Abstract
We consider an optimal quantum key distribution setup based on minimal number of measurement bases with binary yields used by parties against an eavesdropper limited only by the no-signaling principle. We note that in general, the maximal key rate can be achieved by determining the optimal tradeoff between measurements that attain the maximal Bell violation and those that maximise the bit correlation between the parties. We show that higher correlation between shared raw keys at the expense of maximal Bell violation provide for better key rates for low channel disturbance.
Highlights
Quantum cryptography, which is often a reference to the more specific study of quantum key distribution (QKD) had been developed as a secure way of distributing or establishing secure keys between parties[1]
We can immediately observe that the protocol of Version II outperforms Version I for D up to about 3% and 2.4% respectively when the terms related to error correction play a more prominent role in determining the maximal achievable key rate as opposed to privacy amplification
In this work we have noted that deriving a secure key and determining a Bell violation are clearly two incompatible processes; one can only be achieved maximally at the expense of the other and generating the most optimal secure key rate must necessarily capitalise on a possible trade-off
Summary
Quantum cryptography, which is often a reference to the more specific study of quantum key distribution (QKD) had been developed as a secure way of distributing or establishing secure keys between parties[1]. One of the main setbacks regarding the CHSH protocol is its immediate implementation given Alice and Bob’s quantum framework Such a protocol sees the legitimate users setting their choice of measurements to achieve a maximal CHSH violation for which any subset to be used for sharing a common string would, inherently carry errors due to non-overlapping basis. It is quite obvious to note that measurements to maximally estimate the nature of correlations for a bipartite entangled state; i.e. local or otherwise, is not compatible with measurements which would extract the maximally possible amount of correlation This can be immediately seen as follows: If Alice and Bob wished to extract the maximal number of bits per-entangled pair by local measurements on each half of the pair, every round of measurement requires them to have identical measurement bases and would not enable a determination of the type of correlation involved with certainty as evident from eq (4) where subscribing to maximally overlapping bases results in the maximal value being 2. 1−F 4 hand, any measurement to ascertain the maximal possible local violation with certainty would not allow for Alice and Bob to share an error free string; the CHSH protocol is an immediate example of this
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