You are an expert at summarizing long articles. Proceed to summarize the following text: 
entanglement is a key quantum resource for quantum information processing and it plays a critical role in many important applications in quantum communication , such as quantum key distribution @xcite , quantum dense coding @xcite , quantum teleportation @xcite , and entanglement swapping @xcite . some important goals in quantum communication require the complete and deterministic analysis of the bell states . in 1999 , vaidman s @xcite and l@xmath0tkenhau s @xcite groups put forward a bell - state analysis ( bsa ) for teleportation with only linear optical elements . unfortunately , with linear - optical elements , one can obtain the optimal success probability of 50% both in theory @xcite and in experiment @xcite ( of course , by guessing at random when an ambiguous result is obtained , one can technically achieve a 75% success rate in identifying the four bell states ) . the bsa on photon pairs entangled in one degree of freedom ( dof ) attracted much attention @xcite . the entanglement of photon pairs in several dofs @xcite , called it hyperentanglement , is useful in quantum information processing , especially in quantum communication for completing bsa on polarizations of photon pairs @xcite , performing entanglement purification @xcite , distributing entangled polarization states faithfully @xcite , or improving the channel capacity . for example , kwiat and weinfurter @xcite first introduced the way to distinguish the four orthogonal bell states of photon pairs in the polarization dof with the hyperentanglement in both the polarization dof and the momentum dof in 1998 . in 2003 , walborn et al . @xcite proposed a simple scheme for completing bell - state measurement for photon pairs entangled in the polarization dof or the momentum dof by using hyperentangled states with linear optics . the experiments of a complete bsa have also been reported with polarization - time - bin hyperentanglement @xcite and polarization - momentum hyperentanglement @xcite later . it implies a complete bsa in the polarization dof can be accomplished with hyperentanglement in a larger hilbert space by introducing other dofs . in 2008 , barreiro et al . @xcite beat the channel capacity limit for linear photonic superdense coding with polarization - orbital - angular - momentum hyperentanglement . in 2002 , simon and pan @xcite proposed an entanglement purification protocol ( epp ) using hyperentanglement in both the polarization and the spatial dofs . in 2008 , an efficient epp based on a parametric down - conversion source was proposed , resorting to this hyperentanglement @xcite . in 2010 , deterministic epps were proposed with hyperentanglement @xcite . in 2010 , a faithful entanglement distribution scheme for polarization was proposed @xcite , resorting to the stability of the frequency entanglement of photon pairs .    considering a large hilbert space with an additional dof , e.g. , a quantum system in a hyperentangled state in two dofs which span the hilbert space with 16 orthogonal bell states , one can not distinguish them completely with only linear optics . in 2007 , wei et al . @xcite pointed out that 7 states in the group of 16 orthogonal bell states is distinguishable with only linear optics . in 2011 , pisenti et al . @xcite presented a very general theoretical explanation of the inadequacy of linear evolution and local measurement in ( hyperentangled- ) bell - state analysis , and they pointed out the limitations for manipulation and measurement of entangled systems with inherently linear , unentangling devices . if nonlinear optics is introduced , these 16 orthogonal bell states can be distinguished completely . in 2010 , sheng et al . @xcite presented a complete hyperentangled bsa ( hbsa ) with cross - kerr nonlinearity . although a lot of works have been studied on cross - kerr nonlinearity @xcite , a clean cross - kerr nonlinearity in the optical single - photon regime is still quite a controversial assumption with current technology @xcite . in recent years , a solid state system based on an electron spin in a quantum dot ( qd ) has attracted much attention with its giant nonlinearity . in 2008 , @xcite proposed a quantum nondemolition method using the interaction of left - circularly and right - circularly polarized lights with a one - side qd - cavity system . this nonlinear optics in a qd - cavity system can be used to construct multi - photon entangler @xcite and photonic polarization bsa @xcite . in 2010 , bonato et al . @xcite proposed a photonic polarization bsa using quantum - dot microcavities in the weak - coupling limit . in 2011 , hu et al . @xcite presented some interesting schemes for bsa using the nonlinear optics of a single quantum - dot spin in a one - side optical microcavity .    in this article , we present complete hbsa with the nonlinear optics based on a one - side qd - cavity system . it can be used to distinguish completely the 16 hyperentangled bell states in both the polarization and the spatial - mode dofs of two - photon systems . this scheme divides the process for hbsa into two steps . the first step is to distinguish the four bell states in spatial - mode dof , without destroying the two - photon system itself and its state in the polarization dof . this task should resort to quantum nondemolition detectors ( qnds ) based on nonlinear optics of a one - side qd - cavity system . in the second step , one can adjust the qd - cavity systems to distinguish the four bell states in the polarization dof . this hbsa scheme can be applied to increase the channel capacity of long - distance quantum communication based on hyperentanglement , such as entanglement swapping , teleportation , and superdense coding . we use hyperentanglement swapping as an example to show its application . considering a singly charged qd in a cavity , e.g. , a self - assembled in(ga)as qd or a gaas interface qd inside an optical resonant microcavity , the qd is located in the center of the cavity to achieve a maximal light - matter coupling . with an excess electron injected into the qd , the singly charged qd shows the optical resonance with the negatively charged exciton @xmath1 that consists of two electrons bound to one hole @xcite . according to pauli s exclusion principle , @xmath1 has spin - dependent transitions @xcite . if the excess electron in the qd is in the spin state @xmath2 , only the left circularly polarized light @xmath3 can be resonantly absorbed to create the negatively charged exciton in the state @xmath4 with two antiparallel electron spins . here @xmath5 represents a heavy - hole spin state @xmath6 . if the excess electron in the qd is in the spin state @xmath7 , only the right circularly polarized light @xmath8 can be resonantly absorbed to create the negatively charged exciton in the state @xmath9 with two antiparallel electron spins . here @xmath10 represents the heavy - hole spin state @xmath11 . they have different phase shifts when the photons in these two different circularly polarized states are reflected from the qd - cavity system .    . ( a ) a charged qd inside a micropillar microcavity with circular cross section . ( b ) spin selection rule for optical transitions of negatively charged exciton @xmath1 due to the pauli s exclusion principle . @xmath12 and @xmath13 represent the left and the right circularly polarized lights , respectively.,width=302 ]    the whole process can be represented by heisenberg equations for the cavity field operator @xmath14 and @xmath1 dipole operator @xmath15 in the interaction picture @xcite , @xmath16 a -g\sigma_--\sqrt{\kappa}\ , a_{in } ,   \\ \frac{d\sigma_-}{dt } \;\ ; & = \;\ ; -[i(\omega_{x^-}- \omega ) + \frac{\gamma}{2 } ] \sigma_- - g\sigma_z \ , a,\\ a_{out } \;\ ; & = \;\ ;   a_{in}+\sqrt{\kappa}\ , a ,   \end{split}\ ] ] where @xmath17 , @xmath18 , and @xmath19 are the frequencies of the input probe light , cavity mode , and @xmath1 transition , respectively . @xmath20 is the coupling strength between @xmath1 and the cavity mode , @xmath21 and @xmath22 are the decay rates of @xmath1 and the cavity field , and @xmath23 is the side leakage rate of the cavity .    with a weak excitation condition ( @xmath1 stays in the ground state at most time and @xmath24 ) , the reflection coefficient for the qd - cavity system can be obtained as @xcite @xmath25}{[i(\omega_{x^-}-\omega ) + \frac{\gamma}{2}][i(\omega_c-\omega)+\frac{\kappa}{2}+\frac{\kappa_s}{2}]+g^2}.\end{aligned}\ ] ] one can get the reflection coefficient @xmath26 for a cold cavity with the uncoupled qd by taking @xmath27 as following @xcite : @xmath28 if the excess electron is in the spin state @xmath2 , the @xmath3 light feels a hot cavity ( coupled with the qd - cavity system ) and gets a phase shift of @xmath29 after being reflected ( the subscript @xmath30 represents a hot cavity ) , whereas the @xmath8 light feels a cold cavity and gets a phase shift of @xmath31 . by adjusting the frequencies @xmath17 and @xmath18 , one can get the reflection coefficients @xmath32 for a cold cavity and @xmath33 for a hot cavity . as the linearly polarized probe beam can be regarded as the superposition of two circularly polarized components @xmath34 , the state of the reflected light becomes @xmath35 after it is reflected from the one - side qd - cavity system . conversely , if the excess electron is in the spin state @xmath7 , the @xmath3 light feels a cold cavity and gets a phase shift of @xmath31 after being reflected , while the @xmath8 light feels a hot cavity and gets a phase shift of @xmath29 . the linear polarized probe beam @xmath34 becomes @xmath36 after being reflected . the polarization direction of the reflected light rotates an angle @xmath37 , which is the so - called faraday rotation . if the electron is in a superposition spin state @xmath38 and the photon is in the state @xmath39 , after being reflected , the light - spin state evolves as @xmath40,\end{aligned}\ ] ] where @xmath41 , @xmath42 $ ] , and @xmath43 $ ] . in a one - side cavity , due to spin selection rule above , @xmath3 and @xmath8 lights pick up two different phase shifts after being reflected from the qd - cavity system , and then the state of the system composed of the light and the excess electron becomes an entangled one . a hyperentangled two - photon bell state in both the polarization and the spatial - mode dofs has the form as @xmath44 here , the superscripts @xmath45 and @xmath46 represent the two photons in the hyperentangled state . the subscript @xmath47 denotes the polarization dof and @xmath48 is the spatial - mode dof . @xmath49 ( @xmath50 ) and @xmath51 ( @xmath52 ) are the different spatial modes for the photon @xmath45 ( @xmath46 ) . we denote the four bell states in the polarization dof as @xmath53 and the four bell states in the spatial - mode dof as @xmath54 also we refer to the states @xmath55 and @xmath56 as the odd - parity states , and @xmath57 and @xmath58 as the even - parity states .    . ( a ) the qnd is used to distinguish the odd - parity states @xmath59 from the even - parity states @xmath60 . ( b ) the qnd is used to distinguish the `` + '' phase state @xmath61 ( @xmath62 ) from the `` - '' phase states @xmath63 ( @xmath64 ) . the dashed line presents the case that the photons @xmath45 coming from the spatial mode @xmath65 and @xmath46 coming from @xmath66 pass through qd@xmath67 in sequence . the small mirror is used to reflect the photon for interacting with the cavity twice . hwp represents a half - wave plate which is used to perform a phase - flip operation @xmath68 in the polarization dof , while hwp@xmath67 represents another half - wave plate which is used to perform a bit - flip operation @xmath69 in the polarization dof . bs represents a 50:50 beam splitter.,width=12 ]      the optical properties of a singly charged qd in a strong - coupling single - side microcavity , which has been used for a controlled - phase gate , can be used to construct a quantum nondemolition detector ( qnd ) , as shown in fig.[figure2 ] . let us assume that the initial states of the excess electron in the cavity and a single photon injected are @xmath70 and @xmath71 , respectively . by adjusting the frequencies @xmath72 to get the phase shift difference between the left and the right circular polarization lights as @xmath73 , the function of a single photon interacting with a qd - cavity system twice is @xmath74 one can detect whether or not there is a photon interacting with the qd - cavity system by measuring the spin state of the excess electron with the orthogonal basis @xmath75 , there is a photon interacting with the qd - cavity system ( with a phase - flip operation @xmath76 on the photon , its original polarization state is recovered ) . otherwise , there is no photon ( or there are two photons ) interacting with the qd - cavity system when the state of excess electron does nt change . therefore , if the state of excess electron in qd is not changed , there are an even number of photons detected by the qd - cavity system . with this principle , the qd - cavity system can be used as a qnd to distinguish the case with an even number of photons from that with an odd number of photons . now , we will use this photon - number qnd to construct a parity - check qnd for the spatial - mode states of a photon pair . if the excess electrons in qd@xmath67 in fig.[figure2](a ) is prepared initially in the state @xmath77 , after the photons @xmath45 and @xmath46 pass through qd@xmath67 in sequence , the state of the excess electron is in @xmath77 with the input states @xmath59 ( odd - parity ) . however , the state of the excess electron becomes @xmath78 if the input states are @xmath60 ( even - parity ) . by applying a hadamard gate on the excess electron spin , the spin superposition states @xmath79 and @xmath80 can be rotated to the states @xmath2 and @xmath7 , respectively . if we have an auxiliary photon @xmath81 in the initial state @xmath82 and let it pass through qd@xmath67 , after it is reflected from the cavity , the state of the system composed of the photon and the qd electron spin becomes @xmath83 the output state of the auxiliary photon @xmath81 can be measured in orthogonal linear polarization basis . if the auxiliary photon @xmath81 is in state @xmath84 , the state of the excess electron in qd is @xmath2 . otherwise the state of the excess electron in qd is @xmath7 . in this way , one can construct a parity - check qnd for the spatial - mode states to distinguish the odd - parity states @xmath59 from the even - parity states @xmath60 by detecting the spin state of the excess electron in qd@xmath67 . the spin state of excess electron in qd@xmath67 is changed for even - parity states and unchanged for odd - parity states .    with the qnd in fig.[figure2](a ) , the four bell states in the spatial - mode dof are divided into two groups @xmath59 and @xmath60 . the next task of bsa in spatial - mode dof is to distinguish the different relative phases in each group . the qnd shown in fig.[figure2](b ) is used to distinguish the bell states with the relative phase zero from those with the relative phase @xmath85 . bs can accomplish the following transformations in spatial - mode dof , @xmath86 after the operations by bss in fig.[figure2](b ) , the two groups of bell states become : @xmath87 that is , @xmath62 , @xmath64 , @xmath61 , and @xmath63 become @xmath62 , @xmath61 , @xmath64 , and @xmath63 , respectively . with the parity - check measurement shown in fig.[figure2](b ) , one can read out the information about the relative phases in the groups @xmath60 and @xmath59 . if the states of the excess electrons in qd@xmath88 and qd@xmath89 are both changed ( unchanged ) , the state input is @xmath64 or @xmath63 , and the output ports are @xmath90 and @xmath91 ( @xmath92 and @xmath93 ) . while the state of the excess electron in qd@xmath88 is changed ( unchanged ) and the state of the excess electron in qd@xmath89 is unchanged ( changed ) , the state input is @xmath62 or @xmath61 , and the output ports are @xmath90 and @xmath93 ( @xmath92 and @xmath91 ) . the relation between the initial spatial - mode bell states and the outcomes of the qnds is shown in table [ table1 ] . the two - photon system is in one of the two odd - parity states @xmath94 in spatial - mode dof if the state of excess electron in qd@xmath67 is unchanged . when the state of the excess electron in qd@xmath67 is changed , the two - photon system is in one of the two even - parity states @xmath95 . with qd@xmath88 and qd@xmath89 , we read out the information about the relative phases in the groups @xmath60 and @xmath59 . therefore , for the state @xmath61 , the state of the excess electron in qd@xmath67 is unchanged , and the states of the excess electrons in qd@xmath88 and qd@xmath89 are in combination of one changed and the other unchanged . if the state of the excess electron in qd@xmath67 is unchanged and the states of the excess electrons in qd@xmath88 and qd@xmath89 are both changed or unchanged , the input state of the two - photon system is @xmath63 . for the two - photon state @xmath62 , the state of the excess electron in qd@xmath67 is changed , and the states of the excess electrons in qd@xmath88 and qd@xmath89 are in combination of one changed and the other unchanged . for the input state @xmath64 , the state of the excess electron in qd@xmath67 is changed , and the states of the excess electrons in qd@xmath88 and qd@xmath89 are both changed or unchanged .    from the preceding analysis , one can see that the roles of the two qnds are accomplishing the task of parity check . the first qnd can distinguish the two even - parity states in spatial - mode dof from the two odd - parity states . with two bss , the two states with two different relative phases are transformed into another two states with different parities . after the second qnd , one can distinguish the four bell states in spatial -mode dof without destroying the two photons , which provides the convenience for the bsa in polarization dof . .relation between the four bell states in the spatial - mode dof and the output results of the measurements on electron - spin states . [ cols="^,^,^,^ " , ]     [ tab2 ]    by far , we have described the principle of our complete and deterministic hbsa with the nonlinear optics in one - side qd - cavity systems . the bsa on the spatial and the polarization - mode dofs can be realized by adjusting the frequencies @xmath72 to get the phase shift @xmath73 . as a complete and deterministic analysis on quantum states is important in quantum communication , it is interesting to discuss the applications of hbsa . let us use hyperentanglement swapping as an example to describe its principle .     and @xmath96 ( also the four photons ) . after alice performs the hbsa on the two photons @xmath97 , bob and charlie can get the hyperentangled state between nodes @xmath45 and @xmath98.,width=11 ]    hyperentanglement swapping enables two parties in quantum communication to obtain hyperentanglement between two particles which do not interact with each other initially . suppose that the two entangled pairs @xmath99 and @xmath96 are in the following hyperentangled states : @xmath100 the superscripts @xmath45 and @xmath46 denote that the particles are in nodes @xmath45 and @xmath46 , respectively , as shown in fig . [ figure4 ] . alice shares a photon pair @xmath99 with bob , and she also shares a photon pair @xmath96 with charlie . the task of this hyperentanglement - swapping protocol is to entangle the two photons @xmath45 and @xmath98 in both the polarization and the spatial - mode dofs .    to complete entanglement swapping of hyperentangled states , alice performs hbsa on the two particles @xmath46 and @xmath101 in her hand , as shown in fig . [ figure4 ] . the state of the whole system can be rewritten as @xmath102 if the outcome of hbsa is @xmath103 , the two photons located in the nodes @xmath45 ( bob ) and @xmath98 ( charlie ) is in the hyperentangled state @xmath104 . the other outcomes lead to the other hyperentangled states , such as @xmath105 , @xmath106 , @xmath107 , @xmath108 , and @xmath109 . in principle , it is not difficult for bob and charlie to transform their hyperentangled state into the form @xmath104 . for instance , if bob and charlie obtain the state @xmath110 , the state @xmath104 can be obtained in the way that charlie performs an operation @xmath111 in polarization ( both the two spatial modes @xmath93 and @xmath91 ) and then exchanges the two spatial modes after he introduces a phase @xmath85 in the spatial mode @xmath93 with a @xmath112 wave plate .    the hyperentanglement - swapping protocol presented here is completed by two simultaneous but independent processes , including both the polarization bsa and the spatial - mode bsa . if we only perform the bell - state measurement on the photons @xmath46 and @xmath101 in the polarization dof , photons @xmath45 and @xmath98 will be entangled in the polarization degree of freedom but leave their state in the spatial - mode dof be a mixed one . bsa is essential in quantum communication , especially in long - distance quantum communication assisted by quantum repeater . there are many proposals for analyzing bell states in polarization photon pairs . for the hyperentangled bsa discussed here , the entanglements in different dofs need to be analyzed independently . this is different from the hyperentanglement - assisted bsa in polarization dof , in which another degree of freedom is used as an additional system and is consumed in the analysis .    in our proposal , the bsa in the polarization and the spatial - mode dofs are completed by the relative phase shift @xmath113 of left circularly and right circularly polarized lights . in 2011 , young et al . @xcite performed high - resolution reflection spectroscopy of a quantum dot resonantly coupled to a pillar microcavity with quality factor @xmath114 ( @xmath115 m ) , and their experiment showed that a qd - induced phase shift of 0.2 rad between an ( effectively ) empty cavity and a cavity with a resonantly coupled qd can be deduced , by using a single - photon level probe . if the cavity loss is @xmath116 @xcite , by improving the mode matching and the pillar design , this relative phase shift could achieve @xmath117 . in an ideal condition , the fidelity of the hbsa proposal can reach 100% , but in experiment the fidelity is reduced by the limitation of techniques . when two photons are put into a cavity in sequence , the time interval @xmath118 between the two photons should be shorter than the electron spin decoherence time @xmath119 . the electron spin decoherence time @xmath119 could be extended to @xmath120s using spin echo techniques , which is longer than the time interval @xmath118 ( @xmath121s ) with weak excitation @xcite . the heavy - light hole mixing can reduce the fidelity @xcite , but it can be improved for charged excitons due to the quenched exchanged interaction @xcite . the trion dephasing effect can also reduce the fidelity @xcite , but this dephasing effect of @xmath1 can be neglected with the hole spin coherence time three orders of magnitude longer than the cavity photon lifetime @xcite . as the decoherence effects of electron spin , heavy - light hole , and @xmath1 can be neglected , the main factors that reduce the fidelity of hbsa proposal are the coupling strength and the cavity side leakage . vs the coupling strength @xmath122 and the side leakage rate @xmath123 with @xmath124.,width=230 ]     vs the coupling strength @xmath122 and the side leakage rate @xmath123 with @xmath124.,width=230 ]    if the cavity side leakage is neglected , the fidelity of the hbsa proposal can reach 100% in the strong - coupling regime with @xmath32 and @xmath33 . however , there is rigorous limitation in the qd - micropillar cavity , and the cavity side leakage should be considered . defining fidelity as @xmath125 , the fidelities for hbsa proposal can be calculated . here @xmath126 is the final state of the total system which includes the external reservoirs , and @xmath127 is the final state with an ideal condition . as discussed in ref . @xcite , the fidelity of even parity bell states is larger than odd parity bell states in polarization dof , we calculate the fidelity ( in amplitude ) and the efficiency of the present hbsa proposal for the hyperentangled state @xmath128 . the fidelity of this state is @xmath129 ^ 2 } { ( \zeta^{10}+\xi^{10})^2 + 22\epsilon^8(\zeta^2+\xi^2)^2 + 4\epsilon^2(\zeta^8-\xi^8)^2 + 16\epsilon^6(\zeta^4-\xi^4)^2 + 9\epsilon^4(\zeta^6+\xi^6)^2 } \times\frac{1}{128},\end{aligned}\ ] ] and the efficiency of this state is @xmath130 where @xmath131 , @xmath132 , and @xmath133 . figure.[figure5 ] shows the fidelity and the efficiency of the present hbsa protocol for the hyperentangled state @xmath128 . from fig.[figure5](a ) , we can see that the hbsa proposal works with a high fidelity in both strong the coupling regime ( @xmath134 ) and the weak coupling regime ( @xmath135 ) . however , considering the efficiency in fig.[figure5](b ) , our protocol only works effectively in the strong coupling regime . in experiment , it is easy to achieve the weak coupling , but it is challenging to observe a strong coupling in a qd - cavity system . it has been observed the coupling strength can be increased from @xmath136 ( @xmath137 ) @xcite to @xmath138 ( @xmath139 ) @xcite for @xmath140 m micropillar microcavities by improving the sample designs , growth , and fabrication @xcite . for the strong coupling @xmath136 , the fidelity and efficiency are @xmath141 and @xmath142 when @xmath143 , and they are @xmath144 and @xmath145 when @xmath146 . for the strong coupling @xmath138 , the fidelity and the efficiency are @xmath147 and @xmath148 when @xmath143 , and they are @xmath149 and @xmath150 when @xmath151 . the quality factors in these micropillars are dominated by the side leakage and cavity loss rate , so the top mirrors of high - q micropillars ( @xmath140 m ) are thin down to get @xmath152 and @xmath153 ( @xmath154 ) in ref . for the strong coupling @xmath153 , the fidelity and the efficiency are @xmath155 and @xmath156 when @xmath143 , but they are @xmath157 and @xmath158 when @xmath152 . both the fidelity and the efficiency are largely reduced by the cavity side leakage . to get small @xmath123 in the strong coupling regime , high - efficiency operation is highly demanded . this could be quite challenging for micropillar microcavities . the recent experiments achieve the strong coupling with large micropillars @xcite , while the side leakage is small with small micropillars .    in summary , we have proposed a complete hbsa scheme with the interaction between a circular polarization light and a one - side qd - cavity system ( the nonlinear optics of a one - side qd - cavity system ) . we use the relative phase shift of the right and the left circularly polarized lights to construct parity - check measurements and analyze bell states in different dofs of two - photon systems . we have also discussed its applications in long - distance quantum communication processes in two different dofs simultaneously . this work is supported by the national natural science foundation of china under grant nos . 10974020 and 11174039 , ncet-11 - 0031 , and the fundamental research funds for the central universities .                    c. h. bennett , g. brassard , c. crpeau , r. jozsa , a. peres , and w. k. wootters , `` teleporting an unknown quantum state via dual classical and einstein - podolsky - rosen channels , '' phys . rev . lett . * 70 * , 1895 - 1899 ( 1993 ) . n. k. langford , r. b. dalton , m. d. harvey , j. l. obrien , g. j. pryde , a. gilchrist , s. d. bartlett , and a. g. white , `` measuring entangled qutrits and their use for quantum bit commitment , '' phys . 93 * , 053601 ( 2004 ) . t. yang , q. zhang , j. zhang , j. yin , z. zhao , m. ukowski , z. b. chen , and j. w. pan , `` all - versus - nothing violation of local realism by two - photon , four - dimensional entanglement , '' phys . lett . * 95 * , 240406 ( 2005 )                        y. b. sheng , f. g. deng , and h. y. zhou , `` efficient polarization - entanglement purification based on parametric down - conversion sources with cross - kerr nonlinearity , '' phys . rev . a * 77 * , 042308 ( 2008 ) .                          c. y. hu , a. young , j. l. obrien , w. j. munro , and j. g. rarity , `` giant optical faraday rotation induced by a single - electron spin in a quantum dot : applications to entangling remote spins via a single photon , '' phys . b * 78 * , 085307 ( 2008 ) .      c. bonato , f. haupt , s. s. r. oemrawsingh , j. gudat , d. ding , m. p. van exter , and d. bouwmeester , `` cnot and bell - state analysis in the weak - coupling cavity qed regime , '' phys . lett . * 104 * , 160503 ( 2010 ) . r. j. warburton , c. s. drr , k. karrai , j. p. kotthaus , g. medeiros - ribeiro , and p. m. petroff , `` charged excitons in self - assembled semiconductor quantum dots , '' phys . lett . * 79 * , 5282 - 5285 ( 1997 ) .    c. y. hu , w. ossau , d. r. yakovlev , g. landwehr , t. wojtowicz , g. karczewski , and j. kossut , `` optically detected magnetic resonance of excess electrons in type - i quantum wells with a low - density electron gas , '' phys . b * 58 * , r1766-r1769 ( 1998 ) . a. b. young , r. oulton , c. y. hu , a. c. t. thijssen , c. schneider , s. reitzenstein , m. kamp , s. hfling , l. worschech , a. forchel , and j. g. rarity , `` quantum - dot - induced phase shift in a pillar microcavity , '' phys . a * 84 * , 011803 ( 2011 ) . g. bester , s. nair , and a. zunger , `` pseudopotential calculation of the excitonic fine structure of million - atom self - assembled in@xmath159ga@xmath160as / gaas quantum dots , '' phys . b * 67 * , 161306 ( r ) ( 2003 ) . m. bayer , g. ortner , o. stern , a. kuther , a. a. gorbunov , a. forchel , p. hawrylak , s. fafard , k. hinzer , t. l. reinecke , s. n. walck , j. p. reithmaier , f. klopf , and f. schfer , `` fine structure of neutral and charged excitons in self - assembled in(ga)as/(al)gaas quantum dots , '' phys . b * 65 * , 195315 ( 2002 ) .    j. j. finley , d. j. mowbray , m. s. skolnick , a. d. ashmore , c. baker , a. f. g. monte , and m. hopkinson , `` fine structure of charged and neutral excitons in inas - al@xmath161ga@xmath162as quantum dots , '' phys . b * 66 * , 153316 ( 2002 ) .          d. heiss , s. schaeck , h. huebl , m. bichler , g. abstreiter , j. j. finley , d. v. bulaev , and d. loss , `` observation of extremely slow hole spin relaxation in self - assembled quantum dots , '' phys . rev . b * 76 * , 241306(r ) ( 2007 ) . b. d. gerardot , d. brunner , p. a. dalgarno , p. hberg , s. seidl , m. kroner , k. karrai , n. g. stoltz , p. m. petroff , and r. j. warburton , `` optical pumping of a single hole spin in a quantum dot , '' nature ( london ) * 451 * , 441 - 444 ( 2008 ) . j. p. reithmaier , g. sk , a. lffler , c. hofmann , s. kuhn , s. reitzenstein , l. v. keldysh , v. d. kulakovskii , t. l. reinecke , and a. forchel , `` strong coupling in a single quantum dot - semiconductor microcavity system , '' nature ( london ) * 432 * , 197 - 200 ( 2004 ) . t. yoshie , a. scherer , j. hendrickson , g. khitrova , h. m. gibbs , g. rupper , c. ell , o. b. shchekin , and d. g. deppe , `` vacuum rabi splitting with a single quantum dot in a photonic crystal nanocavity , '' nature ( london ) * 432 * , 200 - 203 ( 2004 ) . s. reitzenstein , c. hofmann , a. gorbunov , m. strau , s. h. kwon , c. schneider , a. lffler , s. hfling , m. kamp , and a. forchel , `` alas / gaas micropillar cavities with quality factors exceeding @xmath163 , '' appl . phys . lett . * 90 * , 251109 ( 2007 ) .    v. loo , l. lanco , a. lematre , i. sagnes , o. krebs , p. voisin , and p. senellart , `` quantum dot - cavity strong - coupling regime measured through coherent reflection spectroscopy in a very high - q micropillar , '' appl . . lett . * 97 * , 241110 ( 2010 ) .
bell - state analysis ( bsa ) is essential in quantum communication , but it is impossible to distinguish unambiguously the four bell states in the polarization degree of freedom ( dof ) of two - photon systems with only linear optical elements , except for the case in which the bsa is assisted with hyperentangled states , the simultaneous entanglement in more than one dof . here , we propose a scheme to distinguish completely the 16 hyperentangled bell states in both the polarization and the spatial - mode dofs of two - photon systems , by using the giant nonlinear optics in quantum dot - cavity systems . 
 this scheme can be applied to increase the channel capacity of long - distance quantum communication based on hyperentanglement , such as entanglement swapping , teleportation , and superdense coding . 
 we use hyperentanglement swapping as an example to show the application of this hbsa .