389 research outputs found
Cloning by positive maps in von Neumann algebras
We investigate cloning in the general operator algebra framework in arbitrary
dimension assuming only positivity instead of strong positivity of the cloning
operation, generalizing thus results obtained so far under that stronger assumption.
The weaker positivity assumption turns out quite natural when considering cloning in
the general C∗-algebra framework
The chain rule implies Tsirelson's bound: an approach from generalized mutual information
In order to analyze an information theoretical derivation of Tsirelson's
bound based on information causality, we introduce a generalized mutual
information (GMI), defined as the optimal coding rate of a channel with
classical inputs and general probabilistic outputs. In the case where the
outputs are quantum, the GMI coincides with the quantum mutual information. In
general, the GMI does not necessarily satisfy the chain rule. We prove that
Tsirelson's bound can be derived by imposing the chain rule on the GMI. We
formulate a principle, which we call the no-supersignalling condition, which
states that the assistance of nonlocal correlations does not increase the
capability of classical communication. We prove that this condition is
equivalent to the no-signalling condition. As a result, we show that
Tsirelson's bound is implied by the nonpositivity of the quantitative
difference between information causality and no-supersignalling.Comment: 23 pages, 8 figures, Added Section 2 and Appendix B, result
unchanged, Added reference
Anonymous quantum communication
We present the first protocol for the anonymous transmission of a quantum
state that is information-theoretically secure against an active adversary,
without any assumption on the number of corrupt participants. The anonymity of
the sender and receiver is perfectly preserved, and the privacy of the quantum
state is protected except with exponentially small probability. Even though a
single corrupt participant can cause the protocol to abort, the quantum state
can only be destroyed with exponentially small probability: if the protocol
succeeds, the state is transferred to the receiver and otherwise it remains in
the hands of the sender (provided the receiver is honest).Comment: 11 pages, to appear in Proceedings of ASIACRYPT, 200
On defining the Hamiltonian beyond quantum theory
Energy is a crucial concept within classical and quantum physics. An
essential tool to quantify energy is the Hamiltonian. Here, we consider how to
define a Hamiltonian in general probabilistic theories, a framework in which
quantum theory is a special case. We list desiderata which the definition
should meet. For 3-dimensional systems, we provide a fully-defined recipe which
satisfies these desiderata. We discuss the higher dimensional case where some
freedom of choice is left remaining. We apply the definition to example toy
theories, and discuss how the quantum notion of time evolution as a phase
between energy eigenstates generalises to other theories.Comment: Authors' accepted manuscript for inclusion in the Foundations of
Physics topical collection on Foundational Aspects of Quantum Informatio
Witnessing causal nonseparability
Our common understanding of the physical world deeply relies on the notion
that events are ordered with respect to some time parameter, with past events
serving as causes for future ones. Nonetheless, it was recently found that it
is possible to formulate quantum mechanics without any reference to a global
time or causal structure. The resulting framework includes new kinds of quantum
resources that allow performing tasks - in particular, the violation of causal
inequalities - which are impossible for events ordered according to a global
causal order. However, no physical implementation of such resources is known.
Here we show that a recently demonstrated resource for quantum computation -
the quantum switch - is a genuine example of "indefinite causal order". We do
this by introducing a new tool - the causal witness - which can detect the
causal nonseparability of any quantum resource that is incompatible with a
definite causal order. We show however that the quantum switch does not violate
any causal nequality.Comment: 15 + 12 pages, 5 figures. Published versio
Quartic quantum theory: an extension of the standard quantum mechanics
We propose an extended quantum theory, in which the number K of parameters
necessary to characterize a quantum state behaves as fourth power of the number
N of distinguishable states. As the simplex of classical N-point probability
distributions can be embedded inside a higher dimensional convex body of mixed
quantum states, one can further increase the dimensionality constructing the
set of extended quantum states. The embedding proposed corresponds to an
assumption that the physical system described in N dimensional Hilbert space is
coupled with an auxiliary subsystem of the same dimensionality. The extended
theory works for simple quantum systems and is shown to be a non-trivial
generalisation of the standard quantum theory for which K=N^2. Imposing certain
restrictions on initial conditions and dynamics allowed in the quartic theory
one obtains quadratic theory as a special case. By imposing even stronger
constraints one arrives at the classical theory, for which K=N.Comment: 30 pages in latex with 6 figures included; ver.2: several
improvements, new references adde
Joint system quantum descriptions arising from local quantumness
Bipartite correlations generated by non-signalling physical systems that
admit a finite-dimensional local quantum description cannot exceed the quantum
limits, i.e., they can always be interpreted as distant measurements of a
bipartite quantum state. Here we consider the effect of dropping the assumption
of finite dimensionality. Remarkably, we find that the same result holds
provided that we relax the tensor structure of space-like separated
measurements to mere commutativity. We argue why an extension of this result to
tensor representations seems unlikely
Geometric measure of entanglement and applications to bipartite and multipartite quantum states
The degree to which a pure quantum state is entangled can be characterized by
the distance or angle to the nearest unentangled state. This geometric measure
of entanglement, already present in a number of settings (see Shimony 1995 and
Barnum and Linden 2001), is explored for bipartite and multipartite pure and
mixed states. The measure is determined analytically for arbitrary two-qubit
mixed states and for generalized Werner and isotropic states, and is also
applied to certain multipartite mixed states. In particular, a detailed
analysis is given for arbitrary mixtures of three-qubit GHZ, W and inverted-W
states. Along the way, we point out connections of the geometric measure of
entanglement with entanglement witnesses and with the Hartree approximation
method.Comment: 13 pages, 11 figures, this is a combination of three previous
manuscripts (quant-ph/0212030, quant-ph/0303079, and quant-ph/0303158) made
more extensive and coherent. To appear in PR
Probability amplitude in quantum like games
Examples of games between two partners with mixed strategies, calculated by
the use of the probability amplitude are given. The first game is described by
the quantum formalism of spin one half system for which two noncommuting
observables are measured.
The second game corresponds to the spin one case.
Quantum logical orthocomplemented nondistributive lattices for these two
games are presented. Interference terms for the probability amplitudes are
analyzed by using so called contextual approach to probability (in the von
Mises frequency approach). We underline that our games are not based on using
of some microscopic systems. The whole scenario is macroscopic.Comment: Quantum-like model
On the lattice structure of probability spaces in quantum mechanics
Let C be the set of all possible quantum states. We study the convex subsets
of C with attention focused on the lattice theoretical structure of these
convex subsets and, as a result, find a framework capable of unifying several
aspects of quantum mechanics, including entanglement and Jaynes' Max-Ent
principle. We also encounter links with entanglement witnesses, which leads to
a new separability criteria expressed in lattice language. We also provide an
extension of a separability criteria based on convex polytopes to the infinite
dimensional case and show that it reveals interesting facets concerning the
geometrical structure of the convex subsets. It is seen that the above
mentioned framework is also capable of generalization to any statistical theory
via the so-called convex operational models' approach. In particular, we show
how to extend the geometrical structure underlying entanglement to any
statistical model, an extension which may be useful for studying correlations
in different generalizations of quantum mechanics.Comment: arXiv admin note: substantial text overlap with arXiv:1008.416
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