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Here I will discuss which of the 16 Gaussian protocols mentioned in section 5.3 can possibly show one sided-device independence. Similar to steering inequalities, the 1SDI nature of the entropic proofs is clear in expressions like equation (5.13) in that it relies only on measuring a known observable upon one side. For example, in the derivation we only need to know that Bob is observing either ˆxB or ˆpB and then
§5.6 One-sided device-independent CVQKD 71
Bob
Alice
Figure 5.2: Schematic diagram of steering task when Alice is affecting Bob’s state. Bob trusts his devices which is shown by the white box, but he has no knowledge about Alice’s devices which is depicted by a black box. Only the outcomes of Alice’s measurement ak are important to Bob. By performing the complete measurement
on his received state and conditioning on Alice’s announced outcomes, Bob will be convinced that Alice has the ability to steer his state if he finds a well defined state
conditioned on Alice’s outcomes
conditioned on the outcomes of Alice’s observation in order to use the entropic un- certainty relations. Alice could choose any measurement and the security would still hold if the conditional variance was sufficiently small to violate Ried EPR criteria (equation 5.35).
Hence for entanglement-base (EB) scheme and homodyne detection, by definition any positive key proved by the entropic uncertainty relation is 1SDI, independent of Alice for RR and Bob for DR protocols. Though the protocols involving heterodyne detection does not necessarily exhibit device independence. This is basically due to the fact that extracting the non-zero key rates for the heterodyne protocols depends upon characterizing the devices utilized in the heterodyne detection. Hence, using a heterodyne measurement by the supposedly untrusted party immediately disproves the device-independence. However, the heterodyne measurement can be performed safely by the trusted party with high efficiency sources and detection, making the im- plementation of 1SDI-CVQKD protocols possible with current technology. It means that Bob can safely perform heterodyne for an RR protocol and Alice may conduct heterodyne for a DR protocol. Finally, for DR protocols where Alice who is trusted and controls the source, we can also benefit from the equivalence between prepare and measure (P&M) and entanglement-based (EB) schemes (see section 5.3.1). Sur- prisingly, this means that for direct reconciliation it is possible to extract 1SDI key utilizing only coherent states. The table in figure 5.3 summarizes the possible Gaus- sian protocols which are potentially 1SDI out of the all 16 Gaussian protocols .
The idea that the 1SDI-QKD protocols should be related to EPR steering was confirmed in DV regime by C.Branciard et al. [19] before. For CV-QKD the EPR- steering criteria is defined by equation 5.35. Comparing Ried EPR criteria with
Alice
Bob
Hom
Het
Hom
Het
Hom
Het
DR
RR
P&M
EB
P&M
EB
Figure 5.3: Gaussian protocols which can potentially be 1SDI. Alice and Bob can choose either homodyne or heterodyne detection. DR and RR reconciliation protocols can be performed for both (EB) and (P&M) schemes. The same colors are chosen to
show the equivalence between the (EB) and (P&M) protocols.
equation (5.13) we can rewrite the key rate as a function of EPR-steeringE.:
K/ ≥log( 2 e√E.
) (5.36)
For the RR protocols the key rate K/ > 0 if and only if E. < (2e)2 ≈ 0.55, with
the similar relation between the DR key rate andE/ following straightforwardly. In
other words, the condition for obtaining the positive one-sided device-independent key is more strict than EPR steering, analogous to the case for DV-QKD [19]. For the protocols where a trusted party performs the heterodyne detection, the security of the protocol is instead based on the steerability of the outcome of the heterodyne measurement which will be more challenging due to the extra loss introduce to the system. Now secure key enforces an EPR conditionE.(/) < 0.22. In the next chap- ters where I present the experimental results, I will demonstrate the connection of achieving the positive key rates and the EPR steering criteria mentioned here. From the 6 possible 1SDI Gaussian protocols, we conducted 5 protocols experimen- tally. However, only 3 of the 5 demonstrated sufficient correlations to allow 1SDI key distribution. Two different experimental setups were used, the first for the (EB) protocols based on EPR correlations and the second for a coherent state (P&M) proto- cols. A schematic diagram of all the performed experiments and the achieved results are summarized in figure 5.4.
§5.6 One-sided device-independent CVQKD 73
Heterodyne
Entanglement
Based
Alice
Source
Bob
1
2
3
4
5
Hom
Het
Hom
Het
Positive key
Transmission distancein fibre optics (km)
Alice
Bob
RR
DR
≈ 2.52
≈7.57
≈ 3.47
E ntang lemen t-ba se d P & M0
0
3 3 5 4 4 2 2 1 1RR
DR
Homodyne
Prepare & Measure
(Coherent States)
5
Homodyne
Heterodyne
Figure 5.4: Schematic diagram of all the experimentally realised 1sDI protocols. Al- ice and Bob can choose between homodyne and heterodyne measurements (indi- cated respectively by green and grey color boxes on each side), using a source that generates either EPR or coherent states (indicated respectively by pink and yellow boxes). Direct (reverse) reconciliation protocols are demonstrated using right (left) pointing arrows. The table summarizes each performed protocol and the experimen- tally achieved results. The same color scheme as figure 5.3 is used here to show the
5.7
Summary
In this chapter I reviewed the entropic uncertainty relations and showed how we used them to derive 1SDI-QKD key rates. I discussed the connection between EPR steering and 1SDI-QKD protocols. I looked at all the 16 Gaussian QKD protocols and showed that only 6 of them can manifest device independence. We experimentally implemented 5 of these 6 protocols. In fact, Implementation of 1SDI-QKD using con- tinuous variables against coherent attacks has been reported recently by T. Gehring et al. in ref [123]. However, they just implemented one protocol, while we extended the notion of 1SDI-QKD to the whole family of continuous variable protocols for the first time. In the next two chapters I will detail our experimental setups, the computer simulation and the results.
Chapter6
Experimental Implementation of
1SDI-QKD Protocols in EB Scheme
6.1
Introduction
In this chapter I will describe the experimental implementation of one-sided device- independent protocols using an entangled source. I will start by giving the overall view of our experimental setup, then I will explain each part in more detail. I will introduce the detection, data acquisition and control systems that we utilized in the experiment, and present the experimental results, error estimation and computer simulation at the end.