“Cat state”的意思、由来-开放百科全书

In quantum computing, the cat state, named after Schrödinger's cat^[1], is a quantum state that is composed of two diametrically opposed conditions at the same time,^[2] such as the possibilities that a cat be alive and dead at the same time.

Generalizing Schrödinger's gedanken experiment, any other quantum superposition of two macroscopically distinct states is also referred to as a cat state. A cat state could be of one or more modes or particles, therefore it is not necessarily an entangled state. This is in contrast to the more specific concept of a Greenberger–Horne–Zeilinger state, which by definition consists of multiple distinct particles or modes and their entanglement. Schrödinger's cat is sometimes connected to the many worlds hypothesis by its proponents.

Concretely, a cat state can refer to the possibilities that six atoms be spin up and spin down, as published by a team led by David Wineland at NIST, December 1, 2005.^[3] Large cat states have also been experimentally created using photons by a team led by Jian-Wei Pan at University of Science and Technology of China, for instance, four-photon entanglement,^[4] five-photon entanglement,^[5] six-photon entanglement,^[6] eight-photon entanglement,^[7] and five-photon ten-qubit cat state.^[8] This spin up/down formulation was proposed by David Bohm, who conceived of spin as an observable in a version of thought experiments formulated in the 1935 EPR paradox.^[9]

In quantum optics

In quantum optics, a cat state is defined as the coherent superposition of two coherent states with opposite phase:

are coherent states defined in the number (Fock) basis. Notice that if we add the two states together, the resulting cat state only contains even Fock state terms:

As a result of this property, the above cat state is often referred to as an even cat state. Alternatively, we can define an odd cat state as

Even and odd coherent states were first introduced by Dodonov, Malkin, and Man'ko in 1974.^[10]

Linear superposition of coherent states

A simple example of a cat state is a linear superposition of coherent states with opposite phases, when each state has the same weight:^[11]

The larger the value of α, the lower the overlap between the two macroscopic classical coherent states exp(-2α²), and the better it approaches an ideal cat state. However, the production of cat states with a large mean photon number (=|α|²) is difficult. A typical way to produce approximate cat states is through photon subtraction from a squeezed vacuum state.^[12]^[13] This method usually is restricted to small values of α, and such states have been referred to as Schrödinger "kitten" states in the literature. Methods have been proposed to produce larger coherent state superpositions through multiphoton subtraction^[14] or through ancilla-assisted subtraction.^[15]

Coherent state superpositions have been proposed for quantum computing by Sanders.^[16]

References

1. ^John Gribbin (1984), In Search of Schrödinger's Cat, {{ISBN|0-552-12555-5}}, 22 February 1985, Transworld Publishers, Ltd, 318 pages.
2. ^Dennis Overbye, "[https://www.nytimes.com/2005/12/27/science/27eins.html?ex=1293339600&en=caf5d835203c3500&ei=5090 Quantum Trickery: Testing Einstein's Strangest Theory]". New York Times Tuesday (Science Times), December 27, 2005 pages D1,D4.
3. ^D. Leibfried, E. Knill, S. Seidelin, J. Britton, R.B. Blakestad, J. Chiaverini, D. Hume, W.M. Itano, J.D. Jost, C. Langer, R. Ozeri, R. Reichle, and D.J. Wineland. "Creation of a six atom 'Schrödinger cat' state". Nature. Dec. 1, 2005, 639–642.
4. ^{{cite journal|title=Phys. Rev. Lett. 91, 180401 (2003) - Experimental Violation of Local Realism by Four-Photon Greenberger-Horne-Zeilinger Entanglement |journal=Physical Review Letters |volume=91 |issue=18 |pages=180401 |date=2003-10-28 |doi=10.1103/PhysRevLett.91.180401 |pmid=14611269 |last1 = Zhao|first1 = Zhi|last2=Yang |first2=Tao |last3=Chen |first3=Yu-Ao |last4=Zhang |first4=An-Ning |last5=Żukowski |first5=Marek |last6=Pan |first6=Jian-Wei |arxiv=quant-ph/0302137 }}
5. ^{{cite journal|url=http://www.nature.com/nature/journal/v430/n6995/full/nature02643.html|title=Experimental demonstration of five-photon entanglement and open-destination teleportation|journal=Nature|accessdate=2016-12-31 | volume=430|issue=6995|pages=54–58|doi=10.1038/nature02643|pmid=15229594|arxiv = quant-ph/0402096 |bibcode = 2004Natur.430...54Z |date=July 2004|last1=Pan|first1=Jian-Wei|last2=Briegel|first2=Hans J.|last3=Yang|first3=Tao|last4=Zhang|first4=An-Ning|last5=Chen|first5=Yu-Ao|last6=Zhao|first6=Zhi}}
6. ^{{cite journal|title=Experimental entanglement of six photons in graph states|journal=Nature Physics|volume=3|issue=2|pages=91–95|doi=10.1038/nphys507|year=2007|last1=Lu|first1=Chao-Yang|last2=Zhou|first2=Xiao-Qi|last3=Gühne|first3=Otfried|last4=Gao|first4=Wei-Bo|last5=Zhang|first5=Jin|last6=Yuan|first6=Zhen-Sheng|last7=Goebel|first7=Alexander|last8=Yang|first8=Tao|last9=Pan|first9=Jian-Wei}}
7. ^{{cite journal|title=Observation of eight-photon entanglement|journal=Nature Photonics|volume=6|issue=4|pages=225–228|doi=10.1038/nphoton.2011.354|year=2012|last1=Yao|first1=Xing-Can|last2=Wang|first2=Tian-Xiong|last3=Xu|first3=Ping|last4=Lu|first4=He|last5=Pan|first5=Ge-Sheng|last6=Bao|first6=Xiao-Hui|last7=Peng|first7=Cheng-Zhi|last8=Lu|first8=Chao-Yang|last9=Chen|first9=Yu-Ao|last10=Pan|first10=Jian-Wei|arxiv = 1105.6318}}
8. ^{{cite journal|title=Experimental demonstration of a hyper-entangled ten-qubit Schrödinger cat state|journal=Nature Physics|volume=6|issue=5|pages=331–335|doi=10.1038/nphys1603|year=2010|last1=Gao|first1=Wei-Bo|last2=Lu|first2=Chao-Yang|last3=Yao|first3=Xing-Can|last4=Xu|first4=Ping|last5=Gühne|first5=Otfried|last6=Goebel|first6=Alexander|last7=Chen|first7=Yu-Ao|last8=Peng|first8=Cheng-Zhi|last9=Chen|first9=Zeng-Bing|last10=Pan|first10=Jian-Wei}}
9. ^Amir D. Aczel (2001), Entanglement: the unlikely story of how scientists, mathematicians, and philosophers proved Einstein's spookiest theory. {{ISBN|0-452-28457-0}} Penguin: paperback, 284 pages, index.
10. ^{{cite journal|url=http://www.sciencedirect.com/science/article/pii/0031891474902158 |author1=V.V. Dodonov|author2=I.A. Malkin|author3=V.I. Man'ko|title= Even and odd coherent states and excitations of a singular oscillator|volume=72|issue=3|date=15 March 1974|pages=597–615|accessdate=2016-12-31|doi=10.1016/0031-8914(74)90215-8|journal=Physica|bibcode = 1974Phy....72..597D }}
11. ^{{cite journal|last1=Souza|first1=L.A.M.|last2=Nemes|first2=M.C.|last3=Santos|first3=M. França|last4=de Faria|first4=J.G. Peixoto|title=Quantifying the decay of quantum properties in single-mode states|journal=Optics Communications|date=2008-09-15|volume=281|issue=18|page=4696–4704|doi=10.1016/j.optcom.2008.06.017|arxiv=0710.5930|bibcode=2008OptCo.281.4696S}}
12. ^{{Cite journal|last=Ourjoumtsev|first=Alexei|last2=Tualle-Brouri|first2=Rosa|last3=Laurat|first3=Julien|last4=Grangier|first4=Philippe|date=2006-04-07|title=Generating Optical Schrödinger Kittens for Quantum Information Processing|url=http://science.sciencemag.org/content/312/5770/83|journal=Science|language=en|volume=312|issue=5770|pages=83–86|doi=10.1126/science.1122858|issn=0036-8075|pmid=16527930|via=|bibcode = 2006Sci...312...83O }}
13. ^{{Cite journal|last=Wakui|first=Kentaro|last2=Takahashi|first2=Hiroki|last3=Furusawa|first3=Akira|last4=Sasaki|first4=Masahide|date=2007-03-19|title=Photon subtracted squeezed states generated with periodically poled KTiOPO4|url=https://www.osapublishing.org/abstract.cfm?uri=oe-15-6-3568|journal=Optics Express|language=EN|volume=15|issue=6|pages=3568–3574|doi=10.1364/OE.15.003568|issn=1094-4087|arxiv = quant-ph/0609153 |bibcode = 2007OExpr..15.3568W }}
14. ^{{Cite journal|last=Takeoka|first=Masahiro|last2=Takahashi|first2=Hiroki|last3=Sasaki|first3=Masahide|date=2008-06-12|title=Large-amplitude coherent-state superposition generated by a time-separated two-photon subtraction from a continuous-wave squeezed vacuum|journal=Physical Review A|volume=77|issue=6|pages=062315|arxiv=0804.0464|doi=10.1103/PhysRevA.77.062315|bibcode = 2008PhRvA..77f2315T }}
15. ^{{Cite journal|last=Takahashi|first=Hiroki|last2=Wakui|first2=Kentaro|last3=Suzuki|first3=Shigenari|last4=Takeoka|first4=Masahiro|last5=Hayasaka|first5=Kazuhiro|last6=Furusawa|first6=Akira|last7=Sasaki|first7=Masahide|date=2008-12-04|title=Generation of Large-Amplitude Coherent-State Superposition via Ancilla-Assisted Photon Subtraction|journal=Physical Review Letters|volume=101|issue=23|pages=233605|arxiv=0806.2965|doi=10.1103/PhysRevLett.101.233605|pmid=19113554|bibcode=2008PhRvL.101w3605T}}
16. ^{{Cite journal|last=Sanders|first=Barry C.|date=1992-05-01|title=Entangled coherent states|journal=Physical Review A|volume=45|issue=9|pages=6811–6815|doi=10.1103/PhysRevA.45.6811|bibcode = 1992PhRvA..45.6811S }}