Boyang Chen

We give a meta-complexity characterization of EFI pairs, which are considered the “minimal” primitive in quantum cryptography (and are equivalent to quantum commitments). More precisely, we show that the existence of EFI pairs is equivalent to the following: there exists a non-uniformly samplable distribution over pure states such that the problem of estimating a certain Kolmogorov-like complexity measure is hard given a single copy. A key technical step in our proof, which may be of independent interest, is to show that the existence of EFI pairs is equivalent to the existence of non-uniform single-copy secure pseudorandom state generators (nu 1-PRS). As a corollary, we get an alternative, arguably simpler, construction of a universal EFI pair.

Quantum simulation is widely regarded as one of the most promising applications of quantum computing. A critical challenge in this domain is understanding and quantifying the accumulation of algorithmic errors over time, which is essential for designing more efficient simulation algorithms and for assessing the resources required to achieve quantum advantage. Conventional error analyses typically rely on the triangle inequality to bound the total simulation error, but such approaches tend to overestimate errors by ignoring error interference-a phenomenon in which errors from different simulation segments partially cancel. Here, we introduce a new framework for directly estimating long-time algorithmic errors in segmented quantum simulations. Our approach captures the full structure of error interference, enabling significantly tighter and more accurate error bounds. We identify both necessary and sufficient conditions for strict error interference and propose the notion of approximate error interference to account for realistic, imperfect cancellation. We demonstrate the broad applicability of our framework across a range of models and settings, including Heisenberg and Fermi-Hubbard systems, lattice Hamiltonians with power-law interactions, higher-order Trotter decompositions, and adiabatic evolution. By providing a unified and practical methodology for analyzing error interference, our Letter advances the theoretical understanding of quantum simulation and informs the design and benchmarking of algorithms for near-term and future quantum hardware.

Quantum measurements can produce unpredictable randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. Unlike projection measurements, there are additional and possibly hidden degrees of freedom in an apparatus for generic measurements. We propose an adversary scenario to characterize the intrinsic randomness of general measurements with arbitrary input states. Interestingly, we discover that certain measurements, including symmetric and information-complete ones, generate nonzero randomness for all states, which suggests a new approach for designing source-independent random number generators without state characterization. Furthermore, our results reveal that intrinsic randomness can quantify coherence under general measurements, which generalizes the result in the standard resource theory of state coherence.

Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. Unlike projection measurements, there are additional and possibly hidden degrees of freedom in apparatus for generic measurements. We propose an adversary scenario for general measurements with arbitrary input states, based on which, we characterize the intrinsic randomness. Interestingly, we discover that under certain measurements, such as the symmetric and information-complete measurement, all states have nonzero randomness, inspiring a new design of source-independent random number generators without state characterization. Furthermore, our results show that intrinsic randomness can quantify coherence under general measurements, which generalizes the result in the standard resource theory of state coherence.