94 research outputs found
Couplers for Non-Locality Swapping
Studying generalized non-local theories brings insight to the foundations of
quantum mechanics. Here we focus on non-locality swapping, the analogue of
quantum entanglement swapping. In order to implement such a protocol, one needs
a coupler that performs the equivalent of quantum joint measurements on
generalized `box-like' states. Establishing a connection to Bell inequalities,
we define consistent couplers for theories containing an arbitrary amount of
non-locality, which leads us to introduce the concepts of perfect and minimal
couplers. Remarkably, Tsirelson's bound for quantum non-locality naturally
appears in our study.Comment: 16 pages, 3 figure
Tsirelson's bound and supersymmetric entangled states
A superqubit, belonging to a -dimensional super-Hilbert space,
constitutes the minimal supersymmetric extension of the conventional qubit. In
order to see whether superqubits are more nonlocal than ordinary qubits, we
construct a class of two-superqubit entangled states as a nonlocal resource in
the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the
result depends on how we extract real probabilities and we examine three
choices of map: (1) DeWitt (2) Trigonometric (3) Modified Rogers. In cases (1)
and (2) the winning probability reaches the Tsirelson bound
of standard quantum mechanics. Case (3)
crosses Tsirelson's bound with . Although all states used
in the game involve probabilities lying between 0 and 1, case (3) permits other
changes of basis inducing negative transition probabilities.Comment: Updated to match published version. Minor modifications. References
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Generalizations of Boxworld
Boxworld is a toy theory that can generate extremal nonlocal correlations
known as PR boxes. These have been well established as an important tool to
examine general nonlocal correlations, even beyond the correlations that are
possible in quantum theory. We modify boxworld to include new features. The
first modification affects the construction of joint systems such that the new
theory allows entangled measurements as well as entangled states in contrast to
the standard version of boxworld. The extension to multipartite systems and the
consequences for entanglement swapping are analysed. Another modification
provides continuous transitions between classical probability theory and
boxworld, including the algebraic expression for the maximal CHSH violation as
a function of the transition parameters.Comment: In Proceedings QPL 2011, arXiv:1210.029
Deriving the Qubit from Entropy Principles
The Heisenberg uncertainty principle is one of the most famous features of
quantum mechanics. However, the non-determinism implied by the Heisenberg
uncertainty principle --- together with other prominent aspects of quantum
mechanics such as superposition, entanglement, and nonlocality --- poses deep
puzzles about the underlying physical reality, even while these same features
are at the heart of exciting developments such as quantum cryptography,
algorithms, and computing. These puzzles might be resolved if the mathematical
structure of quantum mechanics were built up from physically interpretable
axioms, but it is not. We propose three physically-based axioms which together
characterize the simplest quantum system, namely the qubit. Our starting point
is the class of all no-signaling theories. Each such theory can be regarded as
a family of empirical models, and we proceed to associate entropies, i.e.,
measures of information, with these models. To do this, we move to phase space
and impose the condition that entropies are real-valued. This requirement,
which we call the Information Reality Principle, arises because in order to
represent all no-signaling theories (including quantum mechanics itself) in
phase space, it is necessary to allow negative probabilities (Wigner [1932]).
Our second and third principles take two important features of quantum
mechanics and turn them into deliberately chosen physical axioms. One axiom is
an Uncertainty Principle, stated in terms of entropy. The other axiom is an
Unbiasedness Principle, which requires that whenever there is complete
certainty about the outcome of a measurement in one of three mutually
orthogonal directions, there must be maximal uncertainty about the outcomes in
each of the two other directions.Comment: 8 pages, 3 figure
Probabilistic models on contextuality scenarios
We introduce a framework to describe probabilistic models in Bell
experiments, and more generally in contextuality scenarios. Such a scenario is
a hypergraph whose vertices represent elementary events and hyperedges
correspond to measurements. A probabilistic model on such a scenario associates
to each event a probability, in such a way that events in a given measurement
have a total probability equal to one. We discuss the advantages of this
framework, like the unification of the notions of contexuality and nonlocality,
and give a short overview of results obtained elsewhere.Comment: In Proceedings QPL 2013, arXiv:1412.791
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