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Outbyte Driver Updater FREEScan for outdated or missing drivers - takes under a minuteDriver Scan →Outbyte PC Repair FREEClear out junk files and repair common Windows errorsFree Scan →Quantum coherence describes phase relationships between alternatives in a quantum state; entanglement describes a joint state that cannot be separated into independent states for its parts. A single system can be coherent, but entanglement requires a composite system and a stated division into subsystems. A superposition by itself does not prove entanglement.
What coherence and entanglement describe
| Question | Coherence | Entanglement |
|---|---|---|
| What does it describe? | Relative phases among components of a state, defined with respect to a chosen reference basis. | Whether a composite state can be described as independent states of its subsystems, or as a mixture of such product states. |
| What must be specified? | A reference basis: a state may be coherent in one basis and not in another. | The subsystems and the partition between them. |
| Can one system have it? | Yes. A single qubit can be coherent. | No. Entanglement is a property of a composite system across a specified partition. |
| What is a useful illustration? | Off-diagonal terms in a state’s density matrix in the chosen basis, associated with interference. | Failure of the joint state to factor into subsystem states; for mixed states, failure to express it as a mixture of product states. |
| Why does it matter? | It enables interference and is treated as a resource in some quantum-information tasks. | It captures nonseparability and supports quantum-information tasks involving correlations between subsystems. |
These are different concepts, not competing degrees of the same property. Their measures and practical meaning depend on the basis, subsystem partition, and operations allowed in a particular setting. Quantum resource-theory work examines links between them under specified operational rules, rather than treating them as interchangeable.
What coherence means
In the standard resource-theory treatment, coherence is defined relative to a reference basis. For a qubit, take the computational basis, written as |0⟩ and |1⟩. A state such as α|0⟩ + β|1⟩ can have coherence in that basis when both alternatives are present with a definite relative phase. That phase relation is what allows the alternatives to contribute to interference.
The basis matters. Describing a state as coherent without naming or implying a basis is incomplete: changing the basis can change whether its components are represented as coherent. In density-matrix terms, coherence relative to a chosen basis is associated with off-diagonal elements in that basis. This is not a universal test detached from context; the basis is part of the definition. A review of quantum coherence as a resource discusses this framework.
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What entanglement means
Entanglement concerns how a composite quantum state relates to its parts. For a pure bipartite state, the state is entangled if it cannot be factored into a state for subsystem A times a state for subsystem B. For a mixed state, separability means the joint state can be written as a probabilistic mixture of product states. If it cannot, it is entangled.
The partition is essential: one must say which subsystems are being considered. Entanglement is not limited to two particles; it can involve more subsystems. What matters is whether the joint state is separable across the division under discussion. A review of entanglement theory covers these definitions and their broader context.
Why superposition is not the same as entanglement
A superposition is a combination of alternatives in a quantum state. It can occur for one system, as in α|0⟩ + β|1⟩, so it does not by itself establish entanglement. To ask whether a state is entangled, identify a composite system and test whether its joint state is separable across a chosen partition.
Coherence and entanglement can also appear together. A joint state may have phase relations among alternatives and be nonseparable across its subsystems. The terms describe different features: coherence is basis-relative phase structure, while entanglement is nonseparability across a partition.
A Bell state shows the distinction
Consider the two-qubit Bell state (|00⟩ + |11⟩)/√2. It is a superposition of two joint alternatives. Measuring both qubits in the computational basis gives 00 or 11, each with probability 1/2. The state is entangled because it cannot be factored into a state for qubit A multiplied by a state for qubit B.
The matching measurement outcomes are an illustration, not the definition of entanglement: the defining point is that the joint state is nonseparable. This example also contains coherence between the joint alternatives |00⟩ and |11⟩, showing how coherence and entanglement can be present in the same state without being synonyms. The formal relationship between coherence and entanglement depends on which operations and resource measures are being considered.
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How the concepts are connected in quantum information
Quantum resource theories specify which operations are allowed and which states count as resources. Under those rules, coherence and entanglement can be related or converted in particular ways. A 2022 Physical Review A paper reports that coherence of a quantum measurement can be converted into entanglement in a bipartite quantum measurement through coherence-nongenerating transformations; it also shows how an entanglement monotone can induce a coherence monotone. These are results for a defined operational setting, not a general claim that every coherent state can be turned into entanglement by any process.
A 2016 Physical Review Letters study examines both resources under local incoherent operations and classical communication, including trade-offs in state formation and resource distillation. Together, such work shows that the resources have meaningful links while remaining distinct; the allowed operations and setup affect what the connection means. The 2016 study analyzes those trade-offs.
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