In this project, our aim is to present a new platform, i.e. the so-called instrumental process, to generate and certify a form of strong randomness, which can be achieved through the intrinsically random nature of quantum physics.
We adopt a photonic platform to implement an instrumental process, equipped with active feed-forward of information and gain random bits from the measurement outputs of two parties (Alice and Bob), who share a bipartite entangled state.
The generation of random numbers constitutes a cardinal challenge for a plethora of fields, ranging from scientific numerical simulations, cryptography, to safeguarding privacy and gambling.
Indeed, the non-local correlations of entangled particles allow to gain string of numbers whose randomness can be certified with no assumptions about the internal working of the adopted device. With respect to the aforementioned seminal work in this direction and its newest developments, the instrumental scenario represents a most convenient choice, since it does not require any space-like separation between the parties. Besides the ease of implementation, the instrumental scenario enables to adopt only one input random seed for the generator, without suffering any locality loophole, therefore requiring less initial randomness. Moreover, this process ensures also a higher gain of random bits than the usual Bell scenario, since it gets only one trit as input to generate two output bits.
Our protocol is the first to exploit the instrumental scenario with the purpose to generate certified random numbers. This platform we are proposing is way more convenient than the Bell's scenario, which was used in previous works. Indeed, the certification of randomness relies on the correct implementation of the causal structure. Considering this request, Bell's structure is affected by many loopholes, the most ardous being the "locality loophole", which requires that Alice and Bob must not influence each other. This is very tricky to achieve experimentally, because it requires space-like separation between the parties, i.e. the spacial separation of Alice and Bob, must be larger than the space light can cover in the time between their choice of the observables. In this way, any communication between them is unfeasible. Some loophole-free Bell tests have been reaized, but they involve very large distances, making the protocol unpractical and very demanding to be realized.
The instrumental process is not affected by this loophole, because Alice and Bob must communicate, specifically Bob's choice directly depends on Alice's choice. Therefore, it is largely easier to implement.
Another great advantage provided by this scenario, is the rate of bit generation. Indeed, in a Bell's scenario, two random bits are required as input of the generator (being Alice's and Bob's observables choice), to get still two output bits. Therefore, there is no gain on the number of generated bits, with respect to the input. In the instrumental scenario, only one input trit is needed, which is Alice's choice. Therefore there is an increase of roughly 0.41 bit per experimental run.
Moreover, in the previous implementations of random number generation adopting a Bell's scenario, Alice's and Bob's choices are given by an initial random seed. Using an unique and previouly seed, however, affects the independence between Alice's and Bob's choices.
In our implementation, we can adopt a unique seed, generated by a quantum source, independent from the one that generates the bipartite entangled system, without affecting the correct implementation of the causal structure.