Causal Boxes: Quantum Information-Processing Systems Closed under Composition

Portmann, Christopher; Matt, Christian; Maurer, Ueli; Renner, Renato; Tackmann, Björn

doi:10.1109/tit.2017.2676805

Cited by 50 publications

(107 citation statements)

References 66 publications

(266 reference statements)

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“…In this work we introduce a framework for modelling composable cryptographic security in the presence of classical, quantum and no-signalling adversaries, and apply it to prove new positive and negative results in relativistic quantum cryptography. We do this by modelling the abstract information-processing systems of the Abstract Cryptography framework [4] as Causal Boxes [22], which we instantiate with Minkowski space-time. Our framework can also be applied to situations where agents exchange a superposition of different numbers of messages in a superposition of orders in time, and provides an operational formalism for studying indefinite causal structures.…”

Section: Overview and Scope Of Our Resultsmentioning

confidence: 99%

“…Superpositions of causal orders. A unique feature of the causal boxes formalism [22], is that it can model superpositions of messages exchanged in a superposition of orders in (space-)time (e.g. the quantum switch [31]) by assigning different space-time stamps (or superpositions thereof) to different messages.…”

Section: Discussionmentioning

confidence: 99%

“…In this section we introduce the building blocks of the framework-resources, converters (e.g. protocols) and a notion of distance (distinguishability) between resources-and in section 2.2 we explain how these objects are instantiated with Causal Boxes [22].…”

Section: Composable Security: the Abstract Cryptography Framework [4]mentioning

confidence: 99%

“…Causal boxes [22] are a model of information-processing systems which may interact with each other in arbitrary ways, so long as they respect causality (figure 5(a)). In broad lines, a causal box F is a system with input and output wires which may carry quantum or classical information.…”

Section: Cryptography In Relativistic Settings: the Causal Boxes Frammentioning

confidence: 99%

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Composable security in relativistic quantum cryptography

2019

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Relativistic protocols have been proposed to overcome certain impossibility results in classical and quantum cryptography. In such a setting, one takes the location of honest players into account, and uses the signalling limit given by the speed of light to constraint the abilities of dishonest agents. However, composing such protocols with each other to construct new cryptographic resources is known to be insecure in some cases. To make general statements about such constructions, a composable framework for modelling cryptographic security in Minkowski space is required. Here, we introduce a framework for performing such a modular security analysis of classical and quantum cryptographic schemes in Minkowski space. As an application, we show that (1) fair and unbiased coin flipping can be constructed from a simple resource called channel with delay; (2) biased coin flipping, bit commitment and channel with delay through any classical, quantum or post-quantum relativistic protocols are all impossible without further setup assumptions; (3) it is impossible to securely increase the delay of a channel, given several short-delay channels as ingredients. Results (1) and (3) imply in particular the non-composability of existing relativistic bit commitment and coin flipping protocols.

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Section: Overview and Scope Of Our Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Composable Security: the Abstract Cryptography Framework [4]mentioning

confidence: 99%

Section: Cryptography In Relativistic Settings: the Causal Boxes Frammentioning

confidence: 99%

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Composable security in relativistic quantum cryptography

2019

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“…[6] researched Classical Information Storage in an n-Level Quantum System, and [7] implied a certifying single-system steering for quantum-information processing. Then, [8] illustrated causal boxes: quantum information-processing systems closed under composition, and [9] gave the dynamics of entanglement and quantum Fisher information for N-level atomic system under intrinsic decoherence. Apparently, the entanglement activity brought more uncertainty into quantum information.…”

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confidence: 99%

An Entropy Measurement Method of Quantum Information System under Uncertain Environment

Li¹,

Deng²,

Zhou³

et al. 2018

IJIS

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Under uncertain environment, it is very difficult to measure the entropy of quantum information system, because there is no effective method to model the randomness. First, different from the traditional classic uncertainty, a quantum uncertain model is proposed to simulate a quantum information system under uncertain environment, and to simplify the entropy measurement of quantum information system. Second, different from the classic random seed under uncertain environment which is often called as pseudo-random number, here the quantum random is employed to provide us a true random model for the entropy of quantum information system. Third, the complex interaction and entangling activity of uncertain factors of quantum information is modeled as quantum binary instead of classic binary, which can help us to evaluate the entropy of uncertain environment, to analyze the entropy divergence in quantum information system. This work presents a non-classic risk factor measurement for quantum information system and a helpful entropy measurement.

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Causal and Causally Separable Processes

Giarmatzi¹

2019

Rethinking Causality in Quantum Mechanics

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The idea that events are equipped with a partial causal order is central to our understanding of physics in the tested regimes: given two pointlike events A and B, either A is in the causal past of B, B is in the causal past of A, or A and B are space-like separated. Operationally, the meaning of these order relations corresponds to constraints on the possible correlations between experiments performed in the vicinities of the respective events: if A is in the causal past of B, an experimenter at A could signal to an experimenter at B but not the other way around, while if A and B are space-like separated, no signaling is possible in either direction. In the context of a concrete physical theory, the correlations compatible with a given causal configuration may obey further constraints. For instance, space-like correlations in quantum mechanics arise from local measurements on joint quantum states, while time-like correlations are established via quantum channels. Similarly to other variables, however, the causal order of a set of events could be random, and little is understood about the constraints that causality implies in this case. A main difficulty concerns the fact that the order of events can now generally depend on the operations performed at the locations of these events, since, for instance, an operation at A could influence the order in which B and C occur in A's future. So far, no formal theory of causality compatible with such dynamical causal order has been developed. Apart from being of fundamental interest in the context of inferring causal relations, such a theory is imperative for understanding recent suggestions that the causal order of events in quantum mechanics can be indefinite. Here, we develop such a theory in the general multipartite case. Starting from a background-independent definition of causality, we derive an iteratively formulated canonical decomposition of multipartite causal correlations. For a fixed number of settings and outcomes for each party, these correlations form a polytope whose facets define causal inequalities. The case of quantum correlations in this paradigm is captured by the process matrix formalism. We investigate the link between causality and the closely related notion of causal separability of quantum processes, which we here define rigorously in analogy with the link between Bell locality and separability of quantum states. We show that causality and causal separability are not equivalent in general by giving an example of a physically admissible tripartite quantum process that is causal but not causally separable. We also show that there are causally separable quantum processes that become non-causal if extended by supplying the parties with entangled ancillas. This motivates the concepts of extensibly causal and extensibly causally separable (ECS) processes, for which the respective property remains invariant under extension. We characterize the class of ECS quantum processes in the tripartite case via simple conditions on the form of the process matrix. W...

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Causal Boxes: Quantum Information-Processing Systems Closed under Composition

Cited by 50 publications

References 66 publications

Composable security in relativistic quantum cryptography

Composable security in relativistic quantum cryptography

An Entropy Measurement Method of Quantum Information System under Uncertain Environment

Causal and Causally Separable Processes

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