Verification of a resetting protocol for an uncontrolled superconducting qubit

Quantum resetting protocols allow a quantum system to be sent to a state in the past by making it interact with quantum probes when neither the free evolution of the system nor the interaction is controlled. We experimentally verify the simplest non-trivial case of a quantum resetting protocol, known as the $${{\mathcal{W}}}_{4}$$ W 4 protocol, with five superconducting qubits, testing it with different types of free evolutions and target–probe interactions. After projection, we obtained a reset state fidelity as high as 0.951, and the process fidelity was found to be 0.792. We also implemented 100 randomly chosen interactions and demonstrated an average success probability of 0.323 for $$\left|1\right\rangle$$ 1 and 0.292 for $$\left|-\right\rangle$$ − , and experimentally confirmed the nonzero probability of success for unknown interactions; the numerical simulated values are about 0.3. Our experiment shows that the simplest quantum resetting protocol can be implemented with current technologies, making such protocols a valuable tool in the eternal fight against unwanted evolution in quantum systems.

Consequentialism in infinite worlds

We show that in infinite worlds the following three conditions are incompatible: (1) The spatiotemporal ordering of individuals is morally irrelevant. (2) All else being equal, the act of bringing about a good outcome with a high probability is better than the act of bringing about the same outcome with a low probability. (3) One act is better than another only if there is a nonzero probability that it brings about a better outcome. The impossibility of combining these conditions shows that it is more costly to endorse (1) than has been previously acknowledged.

Evolution in alternating environments with tunable inter-landscape correlations

Natural populations are often exposed to temporally varying environments. Evolutionary dynamics in varying environments have been extensively studied, though understanding the effects of varying selection pressures remains challenging. Here we investigate how cycling between a pair of statistically related fitness landscapes affects the evolved fitness of an asexually reproducing population. We construct pairs of fitness landscapes that share global fitness features but are correlated with one another in a tunable way, resulting in landscape pairs with specific correlations. We find that switching between these landscape pairs, depending on the ruggedness of the landscape and the inter-landscape correlation, can either increase or decrease steady-state fitness relative to evolution in single environments. In addition, we show that switching between rugged landscapes often selects for increased fitness in both landscapes, even in situations where the landscapes themselves are anti-correlated. We demonstrate that positively correlated landscapes often possess a shared maximum in both landscapes that allows the population to step through sub-optimal local fitness maxima that often trap single landscape evolution trajectories. Finally, we demonstrate that switching between anti-correlated paired landscapes leads to ergodic-like dynamics where each genotype is populated with nonzero probability, dramatically lowering the steady-state fitness in comparison to single landscape evolution.

Zero-knowledge convincing protocol on quantum bit is impossible

Consider two parties: Alice and Bob and suppose that Bob is given a qubit system in a quantum state ϕ, unknown to him. Alice knows ϕ and she is supposed to convince Bob that she knows ϕ sending some test message. Is it possible for her to convince Bob providing him "zero knowledge" i. e. no information about ϕ he has? We prove that there is no "zero knowledge" protocol of that kind. In fact it turns out that basing on Alice message, Bob (or third party - Eve - who can intercept the message) can synthetize a copy of the unknown qubit state ϕ with nonzero probability. This "no-go" result puts general constrains on information processing where information about quantum state is involved.

On the singular components of a copula

We analyze copulas with a nontrivial singular component by using their Markov kernel representation. In particular, we provide existence results for copulas with a prescribed singular component. The constructions not only help to deal with problems related to multivariate stochastic systems of lifetimes when joint defaults can occur with a nonzero probability, but even provide a copula maximizing the probability of joint default.

On the singular components of a copula

We analyze copulas with a nontrivial singular component by using their Markov kernel representation. In particular, we provide existence results for copulas with a prescribed singular component. The constructions not only help to deal with problems related to multivariate stochastic systems of lifetimes when joint defaults can occur with a nonzero probability, but even provide a copula maximizing the probability of joint default.

COSMOLOGICAL MEASURES WITH VOLUME AVERAGING

It has been common for cosmologists to advocate volume weighting for the cosmological measure problem, weighting spatial hypersurfaces by their volume. However, this often leads to the Boltzmann brain problem, that almost all observations would be by momentary Boltzmann brains that arise very briefly as quantum fluctuations in the late universe when it has expanded to a huge size, so that our observations (too ordered for Boltzmann brains) would be highly atypical and unlikely. Here it is suggested that volume weighting may be a mistake. Volume averaging is advocated as an alternative. One consequence may be a loss of the argument that eternal inflation gives a nonzero probability that our universe now has infinite volume.

Scan statistics of Lévy noises and marked empirical processes

Let n points be chosen independently and uniformly in the unit cube [0,1] d , and suppose that each point is supplied with a mark, the marks being independent and identically distributed random variables independent of the location of the points. To each cube R contained in [0,1] d we associate its score defined as the sum of marks of all points contained in R. The scan statistic is defined as the maximum of taken over all cubes R contained in [0,1] d . We show that if the marks are nonlattice random variables with finite exponential moments, having negative mean and assuming positive values with nonzero probability, then the appropriately normalized distribution of the scan statistic converges as n → ∞ to the Gumbel distribution. We also prove a corresponding result for the scan statistic of a Lévy noise with negative mean. The more elementary cases of zero and positive mean are also considered.

Scan statistics of Lévy noises and marked empirical processes

Let n points be chosen independently and uniformly in the unit cube [0,1]d, and suppose that each point is supplied with a mark, the marks being independent and identically distributed random variables independent of the location of the points. To each cube R contained in [0,1]d we associate its score defined as the sum of marks of all points contained in R. The scan statistic is defined as the maximum of taken over all cubes R contained in [0,1]d. We show that if the marks are nonlattice random variables with finite exponential moments, having negative mean and assuming positive values with nonzero probability, then the appropriately normalized distribution of the scan statistic converges as n → ∞ to the Gumbel distribution. We also prove a corresponding result for the scan statistic of a Lévy noise with negative mean. The more elementary cases of zero and positive mean are also considered.

Unambiguous unitary quantum channels

Unambiguous unitary maps and unambiguous unitary quantum channels are introduced and some of their properties are derived. These properties ensures certain simple form for the measurements involved in realizing an unambiguous unitary quantum channel. Error correction and unambiguous error correction with nonzero probability are discussed in terms of unambiguous unitary quantum channels. We not only re-derive the well-known condition for a set of errors to be correctable with certainty, but also obtain a necessary and sufficient condition for the errors caused by a noisy channel to be correctable with any nonzero probability. Dense coding with a partially entangled state can also be viewed as an unambiguous unitary quantum channel when all messages are required to be transmitted with equal probability of success, the maximal achievable probability of success is derived and the optimum protocol is also obtained.