Kaiyuan Ji

The ultimate limits of quantum state discrimination are often thought to be captured by asymptotic bounds that restrict the achievable error probabilities, notably the quantum Chernoff and Hoeffding bounds. Here we study hypothesis testing protocols that are permitted a probability of producing an inconclusive discrimination outcome, and investigate their performance when this probability is suitably constrained. We show that even by allowing an arbitrarily small probability of inconclusiveness, the limits imposed by the quantum Hoeffding and Chernoff bounds can be significantly exceeded. This completely circumvents the conventional trade-offs between error exponents in hypothesis testing while incurring only a vanishingly small overhead over conventional approaches. Such improvements over standard state discrimination are robust and can be obtained even when an exponentially vanishing probability of inconclusive outcomes is demanded. Relaxing the constraints on the inconclusive probability can enable even larger advantages, but this comes at a price. We show a 'strong converse' property of this setting: targeting error exponents beyond those achievable with vanishing inconclusiveness necessarily forces the probability of inconclusive outcomes to converge to one. By exactly quantifying the rate of this convergence, we give a complete characterisation of the trade-offs between error exponents and rates of conclusive outcome probabilities. Overall, our results provide a comprehensive asymptotic picture of how the allowance for inconclusive measurement outcomes reshapes optimal quantum hypothesis testing.

The study of feedback control inspired by Maxwell's demon is central to the understanding of the relationship between thermodynamics and information. In this paper, we establish fundamental lower limits on the work costs of system conversion with quantum feedback, where quantum side information acquired in advance can be fed back to the system coherently by a controller. From two basic operational principles that every physically admissible feedback-control scheme should satisfy, we derive the tightest possible bounds on the single-shot work of formation and extractable work of an arbitrary quantum system given arbitrary quantum side information held by the controller. These bounds are expressed in terms of information measures generalizing both mutual informations and relative entropies. In the asymptotic limit, they lead to a generalized second law of thermodynamics with quantum feedback, featuring a conditional Helmholtz free energy. Our findings provide precise thermodynamic meanings for the negativity of single-shot conditional entropies and resolve an open problem in the axiomatic reconstruction of such conditional entropies.

We study the capacity of a quantum channel for retrocausal communication, where messages are transmitted backward in time, from a sender in the future to a receiver in the past, through a noisy postselected closed timelike curve (P-CTC) mathematically represented by the channel. We completely characterize the one-shot retrocausal quantum and classical capacities, and we show that the corresponding asymptotic capacities are equal to the average and sum, respectively, of the channel's max-information and its regularized Doeblin information. This endows these information measures with a novel operational interpretation. Furthermore, our characterization can be generalized beyond quantum channels to all completely positive maps. This imposes information-theoretic limits on transmitting messages via postselected-teleportation-like mechanisms with arbitrary initial- and final-state boundary conditions, including those considered in various black-hole final-state models.