A Note on the correspondence between Qubit Quantum Operations and Special Relativity

We exploit a well-known isomorphism between complex hermitian $2\times 2$ matrices and $\mathbb{R}^4$, which yields a convenient real vector representation of qubit states. Because these do not need to be normalized we find that they map onto a Minkowskian future cone in $\mathbb{E}^{1,3}$, whose vertical cross-sections are nothing but Bloch spheres. Pure states are represented by light-like vectors, unitary operations correspond to special orthogonal transforms about the axis of the cone, positive operations correspond to pure Lorentz boosts. We formalize the equivalence between the generalized measurement formalism on qubit states and the Lorentz transformations of special relativity, or more precisely elements of the restricted Lorentz group together with future-directed null boosts. The note ends with a discussion of the equivalence and some of its possible consequences.Comment: 6 pages, revtex, v3: revised discussio

Composable security of delegated quantum computation

Delegating difficult computations to remote large computation facilities, with appropriate security guarantees, is a possible solution for the ever-growing needs of personal computing power. For delegated computation protocols to be usable in a larger context---or simply to securely run two protocols in parallel---the security definitions need to be composable. Here, we define composable security for delegated quantum computation. We distinguish between protocols which provide only blindness---the computation is hidden from the server---and those that are also verifiable---the client can check that it has received the correct result. We show that the composable security definition capturing both these notions can be reduced to a combination of several distinct "trace-distance-type" criteria---which are, individually, non-composable security definitions. Additionally, we study the security of some known delegated quantum computation protocols, including Broadbent, Fitzsimons and Kashefi's Universal Blind Quantum Computation protocol. Even though these protocols were originally proposed with insufficient security criteria, they turn out to still be secure given the stronger composable definitions.Comment: 37+9 pages, 13 figures. v3: minor changes, new references. v2: extended the reduction between composable and local security to include entangled inputs, substantially rewritten the introduction to the Abstract Cryptography (AC) framewor

Delegating Quantum Computation in the Quantum Random Oracle Model

A delegation scheme allows a computationally weak client to use a server's resources to help it evaluate a complex circuit without leaking any information about the input (other than its length) to the server. In this paper, we consider delegation schemes for quantum circuits, where we try to minimize the quantum operations needed by the client. We construct a new scheme for delegating a large circuit family, which we call "C+P circuits". "C+P" circuits are the circuits composed of Toffoli gates and diagonal gates. Our scheme is non-interactive, requires very little quantum computation from the client (proportional to input length but independent of the circuit size), and can be proved secure in the quantum random oracle model, without relying on additional assumptions, such as the existence of fully homomorphic encryption. In practice the random oracle can be replaced by an appropriate hash function or block cipher, for example, SHA-3, AES. This protocol allows a client to delegate the most expensive part of some quantum algorithms, for example, Shor's algorithm. The previous protocols that are powerful enough to delegate Shor's algorithm require either many rounds of interactions or the existence of FHE. The protocol requires asymptotically fewer quantum gates on the client side compared to running Shor's algorithm locally. To hide the inputs, our scheme uses an encoding that maps one input qubit to multiple qubits. We then provide a novel generalization of classical garbled circuits ("reversible garbled circuits") to allow the computation of Toffoli circuits on this encoding. We also give a technique that can support the computation of phase gates on this encoding. To prove the security of this protocol, we study key dependent message(KDM) security in the quantum random oracle model. KDM security was not previously studied in quantum settings.Comment: 41 pages, 1 figures. Update to be consistent with the proceeding versio

Impurity and quaternions in nonrelativistic scattering from a quantum memory

Models of quantum computing rely on transformations of the states of a quantum memory. We study mathematical aspects of a model proposed by Wu in which the memory state is changed via the scattering of incoming particles. This operation causes the memory content to deviate from a pure state, i.e. induces impurity. For nonrelativistic particles scattered from a two-state memory and sufficiently general interaction potentials in 1+1 dimensions, we express impurity in terms of quaternionic commutators. In this context, pure memory states correspond to null hyperbolic quaternions. In the case with point interactions, the scattering process amounts to appropriate rotations of quaternions in the frequency domain. Our work complements a previous analysis by Margetis and Myers (2006 J. Phys. A 39 11567--11581).Comment: 16 pages, no figure

Earth incorporated: centralization and variegation in the global company network

Over the past 20 years, a widening gulf has appeared between the increasingly internationalized financing arrangements of the world’s leading corporations, and the persistence of nationally compartmentalized approaches to the study of corporate control. In lieu of direct empirical evidence on corporate control at the global level, the most widespread assumption is that the globalization of ownership has taken the form of an expansion of arms-length, market-based arrangements traditionally prevailing in the Anglo-American economies. Here, however, we challenge this assumption, both empirically and conceptually. Empirically, we show that three quarters of the world’s 205 largest firms by sales are linked to a single global company network of concentrated (5%) ownership ties. This network has a hierarchically centralized organization, with a dominant “global network core” of US fund managers ringed by a more geographically diverse “state capitalist periphery.” Conceptually, we argue that the this architecture can be broadly explained through a Polanyian “variegated capitalist” model of contradictory market institutionalization, with the formation of the global company network actually a counterintuitive product of global financial marketization. In order to understand this process of network formation, however, it is necessary to extend Polanyi’s model of a double movement mediated through political interventions in the market, to incorporate Veblenian processes of evolutionary institutional change mediated through the market

Greening Capitalism? A Marxist Critique of Carbon Markets

Climate change is increasingly being recognized as a serious threat to dominant modes of social organization, inspiring suggestions that capitalism itself needs to be transformed if we are to ‘decarbonize’ the global economy. Since the Kyoto Protocol in 1997, carbon markets have emerged as the main politico-economic tools in global efforts to address climate change. Newell and Paterson (2010) have recently claimed that the embrace of carbon markets by financial and political elites constitutes a possible first step towards the transformation of current modes of capitalist organization into a new form of greener, more sustainable ‘climate capitalism.’ In this paper, we argue that the institutionalization of carbon markets does not, in fact, represent a move towards the radical transformation of capitalism, but is better understood as the most recent expression of ongoing trends of ecological commodification and expropriation, driving familiar processes of uneven and crisis-prone development. In this paper, we review four critical Marxist concepts: metabolic rift (Foster, 1999), capitalism as world ecology (Moore, 2011a), uneven development and accumulation through dispossession (Harvey, 2003, 2006), and sub-imperialism (Marini, 1972, 1977), developing a framework for a Marxist analysis of carbon markets. Our analysis shows that carbon markets form part of a longer historical development of global capitalism and its relation to nature. Carbon markets, we argue, serve as creative new modes of accumulation, but are unlikely to transform capitalist dynamics in ways that might foster a more sustainable global economy. Our analysis also elucidates, in particular, the role that carbon markets play in exacerbating uneven development within the Global South, as elites in emerging economies leverage carbon market financing to pursue new strategies of sub-imperial expansion. </jats:p

Securitization and financialization

Securitization and financialization are the main causes of the financial crisis. These two concepts explain not only Minsky’s financial instability hypothesis but also the off-balance-sheet operations represented by erivative products, which are closely related to mortgage loans. Financial intermediaries in need of liquidity did everything in their power so that the securitization of assets could have a life of its own in financial operations. This is a process that is endogenous to the development of financialization. Because said process was a violation of the monetary economy, it was necessary for central banks to intervene as “lenders of last resort” as well as to nationalize and restructure all the financial intermediaries