Quantum Coherence and Intrinsic Randomness

Abstract

The peculiar uncertainty or randomness of quantum measurements stems from quantum coherence, whose information‐theoretic characterization is currently under investigation. The resource theory of coherence investigates interpretations of coherence measures and the interplay with other quantum properties, such as quantum correlations and intrinsic randomness. Coherence can be viewed as a resource for generating intrinsic randomness by measuring a state in the computational basis. It is observed in a previous work that the coherence of formation, which measures the asymptotic coherence dilution rate, indeed quantifies the uncertainty of a correlated party (classical system) about the system measurement outcome. In this work, the result is re‐derived from a quantum point of view, and then the intrinsic randomness is connected to the relative entropy of coherence, another important coherence measure that quantifies the asymptotic distillable coherence. Even though there do not exist bound coherent states, these two coherence measures—intrinsic randomness quantified by coherence of formation and by relative entropy of coherence—are different. Interestingly, it is shown that this gap is equal to the quantum discord, a general form of quantum correlations, in the state of the system of interest and the correlated party, after a local measurement on the former system.

Intrinsic randomness under general quantum measurements

“…In the second case, Eve can collect all the purification states and perform a joint measurement. In this case, randomness is quantified by [15,33],…”

“…The intrinsic randomness functions, Eq. ( A1) and (A2) directly give coherence measures for both R c [13] and R q [14,15] for von Neumann measurements.…”

“…In resource theory, superposition is quantified by quantum coherence with respect to the measurement basis, {|i } [11,12]. In fact, for a generic input state described by a density matrix, the link between output intrinsic randomness and state coherence has been established [13][14][15]. A projection measurement is an idealized model for detection devices.…”

“…(1). For the special case of von Neumann measurements, the randomness quantification R(̺, P) is well studied in the literature under different adversary scenarios [15,33]. As the starting point of our randomness quantification of POVMs, we generalize the results to the general PVM case and give two widely used mea-…”

18.8 Gbps real-time quantum random number generator with a photonic integrated chip

“…We note that in the current theoretical analysis, a non-adversarial model is considered. The extracted randomness includes both the intrinsic randomness originated from quantum shot noise and the nominal randomness from mixed states, where the latter might be controlled by classical or quantum side information 31,32 . In principle, one can take account of the po- tential leakage of side information and quantify the amount of intrinsic randomness with condition min-entropy, which deserves future investigations.…”