Antitrust and Regulation

Since the passage of the Interstate Commerce Act (1897) and the Sherman Act (1890), regulation and antitrust have operated as competing mechanisms to control competition. Regulation produced cross-subsidies and favors to special interests, but specified prices and rules of mandatory dealing. Antitrust promoted competition without favoring special interests, but couldn't formulate rules for particular industries. The deregulation movement reflected the relative competencies of antitrust and regulation. Antitrust and regulation can also be viewed as complements in which regulation and antitrust assign control of competition to courts and regulatory agencies based on their relative strengths. Antitrust also can act as a constraint on what regulators can do. This paper uses the game-theoretic framework of political bargaining and the historical record of antitrust and regulation to establish and illustrate these points.

Sufficient Conditions for Efficient Classical Simulation of Quantum Optics

We provide general sufficient conditions for the efficient classical simulation of quantum-optics experiments that involve inputting states to a quantum process and making measurements at the output. The first condition is based on the negativity of phase-space quasiprobability distributions (PQDs) of the output state of the process and the output measurements; the second one is based on the negativity of PQDs of the input states, the output measurements, and the transition function associated with the process. We show that these conditions provide useful practical tools for investigating the effects of imperfections in implementations of boson sampling. In particular, we apply our formalism to boson-sampling experiments that use single-photon or spontaneous-parametric-down-conversion sources and on-off photodetectors. Considering simple models for loss and noise, we show that above some threshold for the probability of random counts in the photodetectors, these boson-sampling experiments are classically simulatable. We identify mode mismatching as the major source of error contributing to random counts and suggest that this is the chief challenge for implementations of boson sampling of interesting size.Comment: 12 pages, 1 figur

Verification of quantum discord

We introduce a measurement-based method for verifying quantum discord of any bipartite quantum system. We show that by performing an informationally complete POVM (IC-POVM) on one subsystem and checking the commutativity of the conditional states of the other subsystem, quantum discord from the second subsystem to the first can be verified. This is an improvement upon previous methods, which enables us to efficiently apply our method to continuous-variable systems, as IC-POVMs are readily available from homodyne or heterodyne measurements. We show that quantum discord for Gaussian states can be verified by checking whether the peaks of the conditional Wigner functions corresponding to two different outcomes of heterodyne measurement coincide at the same point in the phase space. Using this method, we also prove that the only Gaussian states with zero discord are product states; hence, Gaussian states with Gaussian discord have nonzero quantum discord.Comment: 5 page