462 research outputs found
Quantum Control of Two-Qubit Entanglement Dissipation
We investigate quantum control of the dissipation of entanglement under
environmental decoherence. We show by means of a simple two-qubit model that
standard control methods - coherent or open-loop control - will not in general
prevent entanglement loss. However, we propose a control method utilising a
Wiseman-Milburn feedback/measurement control scheme which will effectively
negate environmental entanglement dissipation.Comment: 11 pages,4 figures, minor correctio
qBitcoin: A Peer-to-Peer Quantum Cash System
A decentralized online quantum cash system, called qBitcoin, is given. We
design the system which has great benefits of quantization in the following
sense. Firstly, quantum teleportation technology is used for coin transaction,
which prevents from the owner of the coin keeping the original coin data even
after sending the coin to another. This was a main problem in a classical
circuit and a blockchain was introduced to solve this issue. In qBitcoin, the
double-spending problem never happens and its security is guaranteed
theoretically by virtue of quantum information theory. Making a block is time
consuming and the system of qBitcoin is based on a quantum chain, instead of
blocks. Therefore a payment can be completed much faster than Bitcoin. Moreover
we employ quantum digital signature so that it naturally inherits properties of
peer-to-peer (P2P) cash system as originally proposed in Bitcoin.Comment: 11 pages, 2 figure
Hamilton-Jacobi Theory and Information Geometry
Recently, a method to dynamically define a divergence function for a
given statistical manifold by means of the
Hamilton-Jacobi theory associated with a suitable Lagrangian function
on has been proposed. Here we will review this
construction and lay the basis for an inverse problem where we assume the
divergence function to be known and we look for a Lagrangian function
for which is a complete solution of the associated
Hamilton-Jacobi theory. To apply these ideas to quantum systems, we have to
replace probability distributions with probability amplitudes.Comment: 8 page
Complementarity Endures: No Firewall for an Infalling Observer
We argue that the complementarity picture, as interpreted as a reference
frame change represented in quantum gravitational Hilbert space, does not
suffer from the "firewall paradox" recently discussed by Almheiri, Marolf,
Polchinski, and Sully. A quantum state described by a distant observer evolves
unitarily, with the evolution law well approximated by semi-classical field
equations in the region away from the (stretched) horizon. And yet, a classical
infalling observer does not see a violation of the equivalence principle, and
thus a firewall, at the horizon. The resolution of the paradox lies in careful
considerations on how a (semi-)classical world arises in unitary quantum
mechanics describing the whole universe/multiverse.Comment: 11 pages, 1 figure; clarifications and minor revisions; v3: a small
calculation added for clarification; v4: some corrections, conclusion
unchange
Generalised Compositional Theories and Diagrammatic Reasoning
This chapter provides an introduction to the use of diagrammatic language, or
perhaps more accurately, diagrammatic calculus, in quantum information and
quantum foundations. We illustrate the use of diagrammatic calculus in one
particular case, namely the study of complementarity and non-locality, two
fundamental concepts of quantum theory whose relationship we explore in later
part of this chapter.
The diagrammatic calculus that we are concerned with here is not merely an
illustrative tool, but it has both (i) a conceptual physical backbone, which
allows it to act as a foundation for diverse physical theories, and (ii) a
genuine mathematical underpinning, permitting one to relate it to standard
mathematical structures.Comment: To appear as a Springer book chapter chapter, edited by G.
Chirabella, R. Spekken
The problem of mutually unbiased bases in dimension 6
We outline a discretization approach to determine the
maximal number of mutually unbiased bases in dimension 6. We
describe the basic ideas and introduce the most important definitions
to tackle this famous open problem which has been open for
the last 10 years. Some preliminary results are also listed
Semantics for first-order affine inductive data types via slice categories
Affine type systems are substructural type systems where copying of
information is restricted, but discarding of information is permissible at all
types. Such type systems are well-suited for describing quantum programming
languages, because copying of quantum information violates the laws of quantum
mechanics. In this paper, we consider a first-order affine type system with
inductive data types and present a novel categorical semantics for it. The most
challenging aspect of this interpretation comes from the requirement to
construct appropriate discarding maps for our data types which might be defined
by mutual/nested recursion. We show how to achieve this for all types by taking
models of a first-order linear type system whose atomic types are discardable
and then presenting an additional affine interpretation of types within the
slice category of the model with the tensor unit. We present some concrete
categorical models for the language ranging from classical to quantum. Finally,
we discuss potential ways of dualising and extending our methods and using them
for interpreting coalgebraic and lazy data types
Information-theoretic postulates for quantum theory
Why are the laws of physics formulated in terms of complex Hilbert spaces?
Are there natural and consistent modifications of quantum theory that could be
tested experimentally? This book chapter gives a self-contained and accessible
summary of our paper [New J. Phys. 13, 063001, 2011] addressing these
questions, presenting the main ideas, but dropping many technical details. We
show that the formalism of quantum theory can be reconstructed from four
natural postulates, which do not refer to the mathematical formalism, but only
to the information-theoretic content of the physical theory. Our starting point
is to assume that there exist physical events (such as measurement outcomes)
that happen probabilistically, yielding the mathematical framework of "convex
state spaces". Then, quantum theory can be reconstructed by assuming that (i)
global states are determined by correlations between local measurements, (ii)
systems that carry the same amount of information have equivalent state spaces,
(iii) reversible time evolution can map every pure state to every other, and
(iv) positivity of probabilities is the only restriction on the possible
measurements.Comment: 17 pages, 3 figures. v3: some typos corrected and references updated.
Summarizes the argumentation and results of arXiv:1004.1483. Contribution to
the book "Quantum Theory: Informational Foundations and Foils", Springer
Verlag (http://www.springer.com/us/book/9789401773027), 201
Measurements in two bases are sufficient for certifying high-dimensional entanglement
High-dimensional encoding of quantum information provides a promising method
of transcending current limitations in quantum communication. One of the
central challenges in the pursuit of such an approach is the certification of
high-dimensional entanglement. In particular, it is desirable to do so without
resorting to inefficient full state tomography. Here, we show how carefully
constructed measurements in two bases (one of which is not orthonormal) can be
used to faithfully and efficiently certify bipartite high-dimensional states
and their entanglement for any physical platform. To showcase the practicality
of this approach under realistic conditions, we put it to the test for photons
entangled in their orbital angular momentum. In our experimental setup, we are
able to verify 9-dimensional entanglement for a pair of photons on a
11-dimensional subspace each, at present the highest amount certified without
any assumptions on the state.Comment: 11+14 pages, 2+7 figure
Operator entanglement of two-qubit joint unitary operations revisited: Schmidt number approach
Operator entanglement of two-qubit joint unitary operations is revisited.
Schmidt number is an important attribute of a two-qubit unitary operation, and
may have connection with the entanglement measure of the unitary operator. We
found the entanglement measure of two-qubit unitary operators is classified by
the Schmidt number of the unitary operators. The exact relation between the
operator entanglement and the parameters of the unitary operator is clarified
too.Comment: To appear in the Brazilian Journal of Physic
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