16 research outputs found
Spacetime-constrained oblivious transfer
In 1-out-of-2 oblivious transfer (OT), Alice inputs numbers x_0, x_1, Bob
inputs a bit b and outputs x_b. Secure OT requires that Alice and Bob learn
nothing about b and x_{\bar{b}}, respectively. We define spacetime-constrained
oblivious transfer (SCOT) as OT in Minkowski spacetime in which Bob must output
x_b within R_b, where R_0 and R_1 are fixed spacelike separated spacetime
regions. We show that unconditionally secure SCOT is impossible with classical
protocols in Minkowski (or Galilean) spacetime, or with quantum protocols in
Galilean spacetime. We describe a quantum SCOT protocol in Minkowski spacetime,
and we show it unconditionally secure.Comment: Improved theorem on the impossibility of classical SCOT to allow for
small errors. Figure added and discussion extended in response to referee
comments. Protocol and security proof unaltered. Final versio
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Unconditionally secure relativistic multi-party biased coin flipping and die rolling.
We introduce relativistic multi-party biased die-rolling protocols, generalizing coin flipping to M â„ 2 parties and to N â„ 2 outcomes for any chosen outcome biases and show them unconditionally secure. Our results prove that the most general random secure multi-party computation, where all parties receive the output and there is no secret input by any party, can be implemented with unconditional security. Our protocols extend Kent's (Kent A. 1999 Phys. Rev. Lett. 83, 5382) two-party unbiased coin-flipping protocol, do not require any quantum communication, are practical to implement with current technology and to our knowledge are the first multi-party relativistic cryptographic protocols
Hyperdense coding and superadditivity of classical capacities in hypersphere theories
In quantum superdense coding, two parties previously sharing entanglement can
communicate a two bit message by sending a single qubit. We study this feature
in the broader framework of general probabilistic theories. We consider a
particular class of theories in which the local state space of the
communicating parties corresponds to Euclidean hyperballs of dimension n (the
case n = 3 corresponds to the Bloch ball of quantum theory). We show that a
single n-ball can encode at most one bit of information, independently of n. We
introduce a bipartite extension of such theories for which there exist dense
coding protocols such that log_2 (n+1) bits are communicated if entanglement is
previously shared by the communicating parties. For n > 3, these protocols are
more powerful than the quantum one, because more than two bits are communicated
by transmission of a system that locally encodes at most one bit. We call this
phenomenon hyperdense coding. Our hyperdense coding protocols imply
superadditive classical capacities: two entangled systems can encode log_2
(n+1) > 2 bits, even though each system individually encodes at most one bit.
In our examples, hyperdense coding and superadditivity of classical capacities
come at the expense of violating tomographic locality or dynamical continuous
reversibility.Comment: Expanded discussion in response to referee comments. Accepted for
publication in New Journal of Physic
Practical and unconditionally secure spacetime-constrained oblivious transfer
Spacetime-constrained oblivious transfer (SCOT) extends the fundamental
primitive of oblivious transfer to Minkowski space. SCOT and location oblivious
data transfer (LODT) are the only known cryptographic tasks with classical
inputs and outputs for which unconditional security needs both quantum theory
and relativity. We give an unconditionally secure SCOT protocol that,
contrasting previous SCOT and LODT protocols, is practical to implement with
current technology, where distant agents need only communicate classical
information, while quantum communication occurs at a single location. We also
show that our SCOT protocol can be used to implement unconditionally secure
quantum relativistic bit commitment.Comment: Accepted manuscrip
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Quantum information, Bell inequalities and the no-signalling principle
This PhD thesis contains a general introduction and three main chapters. Chapter 2 investigates Bell inequalities that generalize the CHSH and Braunstein-Caves inequalities. Chapter 3 shows a derivation of an upper bound on the success probability of a class of quantum teleportation protocols, denoted as port-based teleportation, from the no-cloning theorem and the no-signalling principle. Chapter 4 introduces the principle of quantum information causality.
Chapter 2 considers the predictions of quantum theory and local hidden variable theories (LHVT) for the correlations obtained by measuring a pair of qubits by projections defined by randomly chosen axes separated by a given angle Ξ. The predictions of LHVT correspond to binary colourings of the Bloch sphere with antipodal points oppositely coloured. We show a Bell inequality for all Ξ, which generalizes the CHSH and the Braunstein-Caves inequalities in the sense that the measurement choices are not restricted to be in a finite set, but are constrained only by the angle Ξ. We motivate and explore the hypothesis that for a continuous range of Ξ > 0, the maximum correlation (anticorrelation) is obtained by assigning to one qubit the colouring with one hemisphere black and the other white, and assigning the same (reverse) colouring to the other qubit. We describe numerical tests that are consistent with this hypothesis and bound the range of Ξ.
Chapter 3 shows a derivation of an upper bound on the success probability of port-based teleportation from the no-cloning theorem and the no-signalling principle.
Chapter 4 introduces the principle of quantum information causality, a quantum version of the information causality principle. The quantum information causality principle states the maximum amount of quantum information that a transmitted quantum system can communicate as a function of its dimension, independently of any quantum physical resources previously shared by the communicating parties. These principles reduce to the no-signalling principle if no systems are transmitted. We present a new quantum information task, the quantum information causality game, whose success probability is upper bounded by the new principle, and show that an optimal strategy to perform it combines the quantum teleportation and superdense coding protocols with a task that has classical inputs.This work was supported by CONACYT MĂ©xico