Lower and Upper Bounds on Nonunital Qubit Channel Capacities

Filippov, S.

doi:10.1016/s0034-4877(18)30083-1

Cited by 14 publications

(12 citation statements)

References 42 publications

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“…Nevertheless, we have managed to derive the explicit form of the Sinkhorn theorem for trace decreasing qubit operations with the matrix representation (13). This analytical result advances our understanding of the quantum Sinkhorn theorem beyond the trace-preserving case of phase-covariant qubit maps, which was the only nontrivial class of maps with explicit analytical expressions for Υ, A, and B [28,33] known before this work.…”

Section: Discussionmentioning

confidence: 87%

“…The optimal state opt 12 (0) makes allowance for that effect and is not maximally entangled in general. A technique to solve the optimization problem posed is based on the quantum Sinkhorn theorem [29][30][31][32] that also finds applications in the study of quantum channel capacity [33]. The quantum Sinkhorn theorem relates strictly positive quantum maps with unital ones and enables us to use the known results on entanglement robustness against unital quantum noises [27,28].…”

Section: Introductionmentioning

confidence: 99%

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Entanglement Robustness in Trace Decreasing Quantum Dynamics

Filippov

2021

Quanta

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Trace decreasing dynamical maps are as physical as trace preserving ones; however, they are much less studied. Here we overview how the quantum Sinkhorn theorem can be successfully applied to find a two-qubit entangled state which has the strongest robustness against local noises and losses of quantum information carriers. We solve a practically relevant problem of finding an optimal initial encoding to distribute entangled polarized qubits through communication lines with polarization dependent losses and extra depolarizing noise. The longest entanglement lifetime is shown to be attainable with a state that is not maximally entangled.Quanta 2021; 10: 15–21.

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Section: Discussionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Entanglement Robustness in Trace Decreasing Quantum Dynamics

Filippov

2021

Quanta

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“…Finally, the multiple photon addition and subtraction operations can be treated in the same way because Interestingly, in contrast to the quantum channels [32][33][34][35], the quantum informational properties of quantum operations such as capacities and entanglement degradation remain essentially unstudied. From this viewpoint, the fair quantum operations (4) and (5) can be analyzed as paradigmatic examples of operations on continuousvariable quantum states.…”

Section: Discussionmentioning

confidence: 99%

On Quantum Operations of Photon Subtraction and Photon Addition

Filippov

2019

Lobachevskii J Math

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The conventional photon subtraction and photon addition transformations, ̺ → ta̺a † and ̺ → ta † ̺a, are not valid quantum operations for any constant t > 0 since these transformations are not trace nonincreasing. For a fixed density operator ̺ there exist fair quantum operations, N− and N+, whose conditional output states approximate the normalized outputs of former transformations with an arbitrary accuracy. However, the uniform convergence for some classes of density operators ̺ has remained essentially unknown. Here we show that, in the case of photon addition operation, the uniform convergence takes place for the energy-second-moment-constrained states such that tr[̺H 2 ] ≤ E2 < ∞, H = a † a. In the case of photon subtraction, the uniform convergence takes place for the energy-second-moment-constrained states with nonvanishing energy, i.e., the states ̺ such that tr[̺H] ≥ E1 > 0 and tr[̺H 2 ] ≤ E2 < ∞. We prove that these conditions cannot be relaxed and generalize the results to the cases of multiple photon subtraction and addition.

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“…We do not show the plot for N = 0.5, because the channel becomes a qubit unital channel and thus its Holevo information is already tight [112]. We do not explicitly depict the weak converse bound in [113] since it is not tight to the cases we present.…”

Section: A Detailed Comparison For Generalized Amplitude Damping Channelsmentioning

confidence: 91%

Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

Fang

Fawzi

2021

Commun. Math. Phys.

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Having a distance measure between quantum states satisfying the right properties is of fundamental importance in all areas of quantum information. In this work, we present a systematic study of the geometric Rényi divergence (GRD), also known as the maximal Rényi divergence, from the point of view of quantum information theory. We show that this divergence, together with its extension to channels, has many appealing structural properties, which are not satisfied by other quantum Rényi divergences. For example we prove a chain rule inequality that immediately implies the “amortization collapse” for the geometric Rényi divergence, addressing an open question by Berta et al. [Letters in Mathematical Physics 110:2277–2336, 2020, Equation (55)] in the area of quantum channel discrimination. As applications, we explore various channel capacity problems and construct new channel information measures based on the geometric Rényi divergence, sharpening the previously best-known bounds based on the max-relative entropy while still keeping the new bounds single-letter and efficiently computable. A plethora of examples are investigated and the improvements are evident for almost all cases.

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Lower and Upper Bounds on Nonunital Qubit Channel Capacities

Cited by 14 publications

References 42 publications

Entanglement Robustness in Trace Decreasing Quantum Dynamics

Entanglement Robustness in Trace Decreasing Quantum Dynamics

On Quantum Operations of Photon Subtraction and Photon Addition

Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

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