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1
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Cambridge University Press, Cambridge, U.K.
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See, e.g., M. Nielsen and I. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, U.K., 2000).
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(2000)
Quantum Computation and Quantum Information
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Nielsen, M.1
Chuang, I.2
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4143119232
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which uses down-conversion, beam splitters, and single-mode fibers to accomplish arbitrary two-photon polarization mixed states. However, that scheme requires coupling of four spatial modes into a single-mode fiber. This is necessarily a nonunitary (and very lossy) process, so that the desired two-qubit states are only generated for a small fraction, since the postselected ensemble is much smaller (by a factor of 16) than the ensemble of emitted pairs. The methods described in the present paper do not require such postselection
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We learned recently of a related work by C. Zhang, Phys. Rev. A 69, 014304 (2004), which uses down-conversion, beam splitters, and single-mode fibers to accomplish arbitrary two-photon polarization mixed states. However, that scheme requires coupling of four spatial modes into a single-mode fiber. This is necessarily a nonunitary (and very lossy) process, so that the desired two-qubit states are only generated for a small fraction, since the postselected ensemble is much smaller (by a factor of 16) than the ensemble of emitted pairs. The methods described in the present paper do not require such postselection.
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Phys. Rev. A
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Zhang, C.1
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10
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18444413782
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note
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P〉 is a straightforward procedure of unitary operations. However, such efficient entangling gates for photon polarizations are not yet available. See also [11].
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11
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0242442577
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However, recently nondeterministic CNOT gates for photon polarizations have been achieved using a postselection method. See, e.g., T. B. Pittman, M. J. Fitch, B. C. Jacobs, and J. D. Franson, Phys. Rev. A 68, 032316 (2003);
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Pittman, T.B.1
Fitch, M.J.2
Jacobs, B.C.3
Franson, J.D.4
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0344011984
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J. L. O'Brien, G. J. Pryde, A. G. White, T. C. Ralph, and D. Branning, Nature (London) 426, 264 (2003);
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19
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20
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18444388952
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note
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2/Δλ. For example, for 700 nm photons with 1 nm (5 nm) bandpass interference filters, the coherence length is roughly 500 urn (100 μm).
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21
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0031485474
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As the opening angle in our down-conversion is small and fixed at ∼3°, we have ignored the effect of variation in polarization direction as the scattering angle varies, the variation being dramatic at large angles. For discussions of this effect, see A. Migdall, J. Opt. Soc. Am. B 14, 1093 (1997).
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Migdall, A.1
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2342467162
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N. Peters, J. Altepeter, E. Jeffrey, D. Branning, and P. Kwiat, Quantum Inf. Comput. 3, 503 (2003).
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Peters, N.1
Altepeter, J.2
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Kwiat, P.5
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23
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18444381559
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note
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0)L/\λ, where L is the thickness of the crystal and λ is the wavelength of light. Retardances that differ by an integer give a phase of multiples of 2π. A true zero-order wave plate has retardance usually less than 1, but is usually too thin for practical use. A multiorder wave plate has δ>1, and is therefore more sensitive to variations in the wavelength. A compound zero-order wave plate is composed of two multiorder wave plates with their optic axes orthogonal to each other such that the net retardance is less than 1. Hence, compound zero-order wave plates are less sensitive to wavelength than are multiorder wave plates (but more sensitive to alignment and beam noncollimation). See, e.g., http://www.meadowlark.com/AppNotes/, Meadowlark Optics, Inc., 2003 (unpublished).
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11944265386
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T. J. Herzog, P. G. Kwiat, H. Weinfurter, and A. Zeilinger, Phys. Rev. Lett. 75, 3034 (1995).
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Herzog, T.J.1
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25
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18444363439
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note
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The local unitary transformations at each stage can be calculated backward, starting with those at the fourth set of crystals. The unitary transformations caused by the nonlinear crystals themselves can be compensated by modifying the local unitary transformations. Decoherence effects arising from wave plates and crystals are assumed to be negligible.
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26
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0032621435
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J. Brendel, N. Gisin, W. Tittel, and H. Zbinden, Phys. Rev. Lett. 82, 2594 (1999).
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27
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18444396370
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note
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U,loss〉+|ψL,loss〉. This loss is of no consequence in practice, as the pump contains large numbers of photons, and the creation of a particular two-photon state will be postselected by coincidence counts.
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18444390051
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note
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2/2].
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18444400342
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note
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One can argue that the state (10) is a purification of the mixed state, with the "ancillas" being the timing information; see also remarks in [10].
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31
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18444406959
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A. J. Berglund, Dartmouth College B. A. thesis, 2000, also in e-print quant-ph/0010001
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A. J. Berglund, Dartmouth College B. A. thesis, 2000, also in e-print quant-ph/0010001.
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32
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18444369729
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note
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s= ω. Hence, the only independent variable to integrate over is the deviation ε from half of the pump frequency (for either idler or signal photon).
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33
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0036150037
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A. G. White, D. F. V. James, W. J. Munro, and P. G. Kwiat Phys. Rev. A 65, 012301 (2002).
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Kwiat, P.G.4
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35
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51349163744
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whereas F(ρ,σ) ≡ Tr√√ρσ√ρ is the definition in Ref. [1]
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2 is the definition given by R. Jozsa, J. Mod. Opt. 41, 2315 (1994), whereas F(ρ,σ) ≡ Tr√√ρσ√ρ is the definition in Ref. [1].
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Jozsa, R.1
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37
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36049056258
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38
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18444398445
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J. B. Altepeter et al. (unpublished)
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J. B. Altepeter et al. (unpublished).
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39
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18444368231
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note
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If p≤ 1/2, we may need to attenuate the intensity of the photon pair from the first set of crystals. Alternatively, to losslessly prepare the state, we can switch the order of the setup such that the pure state |ψ〉 is created in the first set of crystals, and the mixed state σ is created in the second. However, the photons from the former will then have to be precompensated to eliminate the effect of the subsequent decoherence. This can be done by using the same decoherers but with their optic axes rotated by 90°.
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41
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18444386308
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note
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If the pump is decohered before the second set of crystals, the down-conversion pair will be in a mixed state (up to local uni taries) (0 0 0 0 0 λ g√λ(1-λ) 0 0 g* √ λ(1-λ) 1-λ 0 0 0 0 0) where g represents the degree of decoherence of the pump [cf., f in Eq. (14)]. It is not clear whether this additional "knob" boosts the number of independent controlled parameters from 12 to 13.
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42
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0035953740
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J. W. Pan, C. Simon, Č. Brukner, and A. Zeilinger, Nature (London) 410, 1067 (2001);
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43
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0038485625
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18444370360
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A. G. White et al., e-print quant-ph/0308115
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A. G. White et al., e-print quant-ph/0308115.
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