Necessary and sufficient conditions on measurements of quantum channels

  title={Necessary and sufficient conditions on measurements of quantum channels},
  author={John Burniston and Michael Grabowecky and Carlo Maria Scandolo and Giulio Chiribella and Gilad Gour},
  journal={Proceedings of the Royal Society A},
Quantum supermaps are a higher-order genera- lization of quantum maps, taking quantum maps to quantum maps. It is known that any completely positive and trace non-increasing (CPTNI) map can be performed as part of a quantum measurement. By providing an explicit counterexample we show that, instead, not every quantum supermap sending a quantum channel to a CPTNI map can be realized in a measurement on quantum channels. We find that the supermaps that can be implemented in this way are exactly… Expand

Figures and Topics from this paper

Fundamental limitations on distillation of quantum channel resources
This work establishes universal limitations on the processing of both quantum states and channels, expressed in the form of no-go theorems and quantitative bounds for the manipulation of general quantum channel resources under the most general transformation protocols. Expand
Fundamental limitations on quantum channel manipulation
Comprehensive lower bounds for the overhead of any physical distillation protocol in terms of required channel uses are introduced, imposing strong limitations on the practical efficiency and cost of channel manipulation protocols. Expand
Robustness of Quantum Memories: An Operational Resource-Theoretic Approach
Quantum memory -- the capacity to store and faithfully recover unknown quantum states -- is essential for any quantum technology to exhibit operational advantage. There is thus great value inExpand
Symmetries of quantum evolutions
A cornerstone of quantum mechanics is the characterisation of symmetries provided by Wigner’s theorem. Wigner’s theorem establishes that every symmetry of the quantum state space must be either aExpand
Dynamical resource theory of quantum coherence
This work introduces four different types of free superch channels (analogous to MIO, DIO, IO, and SIO) and discusses in detail two of them, namely, dephasing-covariant incoherent superchannels (DISC) and maximally incoherentsuperchannel (MISC). Expand
Entanglement-breaking superchannels
This paper introduces the notions of CPTP- and CP-complete images of a superchannel, which capture deterministic and probabilistic channel convertibility, respectively, and characterize the power of EB superchannels for generating CP maps in different scenarios, and it reveals some fundamental differences between channels and superch channels. Expand
Uniqueness and Optimality of Dynamical Extensions of Divergences
  • G. Gour
  • Mathematics, Physics
  • ArXiv
  • 2020
The optimality of the amortized channel extension of the Umegaki relative entropy is proved, by showing that it provides a lower bound on all channel relative entropies that reduce to the Kullback-Leibler divergence on classical states. Expand


Transforming quantum operations: Quantum supermaps
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 asExpand
Quantifying the magic of quantum channels
A resource theory for magic quantum channels is developed to characterize and quantify the quantum "magic" or non-stabilizerness of noisy quantum circuits, and two efficiently computable magic measures for quantum channels are introduced. Expand
Causal Structures and the Classification of Higher Order Quantum Computations
Quantum operations are the most widely used tool in the theory of quantum information processing, representing elementary transformations of quantum states that are composed to form complex quantumExpand
Comparison of Quantum Channels by Superchannels
  • G. Gour
  • Computer Science, Physics
  • IEEE Transactions on Information Theory
  • 2019
It is shown that the extended conditional min-entropy can be used to fully characterize when two bipartite quantum channels are related to each other via a superchannel (also known as supermap or a comb) that is acting on one of the subsystems. Expand
Theoretical framework for higher-order quantum theory
The present treatment provides a general framework where this kind of analysis can be carried out in full generality of higher-order quantum functions, and can be exported in the context of any operational probabilistic theory. Expand
Reformulating and Reconstructing Quantum Theory
We provide a reformulation of finite dimensional quantum theory in the circuit framework in terms of mathematical axioms, and a reconstruction of quantum theory from operational postulates. TheExpand
Theoretical framework for quantum networks
We present a framework to treat quantum networks and all possible transformations thereof, including as special cases all possible manipulations of quantum states, measurements, and channels, suchExpand
Quartic quantum theory: an extension of the standard quantum mechanics
We propose an extended quantum theory, in which the number K of parameters necessary to characterize a quantum state behaves as fourth power of the number N of distinguishable states. As the simplexExpand
Resource theories of quantum channels and the universal role of resource erasure
We initiate the systematic study of resource theories of quantum channels, i.e. of the dynamics that quantum systems undergo by completely positive maps, in abstracto: Resources are in principle allExpand
Quantum communication in a superposition of causal orders
It is shown that entanglement can enhance the ability to transmit quantum information over noisy communication channels and, when the two channels are traversed in an indefinite order, a quantum bit sent through them has a 25% probability to reach the receiver without any error. Expand