Computing Quantum Channel Capacities

Ramakrishnan, Navneeth; Iten, Raban; Scholz, Volkher B.; Berta, Mario

doi:10.1109/tit.2020.3034471

Cited by 26 publications

(29 citation statements)

References 38 publications

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“…For any two channels B and B, each either degradable or anti-degradable, the joint channel B ⊗ B has additive coherent information. For a degradable channel B, the coherent information ∆(B, ρ a ) is concave in ρ a [64], and thus Q (1) (B) can be computed with relative ease [65,66]. As a result the quantum capacity of a degradable channel, which simply equals Q (1) (B), can also be computed efficiently.…”

Section: Special Channel Classesmentioning

confidence: 99%

Generic nonadditivity of quantum capacity in simple channels

Leditzky¹,

Leung²,

Siddhu³

et al. 2022

Preprint

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Section: Special Channel Classesmentioning

confidence: 99%

Generic nonadditivity of quantum capacity in simple channels

Leditzky¹,

Leung²,

Siddhu³

et al. 2022

Preprint

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“…For any two channels B and B, each either degradable or anti-degradable, the joint channel B ⊗B has additive coherent information, i.e., equality holds in (7) [11,32]. For a degradable channel B, the coherent information ∆(B, ρ a ) is concave in ρ a [64], and thus Q (1) (B) can be computed with relative ease [15,40]. As a result the quantum capacity of a degradable channel, which simply equals Q (1) (B), can also be computed efficiently.…”

Section: Special Channel Classesmentioning

confidence: 99%

“…and 0 ≤ u ≤ 1. In ( 39), (40), and (41) the maximization is over a density operator ρ a (u) which is supported over a subspace of the H ai form (21). In Secs.…”

Section: Channel Coherent Informationmentioning

confidence: 99%

The platypus of the quantum channel zoo

Leditzky¹,

Leung²,

Siddhu³

et al. 2022

Preprint

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Understanding quantum channels and the strange behavior of their capacities is a key objective of quantum information theory. Here we study a remarkably simple, low-dimensional, single-parameter family of quantum channels with exotic quantum information-theoretic features. As the simplest example from this family, we focus on a qutrit-to-qutrit channel that is intuitively obtained by hybridizing together a simple degradable channel and a completely useless qubit channel. Such hybridizing makes this channel's capacities behave in a variety of interesting ways. For instance, the private and classical capacity of this channel coincide and can be explicitly calculated, even though the channel does not belong to any class for which the underlying information quantities are known to be additive. Moreover, the quantum capacity of the channel can be computed explicitly, given a clear and compelling conjecture is true. This "spin alignment conjecture", which may be of independent interest, is proved in certain special cases and additional numerical evidence for its validity is provided. Finally, we generalize the qutrit channel in two ways, and the resulting channels and their capacities display similarly rich behavior. In the companion paper [33], we further show that the qutrit channel demonstrates superadditivity when transmitting quantum information jointly with a variety of assisting channels, in a manner unknown before.

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“…Hence, the optimization ( 30) is a convex optimization that can be carried out efficiently for small system sizes [30]. Indeed, we have successfully computed the thermodynamic capacity of simple example quantum channels acting on few qubits with Python code, using the QuTip framework [31,32] and the CVXOPT optimization software [33] (see also [34] for a direct algorithm). The thermodynamic capacity is additive [21].…”

Section: Propertiesmentioning

confidence: 99%

Thermodynamic Implementations of Quantum Processes

Faist

Berta

Brandão

2021

Commun. Math. Phys.

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Recent understanding of the thermodynamics of small-scale systems have enabled the characterization of the thermodynamic requirements of implementing quantum processes for fixed input states. Here, we extend these results to construct optimal universal implementations of a given process, that is, implementations that are accurate for any possible input state even after many independent and identically distributed (i.i.d.) repetitions of the process. We find that the optimal work cost rate of such an implementation is given by the thermodynamic capacity of the process, which is a single-letter and additive quantity defined as the maximal difference in relative entropy to the thermal state between the input and the output of the channel. Beyond being a thermodynamic analogue of the reverse Shannon theorem for quantum channels, our results introduce a new notion of quantum typicality and present a thermodynamic application of convex-split methods.

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Computing Quantum Channel Capacities

Cited by 26 publications

References 38 publications

Generic nonadditivity of quantum capacity in simple channels

Generic nonadditivity of quantum capacity in simple channels

The platypus of the quantum channel zoo

Thermodynamic Implementations of Quantum Processes

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