7,023 research outputs found
Continuous Time and Consistent Histories
We discuss the use of histories labelled by a continuous time in the approach
to consistent-histories quantum theory in which propositions about the history
of the system are represented by projection operators on a Hilbert space. This
extends earlier work by two of us \cite{IL95} where we showed how a continuous
time parameter leads to a history algebra that is isomorphic to the canonical
algebra of a quantum field theory. We describe how the appropriate
representation of the history algebra may be chosen by requiring the existence
of projection operators that represent propositions about time average of the
energy. We also show that the history description of quantum mechanics contains
an operator corresponding to velocity that is quite distinct from the momentum
operator. Finally, the discussion is extended to give a preliminary account of
quantum field theory in this approach to the consistent histories formalism.Comment: Typeset in RevTe
Localization and its consequences for quantum walk algorithms and quantum communication
The exponential speed-up of quantum walks on certain graphs, relative to
classical particles diffusing on the same graph, is a striking observation. It
has suggested the possibility of new fast quantum algorithms. We point out here
that quantum mechanics can also lead, through the phenomenon of localization,
to exponential suppression of motion on these graphs (even in the absence of
decoherence). In fact, for physical embodiments of graphs, this will be the
generic behaviour. It also has implications for proposals for using spin
networks, including spin chains, as quantum communication channels.Comment: 4 pages, 1 eps figure. Updated references and cosmetic changes for v
Optimal Entanglement Enhancement for Mixed States
We consider the actions of protocols involving local quantum operations and
classical communication (LQCC) on a single system consisting of two separated
qubits. We give a complete description of the orbits of the space of states
under LQCC and characterise the representatives with maximal entanglement of
formation. We thus obtain a LQCC entanglement concentration protocol for a
single given state (pure or mixed) of two qubits which is optimal in the sense
that the protocol produces, with non-zero probability, a state of maximal
possible entanglement of formation. This defines a new entanglement measure,
the maximum extractable entanglement.Comment: Final version: to appear in Phys. Rev. Let
Continuous Histories and the History Group in Generalised Quantum Theory
We treat continuous histories within the histories approach to generalised
quantum mechanics. The essential tool is the `history group': the analogue,
within the generalised history scheme, of the canonical group of single-time
quantum mechanics.Comment: 25 page
Information-entropy and the space of decoherence functions in generalised quantum theory
In standard quantum theory, the ideas of information-entropy and of pure states are closely linked. States are represented by density matrices on a Hilbert space and the information-entropy is minimised on pure states (pure states are the vertices of the boundary of the convex set of states). The space of decoherence functions in the consistent histories approach to generalised quantum theory is also a convex set. However, by showing that every decoherence function can be written as a convex combination of two other decoherence functions we demonstrate that there are no `pure' decoherence functions. The main content of the paper is a new notion of information-entropy in generalised quantum mechanics which is applicable in contexts in which there is no a priori notion of time. Information-entropy is defined first on consistent sets and then we show that it decreases upon refinement of the consistent set. This information-entropy suggests an intrinsic way of giving a consistent set selection criterion
Equilibration of quantum systems and subsystems
We unify two recent results concerning equilibration in quantum theory. We
first generalise a proof of Reimann [PRL 101,190403 (2008)], that the
expectation value of 'realistic' quantum observables will equilibrate under
very general conditions, and discuss its implications for the equilibration of
quantum systems. We then use this to re-derive an independent result of Linden
et. al. [PRE 79, 061103 (2009)], showing that small subsystems generically
evolve to an approximately static equilibrium state. Finally, we consider
subspaces in which all initial states effectively equilibrate to the same
state.Comment: 5 page
Optimal simulation of two-qubit Hamiltonians using general local operations
We consider the simulation of the dynamics of one nonlocal Hamiltonian by
another, allowing arbitrary local resources but no entanglement nor classical
communication. We characterize notions of simulation, and proceed to focus on
deterministic simulation involving one copy of the system. More specifically,
two otherwise isolated systems and interact by a nonlocal Hamiltonian
. We consider the achievable space of Hamiltonians such
that the evolution can be simulated by the interaction
interspersed with local operations. For any dimensions of and , and any
nonlocal Hamiltonians and , there exists a scale factor such that
for all times the evolution can be simulated by acting for
time interspersed with local operations. For 2-qubit Hamiltonians and
, we calculate the optimal and give protocols achieving it. The optimal
protocols do not require local ancillas, and can be understood geometrically in
terms of a polyhedron defined by a partial order on the set of 2-qubit
Hamiltonians.Comment: (1) References to related work, (2) protocol to simulate one
two-qudit Hamiltonian with another, and (3) other related results added. Some
proofs are simplifie
Characterizing the local vectorial electric field near an atom chip using Rydberg state spectroscopy
We use the sensitive response to electric fields of Rydberg atoms to
characterize all three vector components of the local electric field close to
an atom-chip surface. We measured Stark-Zeeman maps of and Rydberg
states using an elongated cloud of ultracold Rubidium atoms ( K)
trapped magnetically m from the chip surface. The spectroscopy of
states yields a calibration for the generated local electric field at the
position of the atoms. The values for different components of the field are
extracted from the more complex response of states to the combined electric
and magnetic fields. From the analysis we find residual fields in the two
uncompensated directions of V/cm and V/cm
respectively. This method also allows us to extract a value for the relevant
field gradient along the long axis of the cloud. The manipulation of electric
fields and the magnetic trapping are both done using on-chip wires, making this
setup a promising candidate to observe Rydberg-mediated interactions on a chip.Comment: 8 pages, 5 figure
Probabilistic teleportation and entanglement matching
Teleportation may be taken as sending and extracting quantum information
through quantum channels. In this report, it is shown that to get the maximal
probability of exact teleportation through partially entangled quantum
channels, the sender (Alice) need only to operate a measurement which satisfy
an ``entanglement matching'' to this channel. An optimal strategy is also
provided for the receiver (Bob) to extract the quantum information by adopting
general evolutions.Comment: 3.5 pages, No figure
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