View source for Quantum Metrology with Entangled States

== Introduction ==

[[Quantum metrology|Quantum Metrology]] is a subfield of [[quantum mechanics|quantum mechanics]] that utilizes [[quantum entanglement|entangled states]] to improve the precision of measurements. This field has gained significant attention due to its potential to surpass the classical limits of precision. 

[[Image:Detail-38517.jpg|thumb|center|Two particles in a state of quantum entanglement.|class=only_on_mobile]]
[[Image:Detail-38518.jpg|thumb|center|Two particles in a state of quantum entanglement.|class=only_on_desktop]]

== Quantum Entanglement ==

[[Quantum entanglement]] is a physical phenomenon that occurs when a pair or group of particles interact in ways such that the quantum state of each particle cannot be described independently of the state of the others, even when the particles are separated by large distances. The entangled states are a key resource in quantum metrology, as they can provide a significant enhancement in measurement precision compared to unentangled states.

== Quantum Metrology ==

[[Quantum metrology]] is the study of making high precision measurements using quantum mechanics. The field exploits quantum properties such as superposition and entanglement to achieve measurement precision beyond what is possible with classical systems. Quantum metrology has potential applications in various fields, including [[quantum computing|quantum computing]], [[quantum communication|quantum communication]], and [[quantum sensing|quantum sensing]].

== Quantum Metrology with Entangled States ==

In quantum metrology with entangled states, the entangled particles are used to measure a parameter with high precision. The entanglement allows for a higher degree of correlation between the particles, which can be used to reduce the statistical noise in the measurement, thereby increasing the precision.

=== Entanglement-enhanced Metrology ===

In entanglement-enhanced metrology, the entangled states are used to improve the precision of measurements. The measurement precision is quantified by the [[Quantum Fisher information|Quantum Fisher Information]] (QFI), which is a measure of the information that an observable carries about a parameter. The QFI can be significantly larger for entangled states than for unentangled states, leading to a higher measurement precision.

=== Quantum Parameter Estimation ===

Quantum parameter estimation is a central task in quantum metrology with entangled states. The goal is to estimate a parameter that characterizes the quantum state or the quantum dynamics. This is achieved by making a series of measurements on the entangled states and using the results to estimate the parameter.

=== Noise and Decoherence ===

In practical applications of quantum metrology with entangled states, noise and decoherence are major challenges. Noise can lead to a loss of entanglement, reducing the precision of the measurements. Decoherence, which is the loss of quantum coherence due to interaction with the environment, can also degrade the performance of quantum metrology.

== Applications ==

Quantum metrology with entangled states has potential applications in various fields. In [[quantum computing]], it can be used to improve the precision of quantum gates. In [[quantum communication]], it can enhance the security and efficiency of quantum key distribution. In [[quantum sensing]], it can improve the sensitivity of sensors for detecting small changes in physical quantities.

== Conclusion ==

Quantum metrology with entangled states is a promising field that has the potential to revolutionize our ability to make precise measurements. Despite the challenges posed by noise and decoherence, ongoing research is paving the way for practical applications in quantum computing, quantum communication, and quantum sensing.

== See Also ==

* [[Quantum Information]]
* [[Quantum Optics]]
* [[Quantum Cryptography]]

[[Category:Quantum Mechanics]]
[[Category:Quantum Metrology]]
[[Category:Quantum Entanglement]]
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