978 research outputs found
A Note on the correspondence between Qubit Quantum Operations and Special Relativity
We exploit a well-known isomorphism between complex hermitian
matrices and , 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 , 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
A Simple n-Dimensional Intrinsically Universal Quantum Cellular Automaton
We describe a simple n-dimensional quantum cellular automaton (QCA) capable
of simulating all others, in that the initial configuration and the forward
evolution of any n-dimensional QCA can be encoded within the initial
configuration of the intrinsically universal QCA. Several steps of the
intrinsically universal QCA then correspond to one step of the simulated QCA.
The simulation preserves the topology in the sense that each cell of the
simulated QCA is encoded as a group of adjacent cells in the universal QCA.Comment: 13 pages, 7 figures. In Proceedings of the 4th International
Conference on Language and Automata Theory and Applications (LATA 2010),
Lecture Notes in Computer Science (LNCS). Journal version: arXiv:0907.382
The Conal representation of Quantum States and Non Trace-Preserving Quantum Operations
We represent generalized density matrices of a -complex dimensional
quantum system as a subcone of a real pointed cone of revolution in
, or indeed a Minkowskian cone in .
Generalized pure states correspond to certain future-directed light-like
vectors of . This extension of the Generalized Bloch
Sphere enables us to cater for non-trace-preserving quantum operations, and in
particluar to view the per-outcome effects of generalized measurements. We show
that these consist of the product of an orthogonal transform about the axis of
the cone of revolution and a positive real linear transform. We give detailed
formulae for the one qubit case and express the post-measurement states in
terms of the initial state vectors and measurement vectors. We apply these
results in order to find the information gain versus disturbance tradeoff in
the case of two equiprobable pure states. Thus we recover Fuchs and Peres'
formula in an elegant manner.Comment: 11 pages, revtex, v3: some typos correcte
Call-by-value non-determinism in a linear logic type discipline
We consider the call-by-value lambda-calculus extended with a may-convergent
non-deterministic choice and a must-convergent parallel composition. Inspired
by recent works on the relational semantics of linear logic and non-idempotent
intersection types, we endow this calculus with a type system based on the
so-called Girard's second translation of intuitionistic logic into linear
logic. We prove that a term is typable if and only if it is converging, and
that its typing tree carries enough information to give a bound on the length
of its lazy call-by-value reduction. Moreover, when the typing tree is minimal,
such a bound becomes the exact length of the reduction
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
Entanglement of distant flux qubits mediated by non-classical electromagnetic field
The mechanism for entanglement of two flux qubits each interacting with a
single mode electromagnetic field is discussed. By performing a Bell state
measurements (BSM) on photons we find the two qubits in an entangled state
depending on the system parameters. We discuss the results for two initial
states and take into consideration the influence of decoherence.Comment: 20 pages, 8 figure
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
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
Securitization and financialization
Securitization and financialization are the main causes of the financial crisis. These two concepts explain not only Minskyâs 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 âlenders of last resortâ as well as to nationalize and restructure all the financial intermediaries
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 âdecarbonizeâ 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 âclimate capitalism.â 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
- âŠ