Theoretical framework for quantum networks

Chiribella, Giulio; D’Ariano, Giacomo Mauro; Perinotti, Paolo

doi:10.1103/physreva.80.022339

Cited by 473 publications

(925 citation statements)

References 30 publications

(47 reference statements)

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“…In this section we introduce the necessary notation and review the general theory of Quantum Networks, as developed in [14,15]. Let us first recall the ChoiJamio lkowsky isomorphism.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

Cloning of a quantum measurement

et al. 2011

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We analyze quantum algorithms for cloning of a quantum measurement. Our aim is to mimic two uses of a device performing an unknown von Neumann measurement with a single use of the device. When the unknown device has to be used before the bipartite state to be measured is available we talk about 1 → 2 learning of the measurement, otherwise the task is called 1 → 2 cloning of a measurement. We perform the optimization for both learning and cloning for arbitrary dimension of the Hilbert space. For 1 → 2 cloning we also propose a simple quantum network that realizes the optimal strategy.

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“…In this section we introduce the necessary notation and review the general theory of Quantum Networks, as developed in [14,15]. Let us first recall the ChoiJamio lkowsky isomorphism.…”

Section: Preliminary Conceptsmentioning

confidence: 99%

Cloning of a quantum measurement

et al. 2011

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“…From different points of view Refs. [33,61,62] studied the structure of multipartite causal channels, showing that they can always be realized as sequences of channels with memory. In this Section we show that all these results, originally obtained in quantum mechanics, actually hold in any causal theory with purification.…”

Section: Causally Ordered Channels and Channels With Memorymentioning

confidence: 99%

“…A concrete example of non-causal theory is the theory studied in Refs. [32,33], where the states are quantum operations, and the transformations are "supermaps" transforming quantum operations into quantum operations. In this case, transforming a "state" means inserting the corresponding quantum operation in a larger circuit, and the sequence of two such transformations is not a causal sequence.…”

Section: A Definition and Main Propertiesmentioning

confidence: 99%

Probabilistic theories with purification

2010

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We investigate general probabilistic theories in which every mixed state has a purification, unique up to reversible channels on the purifying system. We show that the purification principle is equivalent to the existence of a reversible realization of every physical process, that is, to the fact that every physical process can be regarded as arising from a reversible interaction of the system with an environment, which is eventually discarded. From the purification principle we also construct an isomorphism between transformations and bipartite states that possesses all structural properties of the Choi-Jamio lkowski isomorphism in quantum theory. Such an isomorphism allows one to prove most of the basic features of quantum theory, like e.g. existence of pure bipartite states giving perfect correlations in independent experiments, no information without disturbance, no joint discrimination of all pure states, no cloning, teleportation, no programming, no bit commitment, complementarity between correctable channels and deletion channels, characterization of entanglement-breaking channels as measure-and-prepare channels, and others, without resorting to the mathematical framework of Hilbert spaces.

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“…They consist of wires, representing quantum systems, which connect boxes, representing quantum operations. While for quantum circuits, the order of the operations is fixed [14], situations where the order of operations is not well-defined are readily represented in the process matrix formalism [3], which can be thought of as a generalization of the quantum circuit formalism. We will briefly introduce the main elements of the formalism; a more detailed introduction to it can be found in [7].…”

Section: Causal Nonseparability and Causal Inequalitiesmentioning

confidence: 99%

Causally nonseparable processes admitting a causal model

2016

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A recent framework of quantum theory with no global causal order predicts the existence of 'causally nonseparable' processes. Some of these processes produce correlations incompatible with any causal order (they violate so-called 'causal inequalities' analogous to Bell inequalities) while others do not (they admit a 'causal model' analogous to a local model). Here we show for the first time that bipartite causally nonseparable processes with a causal model exist, and give evidence that they have no clear physical interpretation. We also provide an algorithm to generate processes of this kind and show that they have nonzero measure in the set of all processes. We demonstrate the existence of processes which stop violating causal inequalities but are still causally nonseparable when mixed with a certain amount of 'white noise'. This is reminiscent of the behavior of Werner states in the context of entanglement and nonlocality. Finally, we provide numerical evidence for the existence of causally nonseparable processes which have a causal model even when extended with an entangled state shared among the parties.

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Theoretical framework for quantum networks

Cited by 473 publications

References 30 publications

Cloning of a quantum measurement

Cloning of a quantum measurement

Probabilistic theories with purification

Causally nonseparable processes admitting a causal model

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