You are an expert at summarizing long articles. Proceed to summarize the following text: 
one of the most fundamental applications of non - classical light field states is the improvement of measurement precision beyond the standard quantum limits for classical light sources . of particular interest is the possible enhancement of phase sensitivity in interferometry @xcite , which could be useful in a wide range of fields , from quantum lithography @xcite to atomic clocks @xcite . it is well known that the optimal phase resolution @xmath3 that can be achieved using a non - classical @xmath4-photon state is given by the heisenberg limit of @xmath5 . recently , few photon interferometry at this limit has been accomplished by new methods of generating @xmath4-photon path entangled states using parametric downconversion and post - selection @xcite . such path entangled states are an equal superposition of the two @xmath4-photon states where all photons are located in the same optical mode , @xmath6 . they are therefore ideally suited to obtain @xmath4-photon interference fringes with a period of @xmath7 in the optical phase shift between the two paths . in principle , the generation of path entangled states can be extended to higher photon numbers using the methods proposed and realized in @xcite . in practice , however , the statistical bottlenecks in the post - selection ( or heralding ) used to generate the path entangled states rapidly reduce the probabilities of generating an appropriate output as photon number increases . it may therefore be useful to consider alternative few photon states that can be generated more efficiently from a given number of downconverted photon pairs .    in this paper , it is shown that a highly phase sensitive state can be generated by subtracting a single diagonally polarized photon from the @xmath8-photon state generated in collinear type ii downconversion . since single photon subtraction can be performed with equal efficiency for any number of input photons , this method could be very helpful in achieving phase resolutions at the heisenberg limit for higher photon numbers . moreover , the coherence induced between two adjacent photon number states ensures that the narrowness of the photon number distribution is maintained under phase shifts of up to @xmath2 . phase shifts at the heisenberg limit can therefore be observed as nearly deterministic transfers of a single photon between the output modes . the proposed experimental setup is shown schematically in fig . [ setup ] . the initial state generated by collinear type ii parametric downconversion is a superposition of photon number states with equal photon number in the horizontal and vertical polarizations , @xmath9 if it can be assumed that all of the emitted photons will eventually be detected , it is possible to isolate a single @xmath1-photon component by post - selecting only outputs where a total of @xmath1 photons are detected @xcite . effectively , the input state is then given by @xmath10 . this @xmath1-photon input component is reflected at a beam splitter with a reflectivity of @xmath11 close to one , and one photon is detected in the transmitted light . the components of the @xmath1-photon states in the beam splitter output with exactly one transmitted photon are given by @xmath12 & & \sqrt{n(1-r)r^{2n-1}}\left ( \mid \ ! n ; n\!-\!1 \rangle_{hv } \otimes \mid 0 ; 1 \rangle_{hv } + \mid \ ! n \rangle_{hv } \otimes \mid 1 ; 0 \rangle_{hv } \right ) + \ldots,\end{aligned}\ ] ] the beam splitter thus entangles the polarization of the transmitted one photon component and the polarization of the reflected @xmath13-photon component . it is now possible to measure the diagonal polarization of the transmitted photon using a @xmath14-plate set at @xmath15 and a polarization beam splitter . this measurement projects the state of the transmitted photon onto an equal superposition of horizontal and vertical polarization , resulting in a conditional output state of @xmath16 in the reflected light . ( 400,220 ) ( 20,122)(60,36)pdc ( 80,137)(1,0)150 ( 80,143)(1,0)150 ( 100,115)(60,20)@xmath17 ( 178,137)(0,-1)62 ( 172,143)(0,-1)68 ( 175,72)(1,1)10 ( 175,72)(-1,1)10 ( 120,45)(80,20)@xmath18 ( 150,25)(80,20)@xmath19 ( 235,137)(1,0)35 ( 235,143)(1,0)35 ( 300,137)(1,0)30 ( 300,143)(1,0)30 ( 333,140)(-1,1)10 ( 333,140)(-1,-1)10 ( 288,125)(0,-1)30 ( 282,125)(0,-1)30 ( 285,92)(1,1)10 ( 285,92)(-1,1)10 ( 150,175)(50,15)beam ( 150,160)(50,15)splitter ( 160,155)(1,-1)30 ( 190,110)(15,15)@xmath11 ( 220,175)(25,15)@xmath14- ( 220,160)(25,15)plate ( 230,125)(5,30 ) ( 220,105)(25,15)@xmath20 ( 270,160)(30,15)pbs ( 270,155)(1,-1)30 ( 270,125)(30,30 ) ( 290,100)(80,15)photon ( 290,85)(80,15)detectors ( 340,130)(0,1)20 ( 340,130)(350,130)(350,140 ) ( 340,150)(350,150)(350,140 ) ( 350,140)(360,140)(360,130 ) ( 350,110)(20,20)1 " ( 275,85)(1,0)20 ( 275,85)(275,75)(285,75 ) ( 295,85)(295,75)(285,75 ) ( 285,75)(285,65)(295,65 ) ( 298,55)(20,20)0 "    equation ( [ eq : bs ] ) shows that the probability of successfully subtracting exactly one photon from the @xmath8-photon input is given by @xmath21 . this value can be optimized independently for any desired photon number by varying the reflectivity @xmath11 . the maximal efficiency of photon subtraction is obtained at @xmath22 . the probability of successful photon subtraction is then equal to @xmath23 . interestingly , this maximal probability decreases only slightly with photon number , from an initial value of 25% at @xmath24 towards a value of @xmath25 for extremely high photon numbers . by selecting an optimized reflectivity of @xmath22 , it is thus possible to achieve post - selection probabilities greater than 18% for any number of input photons . the efficiency of photon subtraction is therefore almost independent of photon number . it should be noted that this is quite different from the photon bottleneck used to generate the path entangled state @xmath6 , where the corresponding post - selection probability drops rapidly with increasing photon number as more and more beam splitters become necessary to `` bunch up '' the photons in the single mode bottleneck . in the basic scheme introduced in @xcite , the bottleneck efficiency is @xmath26 for an @xmath4 photon state . at 5 photons , this is an efficiency of only 0.24 % , almost a hundred times less than the optimal efficiencies of photon subtraction . it should therefore be much easier to increase the output photon number of wedge states than to achieve the same photon number for path entangled states . the complete polarization statistics of @xmath4-photon quantum states can be expressed by the three stokes parameters describing the photon number differences between horizontal ( h ) and vertical ( v ) , plus ( p ) and minus ( m ) diagonal , and right ( r ) and left ( l ) circular polarization , @xmath28 as can be seen from eq . ( [ eq : wedge ] ) , the stokes parameter @xmath29 describing the @xmath30-polarization takes on values of @xmath31 or @xmath32 , with a 50% probability each . the average of @xmath29 is therefore zero , and its uncertainty is @xmath33 . the low uncertainty in @xmath29 is a direct consequence of the quantum correlations in parametric downconversion . in fact , the original @xmath34-state is an @xmath29 eigenstate with an uncertainty of zero , which already provides phase sensitivities at the heisenberg limit in the photon statistics @xcite . photon subtraction actually increases the @xmath29-uncertainty by one , thus increasing the observed photon number noise in the @xmath30-basis . however , the essential effect of the photon subtraction on the polarization statistics of the output state is the generation of coherence between the horizontal and vertical polarization components . this effect can be observed in the statistics of the stokes parameter @xmath35 , describing the photon number difference between the diagonal polarizations @xmath36 and @xmath37 . due to the coherence between @xmath38 and @xmath39 , the expectation value of this stokes parameter is @xmath40 since the total photon number is @xmath41 , this means that on average , more than 3/4 of all output photons are polarized along the same diagonal as the transmitted photon @xcite . since the wedge state polarization of @xmath42 originates from complete coherence between two adjacent eigenstates of @xmath29 , it is the maximal diagonal polarization possible at an uncertainty of only @xmath33 in the difference between horizontally and vertically polarized photons . as shown in fig . [ wedge ] , the polarization distribution of the output state thus resembles a quantum mechanically narrow `` wedge '' inserted between the @xmath29 eigenstates from the positive side of the diagonal polarization @xmath35 - somewhat like the slice of an orange , with a quantum limited thickness of @xmath43 . ( 120,120 ) ( 20,60)(20,76)(32,88 ) ( 32,88)(44,100)(60,100 ) ( 60,100)(76,100)(88,88 ) ( 88,88)(100,76)(100,60 ) ( 100,60)(100,44)(88,32 ) ( 88,32)(76,20)(60,20 ) ( 60,20)(44,20)(32,32 ) ( 32,32)(20,44)(20,60 )    ( 53,21)(0,1)78 ( 53.5,21)(0,1)78 ( 67,21)(0,1)78 ( 67.5,21)(0,1)78 ( 60,60 ) ( 60,60)(0,-1)21    ( 60,60)(53,41)(46,22 ) ( 60,60)(67,41)(74,22 )    ( 60,15)(-1,0)14 ( 60,15)(1,0)14 ( 60,15 )    ( 30,0)(60,12)@xmath44    due to the narrowness of its @xmath29 distribution and due to its comparatively high expectation value @xmath45 , the wedge state is very suitable for measurements of small phase shifts between the right and left circular polarizations , which result in a rotation of the stokes parameters around the @xmath46 axis . as indicated in fig . [ wedge ] , the phase uncertainty of the polarization wedge can then be estimated by @xmath47 this phase uncertainty is close to the heisenberg limit and corresponds to the phase uncertainties of the various phase squeezed states proposed for optimized phase estimation in quantum interferometry @xcite . the wedge state is therefore an almost ideal phase squeezed @xmath4-photon state . ( 380,200 ) ( 70,130)(20,20)@xmath48 ( 90,140)(1,0)150 ( 110,170)(20,20)@xmath49 ( 120,170)(0,-1)110 ( 170,120)(20,20)@xmath50 ( 122,90)(20,20)@xmath51 ( 240,140)(0,-1)28 ( 240,100 ) ( 255,100)(26,12)phase ( 255,90)(30,12)shift ( 225,85)(30,30)@xmath52 ( 240,88)(0,-1)58 ( 239,30)(-1,2)5 ( 239,30)(1,2)5 ( 120,60)(1,0)150 ( 270,60)(-2,1)10 ( 270,60)(-2,-1)10    ( 270,60)(70,20)@xmath53 ( 295,42)(70,20)@xmath54    ( 180,5)(120,20)@xmath55    ( 70,165)(36,12)beam ( 70,155)(40,12)splitter ( 105,155)(1,-1)30    ( 80,50)(40,12)mirror ( 105,75)(1,-1)30 ( 104,74)(1,-1)30    ( 240,140)(40,12)mirror ( 225,155)(1,-1)30 ( 226,156)(1,-1)30    ( 190,85)(36,12)beam ( 190,75)(40,12)splitter ( 225,75)(1,-1)30    to clarify the application of this phase sensitivity in interferometry , it may be useful to consider the possibility of converting the polarization modes @xmath48 and @xmath49 to spatial input modes with equal polarization . as shown in fig . [ mz ] , the two paths inside the interferometer then correspond to the modes @xmath56 , and the effect of a phase shift @xmath52 between the two paths is to rotate the original @xmath30 basis towards the @xmath57 basis . in terms of the photon number difference @xmath58 observed in the two output ports , this effect can then be expressed as the rotation of the stokes vector around the @xmath46 axis mentioned above , with @xmath59\ ; \hat{s}_1 ( \mbox{in } ) + \sin[\phi]\ ; \hat{s}_2 ( \mbox{in}).\ ] ] the phase shift @xmath52 between the arms of the interferometer thus corresponds directly to the rotation of the linear polarization components obtained e.g. by a half wave plate set at @xmath60 . the phase sensitivity of the @xmath13-photon wedge state can then be described by the average @xmath61 and the variance @xmath62 of the measurement result @xmath63 , @xmath64 \nonumber \\[0.2 cm ] \delta s_1 ^ 2(\mbox{out } ) & = & 1+(n^2 - 2 ) \sin^2[\phi].\end{aligned}\ ] ] for phase shifts @xmath52 smaller than @xmath2 , @xmath65 and @xmath66 corresponds to a phase resolution of @xmath67 , as given by eq.([eq : delta ] ) above . ( @xmath68)-photon wedge states can thus achieve phase resolutions close to the heisenberg limit for arbitrarily high photon numbers . moreover , the variance of the output photon number distribution at phase shifts @xmath52 with @xmath69=\pm 1 $ ] is still smaller than two . even at phase shifts that change the average output photon number difference by one , the photon number distribution is therefore sharper than the difference of two between two adjacent measurement outcomes of @xmath29 . this result indicates that phase shifts at the heisenberg limit are observed as nearly deterministic transfers of a single photon between the horizontal and vertical polarizations , with measurement probabilities greater than 50% of finding a measurement outcome equal to the expectation value of @xmath70 at @xmath69=\pm 1 $ ] . it is interesting to note that the above argument only relies on averages and variances of the photon number differences @xmath71 . it is therefore straightforward to estimate the effect of basic photon counting errors . in particular , a photon loss error may occur when the downconversion actually generates @xmath72 pairs , and two photons are subsequently lost due to limited detector efficiencies . at low detector efficiencies , the probability of such a photon loss error is of the order of @xmath73 , corresponding to the ratio of the @xmath72 pair probability to the @xmath74 pair probability in eq.([eq : pdc ] ) . since random ( = unpolarized ) photon losses do not change the average polarization of the photons , the strong coherence between the @xmath75 and @xmath76 polarization given by @xmath45 is unchanged by this error . however , the polarization fluctuations increase due to the possibility that both of the photons lost had the same polarization . specifically , the increase in @xmath77 is equal to two times the probability of the photon loss error . for reasonably low error probabilities ( e.g. for @xmath78 ) , this additional uncertainty is much smaller than the pure state uncertainty of @xmath33 , and the effect on the phase resolution will be negligible . these considerations indicate that the high phase resolution of wedge states is rather robust against photon loss errors . again , this is an important difference to path entangled states , where the loss of a single photon completely destroys the quantum coherence responsible for the high phase resolution . due to this robustness against photon loss errors , it may be interesting to investigate wedge state generation at high pump powers even if high detector efficiencies can not be achieved @xcite . ( 360,220 ) ( 80,195)(200,20)probability @xmath79 ( 0,0)(320,220 ) [ 1.2 ]   probability of finding two photons in the horizontally polarized mode and three photons in the vertically polarized mode as a function of phase shift @xmath52 between the circular polarizations for the five photon wedge state . the dotted line shows the same probability for a corresponding five photon path - entangled state . , title="fig : " ] ( 130,5)(100,20)phase shift @xmath52 to illustrate the full implications of the phase sensitivity of wedge states at the level of precise photon counting , it may be useful to take a closer look at a specific example . here , a compromise is necessary between the experimental difficulties and the increasing phase resolution permitted by higher photon numbers . a good choice may be the five photon wedge state , generated by subtracting one photon from @xmath80 pairs of downconverted photons , since it should be just within reach of present technological possibilities . a phase shift of @xmath52 transforms this state according to @xmath81 +    \cos[\frac{3}{2}\phi + \frac{\pi}{4 } ] - 2 \cos[\frac{1}{2}\phi -\frac{\pi}{4}]\right ) \nonumber \\ \langle 4;1 \mid \hat{u}_\phi \mid \mbox{wedge } \rangle & = & -\frac{\sqrt{2}}{16 } \left (    5 \cos[\frac{5}{2}\phi + \frac{\pi}{4 } ] - 3 \cos[\frac{3}{2}\phi -\frac{\pi}{4 } ] - 2 \cos[\frac{1}{2}\phi + \frac{\pi}{4}]\right ) \nonumber \\ \langle 3;2 \mid \hat{u}_\phi \mid \mbox{wedge } \rangle & = & \frac{1}{8 } \left (    5 \cos[\frac{5}{2}\phi -\frac{\pi}{4 } ] +    \cos[\frac{3}{2}\phi + \frac{\pi}{4 } ] + 2 \cos[\frac{1}{2}\phi -\frac{\pi}{4}]\right ) \nonumber \\ \langle 2;3 \mid \hat{u}_\phi \mid \mbox{wedge}\rangle & = & \frac{1}{8 } \left (    5 \cos[\frac{5}{2}\phi + \frac{\pi}{4 } ] +    \cos[\frac{3}{2}\phi -\frac{\pi}{4 } ] + 2 \cos[\frac{1}{2}\phi + \frac{\pi}{4}]\right ) \nonumber \\ \langle 1;4 \mid \hat{u}_\phi \mid \mbox{wedge } \rangle & = & -\frac{\sqrt{2}}{16 } \left (    5 \cos[\frac{5}{2}\phi -\frac{\pi}{4 } ] - 3 \cos[\frac{3}{2}\phi + \frac{\pi}{4 } ] - 2 \cos[\frac{1}{2}\phi -\frac{\pi}{4}]\right ) \nonumber \\ \mid \hat{u}_\phi \mid \mbox{wedge } \rangle & = & -\frac{\sqrt{10}}{16 } \left (      \cos[\frac{5}{2}\phi + \frac{\pi}{4 } ] +    \cos[\frac{3}{2}\phi -\frac{\pi}{4 } ] - 2 \cos[\frac{1}{2}\phi + \frac{\pi}{4}]\right).\end{aligned}\ ] ] each of these six amplitudes includes a five photon interference component oscillating at a rate of @xmath82 . this five photon interference effect is particularly strong in the @xmath83 and the @xmath84 components . [ fringes ] shows the interference fringes observed in the @xmath84 component . for comparison , the dashed line shows the corresponding fringes of a five photon path - entangled state . the main difference between the two fringes are the different peak heights of the wedge state indicating the average diagonal polarization of the five photon state . the wedge state thus combines features of the maximal five photon interference of path - entangled states with the well defined polarization direction of a phase squeezed state . ( 240,220 ) ( 0,180)(120,20)(a ) @xmath85 ( @xmath86 ) ( 10,40)(1,0)220 ( 35,40.5)(1,0)20 ( 35,20)(20,20)-5 ( 65,40)(0,1)9 ( 85,40)(0,1)9 ( 65,49)(1,0)20 ( 65,20)(20,20)-3 ( 95,40)(0,1)19 ( 115,40)(0,1)19 ( 95,59)(1,0)20 ( 95,20)(20,20)-1 ( 125,40)(0,1)150 ( 145,40)(0,1)150 ( 125,190)(1,0)20 ( 125,20)(20,20)+1 ( 155,40)(0,1)21 ( 175,40)(0,1)21 ( 155,61)(1,0)20 ( 155,20)(20,20)+3 ( 185,40)(0,1)1 ( 205,40)(0,1)1 ( 185,41)(1,0)20 ( 185,20)(20,20)+5 ( 80,0)(80,20)@xmath87    ( 20,120)(20,136)(32,148 ) ( 32,148)(44,160)(60,160 ) ( 60,160)(76,160)(88,148 ) ( 88,148)(100,136)(100,120 ) ( 100,120)(100,104)(88,92 ) ( 88,92)(76,80)(60,80 ) ( 60,80)(44,80)(32,92 ) ( 32,92)(20,104)(20,120 )    ( 66.5,81)(0,1)78 ( 67.5,81)(0,1)78    ( 60,120 ) ( 60,120)(1,-3)6    ( 160,170)(60,20)@xmath88 ( 160,140)(60,20)@xmath89    ( 240,220 ) ( 0,180)(120,20)(b ) @xmath90 ( @xmath91 ) ( 10,40)(1,0)220 ( 35,40)(0,1)3 ( 55,40)(0,1)3 ( 35,43)(1,0)20 ( 35,20)(20,20)-5 ( 65,40)(0,1)8 ( 85,40)(0,1)8 ( 65,48)(1,0)20 ( 65,20)(20,20)-3 ( 95,40)(0,1)8 ( 115,40)(0,1)8 ( 95,48)(1,0)20 ( 95,20)(20,20)-1 ( 125,40)(0,1)85 ( 145,40)(0,1)85 ( 125,125)(1,0)20 ( 125,20)(20,20)+1 ( 155,40)(0,1)85 ( 175,40)(0,1)85 ( 155,125)(1,0)20 ( 155,20)(20,20)+3 ( 185,40)(0,1)11 ( 205,40)(0,1)11 ( 185,51)(1,0)20 ( 185,20)(20,20)+5 ( 80,0)(80,20)@xmath87    ( 20,120)(20,136)(32,148 ) ( 32,148)(44,160)(60,160 ) ( 60,160)(76,160)(88,148 ) ( 88,148)(100,136)(100,120 ) ( 100,120)(100,104)(88,92 ) ( 88,92)(76,80)(60,80 ) ( 60,80)(44,80)(32,92 ) ( 32,92)(20,104)(20,120 )    ( 67,81)(0,1)78 ( 81,86)(0,1)68    ( 60,120 ) ( 60,120)(3,-4)12    ( 160,170)(60,20)@xmath92 ( 160,140)(60,20)@xmath93    the well defined polarization direction is particularly visible at phase angles of @xmath85 ( or @xmath86 ) , where the probability of measuring @xmath83 has its maximal value of 75.2% , and at @xmath90 ( or @xmath91 ) , where the probabilities of measuring @xmath84 and @xmath94 are both equal to 42.5% . fig . [ prob ] shows these two probability distributions , along with a schematic illustration of the corresponding quantized levels on the poincare sphere . as indicated by fig . [ prob ] ( a ) , the output photon number distribution can be `` switched '' between 75.2 % @xmath95 ( @xmath84 ) at @xmath96 and 75.2 % @xmath97 ( @xmath83 ) at @xmath98 . likewise , fig . [ prob ] ( b ) indicates that the photon number distribution at @xmath99 can be shifted by exactly one photon with only 15% of the outcomes scattered to different photon numbers . considering the fact that the measurement outcomes are discrete , this shift in the probability distribution is surprisingly smooth . specifically , the high fidelity of the @xmath83 component at @xmath98 shown in fig . [ prob ] ( a ) suggests a `` polarization wedge '' that is much sharper than the photon number distribution at @xmath99 @xcite . the quantum coherence between the adjacent photon number states induced by the post - selected photon subtraction thus permits a surprisingly high level of control at the single photon level . although the detailed calculations presented here only apply to the specific case of five photons , it should be remembered that the basic features of the statistics for a general @xmath13-photon wedge state are defined by the stokes parameter statistics given in section [ sec : stokes ] . since the uncertainty of @xmath29 is always one , the photon number distributions will be limited to only a few possible measurement outcomes close to @xmath100 for any number of photons . specifically , the photon number distribution at @xmath101 will always be similar to fig . [ prob ] ( a ) , and the distribution at @xmath102 will be similar to fig . [ prob ] ( b ) . for high @xmath74 , we can therefore expect a maximal probability of @xmath97 at a phase angle of @xmath103 , where , according to eq.([eq : stats ] ) , @xmath101 and @xmath104 . the `` switch '' from @xmath95 to @xmath97 is therefore also observable at higher photon numbers . in conclusion , it has been shown that it is possible to obtain highly phase sensitive @xmath0-photon wedge states by photon subtraction from @xmath74 photon pairs generated in collinear type - ii parametric downconversion . since the post - selection condition for the generation of this state can be higher than 18% regardless of photon number , the only limitation in extending this scheme to high photon numbers is the efficiency of the parametric downconversion . the generation of five photon wedge states should therefore be well within reach of present technological capabilities . quantitatively , the phase sensitivity of wedge states is comparable to that of the recently realized path entangled states , with the advantage that a phase shift can be related directly to a shift in the photon number distribution observed in the output . specifically , phase shifts at the heisenberg limit appear as nearly deterministic transfers of one photon between the two output ports . @xmath0-photon wedge states should therefore be highly suitable for the determination of phase shifts @xmath52 of about @xmath2 . the generation of polarization wedge states by downconversion and photon subtraction thus provides a simple and effective experimental approach to phase measurements at the heisenberg limit with non - classical @xmath4-photon inputs . it should be noted that precise photon counting would require special detectors such as the ones described in s.kim , y.yamamoto , and h.h . hogue , appl . 74 * , 902 ( 1999 ) . without such special technology , the effects of photon losses are usually avoided by using downconverted light with @xmath105 much smaller than one . the effects of higher photon number components can then be neglected even if the detectors have limited quantum efficiencies and can not resolve photon number . however , this method limits the output intensity and makes it difficult to achieve high photon numbers . it may seem a bit counterintuitive that the subtraction of a photon causes the remaining photons to have the same polarization as the photon removed from the state . however , the effect can be understood quite clearly if one remembers that photon bunching implies that the photons preferably have the same diagonal polarization . a similar robustness of bipartite entanglement against the photon losses caused by limited detector efficiencies has recently been investigated in h.s . eisenberg , g. khoury , g.a . durkin , c. simon , and d. bouwmeester , phys . * 93 * , 193901 ( 2004 ) . this paper also gives an interesting example of parametric downconversion with @xmath106 . it may be worth noting that the apparent localization of the `` wedge '' between the quantized measurement results is somewhat similar to the correlation between coherence and half - integer photon number results in observable in finite resolution measurements , as discussed in h.f . hofmann , phys . a * 61 * , 033815 ( 2000 ) .
it is shown that a highly phase sensitive polarization squeezed @xmath0-photon state can be generated by subtracting a diagonally polarized photon from the @xmath1 photon component generated in collinear type ii downconversion . 
 this polarization wedge state has the interesting property that its photon number distribution in the horizontal and vertical polarizations remains sharply defined for phase shifts of up to @xmath2 between the circularly polarized components . 
 phase shifts at the heisenberg limit are therefore observed as nearly deterministic transfers of a single photon between the horizontal and vertical polarization components .