Abstract
We present a scheme for multi-bit quantum random number generation using a single qubit discrete-time quantum walk in one-dimensional space. Irrespective of the initial state of the qubit, quantum interference and entanglement of particle with the position space in the walk dynamics certifies high randomness in the system. Quantum walk in a position space of dimension 2l + 1 ensures string of (l + 2)-bits of random numbers from a single measurement. Bit commitment with the position space and control over the spread of the probability distribution in position space enable us with options to extract multi-bit random numbers. This highlights the power of one qubit, its practical importance in generating multi-bit string in single measurement and the role it can play in quantum communication and cryptographic protocols. This can be further extended with quantum walks in higher dimensions.
Highlights
Random number plays an important role in many applications where unpredictability is a key[1,2], especially in cryptographic protocols[3,4,5] where security is assured because of unpredictability
Since the Quantum Random Number Generator (QRNG) protocol we propose is solely based on Discrete Time Quantum Walk (DTQW) dynamics, it is necessary to have a good measure of randomness contained in both position and coin space
We introduce here a QRNG based on quantum dynamics which can be controlled rather than the “prepare and measure” methods
Summary
Random number plays an important role in many applications where unpredictability is a key[1,2], especially in cryptographic protocols[3,4,5] where security is assured because of unpredictability. Like measuring entangled particles one can assess the randomness of the process independent of it’s quantum description which cannot be described deterministically within the framework of any no-signalling theories. Though there is no direct connection between nonlocality and entanglement[24,25], it is known that any pure entangled states are nonlocal Using this nonlocality of observed statistics in bipartite Bell scenario, a device independent Quantum Random Number Generator (QRNG) has been suggested[16]. Though the device-independent or self-testing QRNG is more secure compared to two other protocols, it is unsuitable in some cases because of the slow generation of random numbers with time constrained under current technologies. Www.nature.com/scientificreports numerical analysis shows that the randomness of an initial state of the particle is being enhanced using the quantum walk dynamics. Each step of DTQW comprises of quantum coin operation, C(θ)
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