66
4 Quantum Conference Key Agreement
D r
D t
HWP
QWP
PBS
Fig. 4.3 The measurement apparatus of each party in the CKA experiment [26] comprises: a
quarter-wave plate (QWP), a half-wave pate (HWP), a polarizing beam splitter (PBS) and two superconducting nanowire single-photon detectors D t and D r collecting the transmitted and reflected
photons. The QWP and HWP are motorized in order to implement measurements in the X , Y (for
state tomography) and Z basis
|−−), depending on the measured basis. The wave plates are motorized and rotate
according to the measurement to be performed. Prior to the execution of the protocol,
the parties also measure in the Y basis (|R, L = (|H ± i|V )/
√
2) to perform state
tomography on the post-selected GHZ state. This is achieved with the QWP oriented
at 45
◦ and the HWP at 0
◦ .
Once the distribution of quantum states is completed, the parties perform one-way
EC from Alice to the Bobs, with a low-density parity-check code (LDPC) adapted to
the multipartite scenario. Here, Alice discloses her parity check bits over the public
channel in order for the Bobs to compute a guess of her raw key. The parity check
matrices are pre-compiled and provided by the Digital Video Broadcasting (DVBS2) standard [29]. The code rate is chosen such that even the Bob with the largest
bit error rate, max i E AB i , can successfully correct his raw key (see discussion in
Sect. 4.1).
Finally the parties perform privacy amplification by applying an appropriate
Toeplitz matrix —a two-universal hash function [30]— randomly picked by Alice
on their error-corrected raw keys, obtaining a secret conference key.
The anonymous CKA experiment [27] generates four-photon GHZ states in a
similar manner. The only difference is that in [27] the down-converted photon pairs
are directly produced as Bell pairs and do not necessitate to be embedded in a Sagnac
loop. This can be achieved by using beta-Barium Borate (BBO) crystals for the SPDC
process, instead of PPKTP crystals as in [26]. Note that BBO crystals typically yield
a lower number of entangled photon pairs compared to PPKTP crystals embedded
in a Sagnac loop, when using the same pump power.
4 Quantum Conference Key Agreement
D r
D t
HWP
QWP
PBS
Fig. 4.3 The measurement apparatus of each party in the CKA experiment [26] comprises: a
quarter-wave plate (QWP), a half-wave pate (HWP), a polarizing beam splitter (PBS) and two superconducting nanowire single-photon detectors D t and D r collecting the transmitted and reflected
photons. The QWP and HWP are motorized in order to implement measurements in the X , Y (for
state tomography) and Z basis
|−−), depending on the measured basis. The wave plates are motorized and rotate
according to the measurement to be performed. Prior to the execution of the protocol,
the parties also measure in the Y basis (|R, L = (|H ± i|V )/
√
2) to perform state
tomography on the post-selected GHZ state. This is achieved with the QWP oriented
at 45
◦ and the HWP at 0
◦ .
Once the distribution of quantum states is completed, the parties perform one-way
EC from Alice to the Bobs, with a low-density parity-check code (LDPC) adapted to
the multipartite scenario. Here, Alice discloses her parity check bits over the public
channel in order for the Bobs to compute a guess of her raw key. The parity check
matrices are pre-compiled and provided by the Digital Video Broadcasting (DVBS2) standard [29]. The code rate is chosen such that even the Bob with the largest
bit error rate, max i E AB i , can successfully correct his raw key (see discussion in
Sect. 4.1).
Finally the parties perform privacy amplification by applying an appropriate
Toeplitz matrix —a two-universal hash function [30]— randomly picked by Alice
on their error-corrected raw keys, obtaining a secret conference key.
The anonymous CKA experiment [27] generates four-photon GHZ states in a
similar manner. The only difference is that in [27] the down-converted photon pairs
are directly produced as Bell pairs and do not necessitate to be embedded in a Sagnac
loop. This can be achieved by using beta-Barium Borate (BBO) crystals for the SPDC
process, instead of PPKTP crystals as in [26]. Note that BBO crystals typically yield
a lower number of entangled photon pairs compared to PPKTP crystals embedded
in a Sagnac loop, when using the same pump power.