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Two equivalent quantum logic circuits. One where measurement happens first, and one where an operation conditioned on the to-be-measured qubit happens first.

Measurement is performed early and the resulting classical bits are sent. The classical bits control if the 1-qubit X and Z gates are executed, allowing teleportation.^[1]

By moving the measurement to the end, the 2-qubit controlled-X and -Z gates need to be applied, which requires both qubits to be near (i.e. at a distance where 2-qubit quantum effects can be controlled), and thus limits the distance of the teleportion. While logically equivalent, deferring the measurement have physical implications.

Example: Two variants of the teleportation circuit. The 2-qubit states

|\Phi ^{+}\rangle

and

|\beta _{00}\rangle

refer to the same Bell state.

The deferred measurement principle is a result in quantum computing which states that delaying measurements until the end of a quantum computation doesn't affect the probability distribution of outcomes.^[2]^[3]

A consequence of the deferred measurement principle is that measuring commutes with conditioning. The choice of whether to measure a qubit before, after, or during an operation conditioned on that qubit will have no observable effect on a circuit's final expected results.

Thanks to the deferred measurement principle, measurements in a quantum circuit can often be shifted around so they happen at better times. For example, measuring qubits as early as possible can reduce the maximum number of simultaneously stored qubits; potentially enabling an algorithm to be run on a smaller quantum computer or to be simulated more efficiently. Alternatively, deferring all measurements until the end of circuits allows them to be analyzed using only pure states.

References

^ Nielsen, Michael A.; Chuang, Isaac (2010). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. pp. 26–28. ISBN 978-1-10700-217-3. OCLC 43641333.
^ Michael A. Nielsen; Isaac L. Chuang (9 December 2010). "4.4 Measurement". Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press. p. 186. ISBN 978-1-139-49548-6.
^ Odel A. Cross (5 November 2012). "5.2.2 Deferred Measurement". Topics in Quantum Computing. O. A. Cross. p. 348. ISBN 978-1-4800-2749-7.

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[1] Nielsen, Michael A.; Chuang, Isaac (2010). Quantum Computation and Quantum Information. Cambridge: Cambridge University Press. pp. 26–28. ISBN 978-1-10700-217-3. OCLC 43641333.

[NielsenChuang2010-2] Michael A. Nielsen; Isaac L. Chuang (9 December 2010). "4.4 Measurement". Quantum Computation and Quantum Information: 10th Anniversary Edition. Cambridge University Press. p. 186. ISBN 978-1-139-49548-6.

[Cross2012-3] Odel A. Cross (5 November 2012). "5.2.2 Deferred Measurement". Topics in Quantum Computing. O. A. Cross. p. 348. ISBN 978-1-4800-2749-7.

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[2]

[3]

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+[[File:Qcircuit measurement-commute.svg|thumb|Two equivalent [[quantum circuit|quantum logic circuits]]. One where measurement happens first, and one where an operation conditioned on the to-be-measured qubit happens first.]]
-{{Multiple issues|
-{{Underlinked|date=August 2017}}
+{{multiple image
-{{Orphan|date=August 2017}}
+ |direction=vertical
+ | width = 400
+ | footer = '''Example:''' Two variants of the [[Quantum_teleportation#Alternative_notations|teleportation circuit]]. The 2-[[qubit]] [[quantum state|state]]s <math>|\Phi^{+}\rangle</math> and <math>|\beta_{00}\rangle</math> refer to the same [[Bell state]].
+ | image1 = Quantum_teleportation_circuit.svg
+ | caption1 = Measurement is performed early and the resulting classical bits are sent. The classical bits control if the 1-qubit [[quantum logic gate#X|X]] and [[quantum logic gate#Z|Z]] gates are executed, allowing teleportation.<ref>{{Cite book|title=Quantum Computation and Quantum Information|last1=Nielsen|first1=Michael A.|last2=Chuang|first2=Isaac|date=2010|publisher=[[Cambridge University Press]]|isbn=978-1-10700-217-3|location=Cambridge|oclc=43641333|author-link=Michael Nielsen|author-link2=Isaac Chuang|url=https://www.cambridge.org/9781107002173|pages=26–28}}</ref>
+ | image2 = AltTeleport.jpg
+ | caption2 = By moving the measurement to the end, the 2-qubit [[quantum logic gate#Controlled gates|controlled]]-X and -Z gates need to be applied, which requires both qubits to be near (i.e. at a distance where 2-qubit quantum effects can be controlled), and thus limits the distance of the teleportion. While logically equivalent, deferring the measurement have physical implications.
 }}
+The '''deferred measurement principle''' is a result in [[quantum computing]] which states that delaying measurements until the end of a quantum computation doesn't affect the [[probability distribution]] of outcomes.<ref name="NielsenChuang2010">{{cite book|author1=Michael A. Nielsen|author2=Isaac L. Chuang|title=Quantum Computation and Quantum Information: 10th Anniversary Edition|url=https://books.google.com/books?id=-s4DEy7o-a0C|date=9 December 2010|publisher=Cambridge University Press|isbn=978-1-139-49548-6 |page=186 |section=4.4 Measurement}}</ref><ref name="Cross2012">{{cite book|author=Odel A. Cross|title=Topics in Quantum Computing|url=https://books.google.com/books?id=b_D9flK2h8QC&pg=PA348|date=5 November 2012|publisher=O. A. Cross|isbn=978-1-4800-2749-7|page=348 |section=5.2.2 Deferred Measurement}}</ref>
-[[File:MeasurementCommutesWithControls.png|thumb|Two equivalent quantum logic circuits. One where measurement happens first, and one where an operation conditioned on the to-be-measured qubit happens first.]]
-The '''Deferred Measurement Principle''' is a result in [[quantum computing]] which states that delaying measurements until the end of a quantum computation doesn't affect the probability distribution of outcomes.<ref name="NielsenChuang2010">{{cite book|author1=Michael A. Nielsen|author2=Isaac L. Chuang|title=Quantum Computation and Quantum Information: 10th Anniversary Edition|url=https://books.google.com/books?id=-s4DEy7o-a0C|date=9 December 2010|publisher=Cambridge University Press|isbn=978-1-139-49548-6 |page=186 |section=4.4 Measurement}}</ref><ref name="Cross2012">{{cite book|author=Odel A. Cross|title=Topics in Quantum Computing|url=https://books.google.com/books?id=b_D9flK2h8QC&pg=PA348|date=5 November 2012|publisher=O. A. Cross|isbn=978-1-4800-2749-7|page=348 |section=5.2.2 Deferred Measurement}}</ref>
 A consequence of the deferred measurement principle is that measuring commutes with conditioning.
-The choice of whether to measure a qubit before, after, or during an operation conditioned on that qubit will have no observable effect on a circuit's final expected results.
+The choice of whether to measure a [[qubit]] before, after, or during an operation conditioned on that qubit will have no observable effect on a circuit's final expected results.
-Thanks to the deferred measurement principle, measurements in a quantum circuit can often be shifted around so they happen at better times.
+Thanks to the deferred measurement principle, measurements in a [[quantum circuit]] can often be shifted around so they happen at better times.
 For example, measuring qubits as early as possible can reduce the maximum number of simultaneously stored qubits; potentially enabling an algorithm to be run on a smaller quantum computer or to be simulated more efficiently.
 Alternatively, deferring all measurements until the end of circuits allows them to be analyzed using only [[pure state]]s.
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 [[Category:Quantum information science]]
 {{quantum-stub}}