Capacity Estimates via Comparison with TRO Channels

Gao, Li; Junge, Marius; LaRacuente, Nicholas

doi:10.1007/s00220-018-3249-y

Cited by 20 publications

(27 citation statements)

References 61 publications

(89 reference statements)

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“…Challenges in computing and checking the positivity of a channel’s quantum capacity can be circumvented in the special case of (anti)-degradable channels 51 , 52 , PPT channels 53 , DSPT channels 54 , and less noisy channels 55 . However, even if one computes a channel’s quantum capacity, nonadditivity implies that this capacity may be an incomplete measure of the channel’s ability to send quantum information.…”

Section: Introductionmentioning

confidence: 99%

Entropic singularities give rise to quantum transmission

Siddhu

2021

Nat Commun

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When can noiseless quantum information be sent across noisy quantum devices? And at what maximum rate? These questions lie at the heart of quantum technology, but remain unanswered because of non-additivity— a fundamental synergy which allows quantum devices (aka quantum channels) to send more information than expected. Previously, non-additivity was known to occur in very noisy channels with coherent information much smaller than that of a perfect channel; but, our work shows non-additivity in a simple low-noise channel. Our results extend even further. We prove a general theorem concerning positivity of a channel’s coherent information. A corollary of this theorem gives a simple dimensional test for a channel’s capacity. Applying this corollary solves an open problem by characterizing all qubit channels whose complement has non-zero capacity. Another application shows a wide class of zero quantum capacity qubit channels can assist an incomplete erasure channel in sending quantum information. These results arise from introducing and linking logarithmic singularities in the von-Neumann entropy with quantum transmission: changes in entropy caused by this singularity are a mechanism responsible for both positivity and non-additivity of the coherent information. Analysis of such singularities may be useful in other physics problems.

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Section: Introductionmentioning

confidence: 99%

Entropic singularities give rise to quantum transmission

Siddhu

2021

Nat Commun

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“…The second term bounds possible additivity violation. Note that using convexity of Holevo information in the input state [31], one may obtain linear correction term O(λ). Here monogamy of entanglement narrows the additivity violation decay when the success probability λ goes to 0, without relying on the detailed form of Φ's.…”

Section: Introductionmentioning

confidence: 99%

Heralded channel Holevo superadditivity bounds from entanglement monogamy

Gao

Junge

LaRacuente

2018

Journal of Mathematical Physics

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We show that for a particular class of quantum channels, which we call heralded channels, monogamy of squashed entanglement limits the superadditivity of Holevo capacity. Heralded channels provide a means to understand the quantum erasure channel composed with an arbitrary other quantum channel, as well as common situations in experimental quantum information that involve frequent loss of qubits or failure of trials. We also show how entanglement monogamy applies to non-classicality in quantum games, and we consider how faithful, monogamous entanglement measures may bound other entanglement-dependent quantities in many-party scenarios.

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“…The same estimates hold for other capacities, i.e. we may replace Q (1) with P (1) , Q, P, χ and C. Important examples of (modified) TRO-channels include random unitary channels using projective unitary representations of finite (quantum) groups and generalized dephasing channels [GJL16].…”

Section: Some Temperley-lieb Channels Are Not Modified Tro-channelsmentioning

confidence: 89%

Entanglement and the Temperley-Lieb category

Brannan¹,

Collins²

2020

Topological Phases of Matter and Quantum Computation

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We study a class of quantum channels arising from the representation theory of compact quantum groups that we call Temperley-Lieb quantum channels. These channels simultaneously extend those introduced in [BC18], [AN14], and [LS14]. (Quantum) Symmetries in quantum information theory arise naturally from many points of view, providing an important source of new examples of quantum phenomena, and also serve as useful tools to simplify or solve important problems. This work provides new applications of quantum symmetries in quantum information theory. Among others, we study entropies and capacitites of Temperley-Lieb channels, their (anti-) degradability, PPT and entanglement breaking properties, as well as the behaviour of their tensor products with respect to entangled inpurs. Finally we compare the Tempereley-Lieb channels with the (modified) TRO-channels recently introduced in [GJL16]. 2 and EBT are actually equivalent in the case of SU(2). One important ingredient here is the diagrammatic calculus for Temperley-Lieb category covered in Section 3.3.• On the other hand, we reveal unexpected results on (anti-)degradability of SU(2)-TLchannels. We show that they are degradable for extremal cases such as lowest or highest weight, whereas it is not true for other intermediate cases. Indeed, we provide an example of a non-degradable SU(2)-TL-channel in low dimensions (see Example 5.9).One crucial point in QIT is that it is often unavoidable to consider tensor products of quantum channels, and in general, computations in tensor products become very involved. However when the channels have nice symmetries, as we show in this paper, computations can remain tractable, even in non-trivial cases. The main techinical tool is an application of diagrammatic calculus explained in Section 3.3, which can be applied to O + N -TL-channels, see Section 6 for the details. Finally, TL-channels bear some resemblance with another important family of operators introduced by [GJL16], called TRO-channels and their modified versions. Here, TRO refers to ternary ring of operators and name "TRO-channel" comes from the fact that its Stinespring space, i.e. the range of the Stinespring isometry actually has a TRO structure. Examples of TRO-channels include random unitary channels from regular representations of finite (quantum) groups and generalized dephasing channels [GJL16]. While the authors were preparing this manuscript and discussing it for the first time publicly, the question of how our TL-channels compare to TRO channels was posed (and, in particular, whether or not TL implies TRO). The answer is that these classes of channels bear important differences, as explained in section 7.This paper is organized as follows. After this introduction, section 2 provides some background and reminders about quantum channels and compact quantum groups. Section 3 recalls some details on free orthogonal quantum groups and their associated representation theory. Then, we introduce Tempereley-Lieb quantum channels (shortly, TL-channels) and collect some...

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Capacity Estimates via Comparison with TRO Channels

Cited by 20 publications

References 61 publications

Entropic singularities give rise to quantum transmission

Entropic singularities give rise to quantum transmission

Heralded channel Holevo superadditivity bounds from entanglement monogamy

Entanglement and the Temperley-Lieb category

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