Necessary and sufficient conditions on measurements of quantum channels

Burniston, John; Grabowecky, Michael; Scandolo, Carlo Maria; Chiribella, Giulio; Gour, Gilad

doi:10.1098/rspa.2019.0832

Cited by 15 publications

(22 citation statements)

References 80 publications

(139 reference statements)

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“…This result shows that the structure of unnormalized maps is much more complex than the structure of unnormalized states, which is one of the reasons why QRTs of channels are often more challenging to formalize than QRTs of states (see also Ref. [17] for a related discussion on this point).…”

Section: Discussion On Cp Imagementioning

confidence: 96%

“…In Ref. [17], the authors introduce the concept of a quantum super-instrument, which is a set of c-CPTNI (completely CP preserving and trace-non-increasing preserving) supermaps {Θ x } such that x Θ x is a superchannel. A quantum super-instrument therefore describes in one sense how a quantum channel can be measured.…”

Section: Ebscs Realized By Measure-and-prepare Superchannelsmentioning

confidence: 99%

“…A quantum super-instrument therefore describes in one sense how a quantum channel can be measured. It is proven in [17] that every super-instrument can be realized with a CPTP pre-processing channel and a post-processing quantum instrument, as shown on the left side of Fig. 7.…”

Section: Ebscs Realized By Measure-and-prepare Superchannelsmentioning

confidence: 99%

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Entanglement-breaking superchannels

Chen

Chitambar

2020

Quantum

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In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization of the well-known EB channels. We give several equivalent characterizations of EB supermaps and superchannels. Unlike its channel counterpart, we find that not every EB superchannel can be implemented as a measure-and-prepare superchannel. We also demonstrate that many EB superchannels can be superactivated, in the sense that they can output non-separable channels when wired in series.We then introduce the notions of CPTP- and CP-complete images of a superchannel, which capture deterministic and probabilistic channel convertibility, respectively. This allows us to characterize the power of EB superchannels for generating CP maps in different scenarios, and it reveals some fundamental differences between channels and superchannels. Finally, we relax the definition of separable channels to include (p,q)-non-entangling channels, which are bipartite channels that cannot generate entanglement using p- and q-dimensional ancillary systems. By introducing and investigating k-EB maps, we construct examples of (p,q)-EB superchannels that are not fully entanglement breaking. Partial results on the characterization of (p,q)-EB superchannels are also provided.

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Section: Discussion On Cp Imagementioning

confidence: 96%

Section: Ebscs Realized By Measure-and-prepare Superchannelsmentioning

confidence: 99%

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Entanglement-breaking superchannels

Chen

Chitambar

2020

Quantum

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“…In theories of dynamical resources, the agent converts different channels by means of a restricted set of supermaps [35,43,[66][67][68][69][70]. In particular, we focus on supermaps that send quantum channels to quantum channels.…”

Section: Introductionmentioning

confidence: 99%

“…A superchannel is a supermap Θ A→B ∈ L (A → B) that takes quantum channels to quantum channels even when tensored with the identity supermap [35,43,[66][67][68][69][70]. More precisely, Θ A→B ∈ L (A → B) is called a superchannel if it satisfies the following two conditions:…”

mentioning

confidence: 99%

Dynamical Resources

Gour¹,

Scandolo²

2021

Preprint

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Quantum channels are quintessential to quantum information, being used in all protocols, and describing how systems evolve in space and time. As such, they play a key role in the manipulation of quantum resources, and they are often resources themselves, called dynamical resources. This forces us to go beyond standard resource theories of quantum states. Here we provide a rigorous foundation for dynamical resource theories, where the resources into play are quantum channels, explaining how to manipulate dynamical resources with free superchannels. In particular, when the set of free superchannels is convex, we present a novel construction of an infinite and complete family of convex resource monotones, giving necessary and sufficient conditions for convertibility under free superchannels. After showing that the conversion problem in convex dynamical resource theories can be solved with conic linear programming, we define various resource-theoretic protocols for dynamical resources. These results serve as the framework for the study of concrete examples of theories of dynamical resources, such as dynamical entanglement theory.

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Fundamental limitations on distillation of quantum channel resources

Regula

Takagi

2021

Nat Commun

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Quantum channels underlie the dynamics of quantum systems, but in many practical settings it is the channels themselves that require processing. We establish 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. Focusing on the class of distillation tasks — which can be understood either as the purification of noisy channels into unitary ones, or the extraction of state-based resources from channels — we develop fundamental restrictions on the error incurred in such transformations, and comprehensive lower bounds for the overhead of any distillation protocol. In the asymptotic setting, our results yield broadly applicable bounds for rates of distillation. We demonstrate our results through applications to fault-tolerant quantum computation, where we obtain state-of-the-art lower bounds for the overhead cost of magic state distillation, as well as to quantum communication, where we recover a number of strong converse bounds for quantum channel capacity.

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Necessary and sufficient conditions on measurements of quantum channels

Cited by 15 publications

References 80 publications

Entanglement-breaking superchannels

Entanglement-breaking superchannels

Dynamical Resources

Fundamental limitations on distillation of quantum channel resources

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