<i>Dephrasure</i>
 Channel and Superadditivity of Coherent Information

Leditzky, Felix; Leung, Debbie; Smith, Graeme

doi:10.1103/physrevlett.121.160501

Cited by 68 publications

(89 citation statements)

References 33 publications

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“…However, in contrast to the GADC the raw ansatz is indeed able to find superadditive quantum codes. For = k 2, these codes found using the raw ansatz are optimal (as already observed in [LLS18a]), while for = k 3, 4 they are clearly outperformed by our neural network codes. Another observation of [LLS18a] is that the dephasing part of  p q , suggests a Schmidt ansatz for quantum codes, a neural network state version of which is discussed in equation (16) in section 5.…”

Section: Dephrasure Channelsupporting

confidence: 77%

“…For = k 2, these codes found using the raw ansatz are optimal (as already observed in [LLS18a]), while for = k 3, 4 they are clearly outperformed by our neural network codes. Another observation of [LLS18a] is that the dephasing part of  p q , suggests a Schmidt ansatz for quantum codes, a neural network state version of which is discussed in equation (16) in section 5. However, in the high-noise regime investigated above, this Schmidt ansatz did not yield codes performing as well as the codes n k resp.n k *.…”

Section: Dephrasure Channelsupporting

confidence: 77%

“…of these codes was derived in [LLS18a], and we state it in appendix B. Similar to the GADC in section 4.1, we note that the optimal single-letter coherent information  Q p q 1 , ].…”

Section: Dephrasure Channelmentioning

confidence: 97%

“…The neural network ansatz is also able to find new quantum codes for the dephrasure channel that was introduced recently in [LLS18a]. It is defined in terms of probabilities Î p q , 0,1 [ ]as…”

Section: Dephrasure Channelmentioning

confidence: 99%

“…The architecture used for the neural network codes is a feedforward net with four hidden layers of width k 2 each, activation functions cos and3 tanh, and a Cartesian output layer (see section 4.1). the two-exhibits superadditivity of coherent information for as little as two uses of the channel [LLS18a]. As a result, the quantum capacity of the dephrasure channel is unknown for a large region in the parameter space.…”

Section: Dephrasure Channelmentioning

confidence: 99%

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Quantum codes from neural networks

Bausch

Leditzky

2020

New J. Phys.

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We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we initiate the study of neural network states in quantum information-processing tasks. We demonstrate that neural network states are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction, supplying further evidence for the usefulness of neural network states to describe multipartite entanglement. In particular, we show the following main results: (a) neural network states yield quantum codes with a high coherent information for two important quantum channels, the generalized amplitude damping channel and the dephrasure channel. These codes outperform all other known codes for these channels, and cannot be found using a direct parametrization of the quantum state. (b) For the depolarizing channel, the neural network state ansatz reliably finds the best known codes given by repetition codes. (c) Neural network states can be used to represent absolutely maximally entangled states, a special type of quantum error-correcting codes. In all three cases, the neural network state ansatz provides an efficient and versatile means as a variational parametrization of these highly entangled states. Structure of this paperThis paper is structured as follows. In section 2 we introduce the quantum capacity of a channel and state the corresponding coding theorem which expresses the quantum capacity as a regularized formula in terms of an entropic quantity called the coherent information. We then discuss how lower bounds on the quantum capacity can be obtained by solving an entropic optimization problem. In section 3 we review neural network states based on RBMs and feed-forward nets. We then present our main results about representing quantum codes with neural network states. In section 4 we discuss the GADC and the dephrasure channel. We show that the neural network state ansatz finds new quantum codes providing the strongest lower bounds to date on the quantum capacities of these channels. Moreover, we demonstrate that these new codes are not found using a 'direct' parametrization of quantum states. We then show in section 5 for the depolarizing channel how tensor products of repetition codes-i.e. the known optimal codes for  k 9 uses of this channel-can be efficiently represented New J. Phys. 22 (2020) 023005 J Bausch and F Leditzky New J. Phys. 22 (2020) 023005

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Section: Dephrasure Channelsupporting

confidence: 77%

Section: Dephrasure Channelsupporting

confidence: 77%

“…of these codes was derived in [LLS18a], and we state it in appendix B. Similar to the GADC in section 4.1, we note that the optimal single-letter coherent information  Q p q 1 , ].…”

Section: Dephrasure Channelmentioning

confidence: 97%

Section: Dephrasure Channelmentioning

confidence: 99%

Section: Dephrasure Channelmentioning

confidence: 99%

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Quantum codes from neural networks

Bausch

Leditzky

2020

New J. Phys.

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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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Conditional channel simulation

2019

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In this work we design a specific simulation tool for quantum channels which is based on the use of a control system. This allows us to simulate an average quantum channel which is expressed in terms of an ensemble of channels, even when these channel-components are not jointly teleportation-covariant. This design is also extended to asymptotic simulations, continuous ensembles, and memory channels. As an application, we derive relative-entropy-of-entanglement upper bounds for private communication over various channels, including non-Gaussian mixtures of bosonic lossy channels. Among other results, we also establish the two-way quantum and private capacity of the so-called "dephrasure" channel.

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Dephrasure Channel and Superadditivity of Coherent Information

Cited by 68 publications

References 33 publications

Quantum codes from neural networks

Quantum codes from neural networks

Geometric Rényi Divergence and its Applications in Quantum Channel Capacities

Conditional channel simulation

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