborators demonstrated the theoretical possibility of quantum teleportation. The development of quantum error correction in the mid-1990s, by Peter Shor and Andrew Steane independently, addressed the central obstacle to building a working quantum computer: the fragility of quantum states.
It is important to distinguish these precursors from the modern field. The early interpretative debates were not quantum information research; they were foundational physics that later provided the conceptual vocabulary. Similarly, the development of classical information theory by Claude Shannon in the 1940s was a necessary precursor, but quantum information is not simply an extension of Shannon's framework. It required new mathematical tools, such as the density matrix formalism and the theory of completely positive maps, and it introduced genuinely new phenomena, such as entanglement as a resource and the impossibility of cloning.
Quantum information is not divided into rival schools in the way that, say, interpretations of quantum mechanics are. Rather, it is organized around a set of interrelated research programs that share a common mathematical language but address different questions and use different methods.
The most prominent approach is quantum computation, which asks what computational problems can be solved more efficiently with quantum resources. The standard model is the quantum circuit: a sequence of unitary operations applied to a register of qubits, followed by a measurement. The central theoretical question is the relationship between the class of problems solvable efficiently by a quantum computer (BQP) and classical complexity classes. Shor's algorithm shows that factoring and the discrete logarithm problem are in BQP, while Grover's algorithm provides a quadratic speedup for unstructured search. However, the full power of quantum computation remains unknown; it is not proven that BQP is strictly larger than the classical class P, nor is it known whether quantum computers can solve NP-complete problems efficiently.
A major subfield is quantum error correction and fault tolerance. Quantum states are extremely sensitive to noise, and the no-cloning theorem seems to forbid the redundancy that classical error correction relies on. Quantum error correction overcomes this by encoding a logical qubit in the correlations among many physical qubits, using entangled states that are robust against certain types of errors. The threshold theorem shows that if the error rate per gate is below a certain threshold, arbitrarily long computations can be performed reliably by using concatenated codes. This result is what makes large-scale quantum computation plausible in principle, though the practical threshold depends on the specific hardware and code.
A second major approach focuses on communication. Quantum key distribution (QKD) uses the no-cloning theorem and the disturbance caused by measurement to guarantee the security of a shared secret key. The first protocol, BB84, encodes bits in the polarization states of single photons; any attempt to eavesdrop introduces errors that the legitimate parties can detect. The security of QKD has been proven under increasingly general assumptions, though practical implementations face challenges from device imperfections.
Quantum teleportation is another communication task that has no classical analog. It uses shared entanglement and classical communication to transfer an unknown quantum state from one party to another. The state is not copied—the original is destroyed—and the process requires the two parties to share entanglement beforehand. Teleportation is not a form of faster-than-light communication, since the classical information must travel at or below light speed, but it is a fundamental primitive for quantum networks.
A related concept is the quantum channel capacity: the maximum rate at which quantum information can be reliably transmitted through a noisy channel. This is a direct generalization of Shannon's classical channel capacity, but it is far more complex, and the general formula for quantum capacity remains an open problem. The field also studies entanglement distillation, the process of extracting a smaller number of highly entangled states from a larger number of weakly entangled ones, which is essential for long-distance quantum communication.
A third approach treats quantum information as a mathematical theory in its own right, generalizing classical information theory. The central object is the density matrix, which describes both pure states and statistical mixtures. The von Neumann entropy, defined as the entropy of the eigenvalues of the density matrix, plays the role that Shannon entropy plays in classical information theory, but it has additional properties, such as being able to decrease under operations that discard information.
This framework addresses questions such as: How much classical information can be extracted from a quantum state? How much quantum information can be encoded in a given number of qubits? What is the information-theoretic meaning of entanglement? The theory of entanglement measures, such as entanglement of formation and distillable entanglement, attempts to quantify entanglement as a resource. These measures are not all equivalent, and their relationships are subtle, reflecting the fact that entanglement is not a single quantity but a family of related phenomena.
A fourth approach connects quantum information to the foundations of quantum mechanics. The resource theory perspective treats quantum phenomena such as superposition, entanglement, and coherence as resources that can be quantified, manipulated, and consumed. This perspective has clarified the role of measurement, the nature of quantum correlations, and the boundary between quantum and classical behavior. It has also led to new results, such as the understanding that quantum contextuality—the dependence of measurement outcomes on the context of other measurements—is itself a resource for certain information-processing tasks.
This approach has also influenced the debate over interpretations of quantum mechanics. The information-theoretic view suggests that quantum mechanics might be best understood as a theory of information, rather than as a theory of waves or particles. However, this is a philosophical stance, not a settled scientific conclusion, and it remains disputed whether the information-theoretic perspective resolves or merely reframes the foundational puzzles.
The current state of quantum information is characterized by a rapid expansion of experimental capability alongside persistent theoretical challenges. On the experimental side, small-scale quantum computers have been built using a variety of physical platforms: superconducting circuits, trapped ions, photonic systems, and neutral atoms, among others. These devices, sometimes called noisy intermediate-scale quantum (NISQ) computers, can perform tasks that are difficult to simulate classically, but they are not yet error-corrected and cannot run the algorithms that would demonstrate a clear quantum advantage for practical problems. The goal of building a fault-tolerant quantum computer remains a major engineering challenge, with the central difficulty being the overhead required for error correction.
Quantum communication has seen the development of quantum networks over increasingly long distances, including satellite-based QKD. However, the range of direct quantum communication is limited by photon loss, and quantum repeaters—devices that would extend the range by using entanglement distillation and swapping—remain largely experimental.
The theoretical landscape is similarly active. The relationship between quantum and classical computation is still not fully understood, and the search for new quantum algorithms continues. The theory of quantum error correction has expanded into new directions, such as topological codes and fault-tolerant gates, and the study of quantum channels and capacities remains an active area. The resource theory perspective has become a unifying framework, connecting topics as diverse as quantum thermodynamics, quantum metrology, and quantum foundations.
One of the most striking features of the present landscape is the convergence of theory and experiment. Theoretical proposals are now routinely tested in the laboratory, and experimental results feed back into theory. This is a young field, and many of its central questions remain open: the precise power of quantum computation, the ultimate limits of quantum communication, and the nature of the boundary between quantum and classical behavior. What is clear is that quantum information has transformed both our understanding of quantum mechanics and our conception of what information is.