Entanglement without nonlocality

We consider the characterization of entanglement from the perspective of a Heisenberg formalism. We derive an original two-party generalized separability criteria, and from this describe a novel physical understanding of entanglement. We find that entanglement may be considered as fundamentally a local effect, and therefore as a separable computational resource from nonlocality. We show how entanglement differs from correlation physically, and explore the implications of this new conception of entanglement for the notion of classicality. We find that this understanding of entanglement extends naturally to multipartite cases.Comment: 9 pages. Expanded introduction and sections on physical entanglement and localit

Developing the Deutsch-Hayden approach to quantum mechanics

The formalism of Deutsch and Hayden is a useful tool for describing quantum mechanics explicitly as local and unitary, and therefore quantum information theory as concerning a "flow" of information between systems. In this paper we show that these physical descriptions of flow are unique, and develop the approach further to include the measurement interaction and mixed states. We then give an analysis of entanglement swapping in this approach, showing that it does not in fact contain non-local effects or some form of superluminal signalling.Comment: 14 pages. Added section on entanglement swappin

Putting North Carolina Through the PACES: Bringing Intrastate Crowdfunding to North Carolina Through the NC PACES Act

The nationwide increase in the number of small businesses over the past several years has led to more small businesses, startups, and entrepreneurs seeking capital investments from the general public in order to build and grow their businesses. In an effort to attract investors, businesses have taken an interest in securities crowdfunding, a method for raising capital whereby businesses offer stock in their companies in exchange for capital from investors. While an offering of securities generally must be registered with the United States Securities and Exchange Commission, companies can circumvent the registration requirement by utilizing one of the available exemptions provided by federal statute. This Comment focuses primarily on the intrastate exemption, which allows businesses to sell securities if the offering is wholly contained within a single state, but only if that state has given businesses the option to use that exemption. Since 2011, over half of the states have passed legislation permitting businesses within those states to take advantage of the intrastate exemption. North Carolina, through the NC PACES Act, is considering passing such legislation, yet that bill has been stalled in the North Carolina General Assembly since April of 2015. This Comment highlights the benefits that North Carolina can enjoy by allowing intrastate securities crowdfunding and ultimately calls for the General Assembly to pass the NC PACES Act

The role of the representational entity in physical computing

We have developed abstraction/representation (AR) theory to answer the question “When does a physical system compute?” AR theory requires the existence of a representational entity (RE), but the vanilla theory does not explicitly include the RE in its definition of physical computing. Here we extend the theory by showing how the RE forms a linked complementary model to the physical computing model, and demonstrate its use in the case of intrinsic computing in a non-human RE: a bacterium

Information-flux approach to multiple-spin dynamics

We introduce and formalize the concept of information flux in a many-body register as the influence that the dynamics of a specific element receive from any other element of the register. By quantifying the information flux in a protocol, we can design the most appropriate initial state of the system and, noticeably, the distribution of coupling strengths among the parts of the register itself. The intuitive nature of this tool and its flexibility, which allow for easily manageable numerical approaches when analytic expressions are not straightforward, are greatly useful in interacting many-body systems such as quantum spin chains. We illustrate the use of this concept in quantum cloning and quantum state transfer and we also sketch its extension to non-unitary dynamics.Comment: 7 pages, 4 figures, RevTeX

Physical Computation, P/poly and P/log*

In this paper we give a framework for describing how abstract systems can be used to compute if no randomness or error is involved. Using this we describe a class of classical "physical" computation systems whose computational capabilities in polynomial time are equivalent to P/poly. We then extend our framework to describe how measurement and transformation times may vary depending on their input. Finally we describe two classes of classical "physical" computation systems in this new framework whose computational capabilities in polynomial time are equivalent to P/poly and P/log*

The Information Content of Systems in General Physical Theories

What kind of object is a quantum state? Is it an object that encodes an exponentially growing amount of information (in the size of the system) or more akin to a probability distribution? It turns out that these questions are sensitive to what we do with the information. For example, Holevo's bound tells us that n qubits only encode n bits of classical information but for certain communication complexity tasks there is an exponential separation between quantum and classical resources. Instead of just contrasting quantum and classical physics, we can place both within a broad landscape of physical theories and ask how non-quantum (and non-classical) theories are different from, or more powerful than quantum theory. For example, in communication complexity, certain (non-quantum) theories can trivialise all communication complexity tasks. In recent work [C. M. Lee and M. J. Hoban, Proc. Royal Soc. A 472 (2190), 2016], we showed that the immense power of the information content of states in general (non-quantum) physical theories is not limited to communication complexity. We showed that, in general physical theories, states can be taken as "advice" for computers in these theories and this advice allows the computers to easily solve any decision problem. Aaronson has highlighted the close connection between quantum communication complexity and quantum computations that take quantum advice, and our work gives further indications that this is a very general connection. In this work, we review the results in our previous work and discuss the intricate relationship between communication complexity and computers taking advice for general theories.Comment: In Proceedings PC 2016, arXiv:1606.0651