Quantum nonlocality is possible in the triangle network with no inputs and binary outputs, which is the smallest such scenario by number of variables and outcomes.
Transforming quantum operations: quantum supermaps
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We introduce the concept of quantum supermap, describing the most general transformation that maps an input quantum operation into an output quantum operation. Since quantum operations include as special cases quantum states, effects, and measurements, quantum supermaps describe all possible transformations between elementary quantum objects (quantum systems as well as quantum devices). After giving the axiomatic definition of supermap, we prove a realization theorem, which shows that any supermap can be physically implemented as a simple quantum circuit. Applications to quantum programming, cloning, discrimination, estimation, information-disturbance trade-off, and tomography of channels are outlined.
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Presents a poly-complexity quantum circuit implementing the random dilation superchannel for parallel channel queries, with approximate sequential extension, a no-go theorem for exact sequential dilation, and an application to exponentially improved channel storage-retrieval.
Defines polyslot pslot[C] and srep[C] constructions on symmetric monoidal categories that reconstruct unitary supermaps and forbid time-loops in composition, with equivalence shown on path-contraction groupoids.
Higher-order quantum map types form a distributive lattice of regular subtypes where signalling relations are determined by type function evaluations and structure poset rank parity, with normal forms derived from maximal chains.
A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.
In bipartite processes and multipartite quantum circuits with quantum control, causal nonseparability persists when any single non-future system remains undephased but becomes separable if all systems or only the future system is undephased.
citing papers explorer
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The minimal example of quantum network Bell nonlocality
Quantum nonlocality is possible in the triangle network with no inputs and binary outputs, which is the smallest such scenario by number of variables and outcomes.
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Random dilation superchannel
Presents a poly-complexity quantum circuit implementing the random dilation superchannel for parallel channel queries, with approximate sequential extension, a no-go theorem for exact sequential dilation, and an application to exponentially improved channel storage-retrieval.
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Polycategorical Constructions for Unitary Supermaps of Arbitrary Dimension
Defines polyslot pslot[C] and srep[C] constructions on symmetric monoidal categories that reconstruct unitary supermaps and forbid time-loops in composition, with equivalence shown on path-contraction groupoids.
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Order structure and signalling in higher order quantum maps
Higher-order quantum map types form a distributive lattice of regular subtypes where signalling relations are determined by type function evaluations and structure poset rank parity, with normal forms derived from maximal chains.
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Probabilistic and approximate universal quantum purification machines
A machine that purifies two quantum inputs of different rank with positive probability cannot be a linear positive map, ruling out universal probabilistic purification from finite copies; approximate strategies exhibit a dimension-dependent trade-off between pure-output and append-environment maps.
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How many systems can be dephased before the quantum switch becomes causally definite?
In bipartite processes and multipartite quantum circuits with quantum control, causal nonseparability persists when any single non-future system remains undephased but becomes separable if all systems or only the future system is undephased.