Superadditivity in Trade-Off Capacities of Quantum Channels

Zhu, Elton Yechao; Zhuang, Quntao; Hsieh, Min-Hsiu

doi:10.1109/tit.2018.2889082

Cited by 19 publications

(9 citation statements)

References 31 publications

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“…In fact, the only known channels that admit an additive CE capacity region are the quantum erasure channels [13] and Hadamard channels [23], many fewer than the class of channels with an additive classical capacity. Coincidentally, these two classes of channels also admit an additive CQE trade-off capacity, suggesting a nontrivial connection [13,23,33]. Also, we do not know the number of shots at which the superadditivity occurs.…”

Section: Conclusion-our Work Unveils the Complications In Characteriz...mentioning

confidence: 91%

Superadditivity of the Classical Capacity with Limited Entanglement Assistance

Zhu¹,

Zhuang²

2017

Phys. Rev. Lett.

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Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the entanglement-assisted classical capacity for any channel is additive, making entanglement across channel uses unnecessary. If the entanglement assistance is limited, the picture is much more unclear. Suppose the classical capacity is superadditive, then the classical capacity with limited entanglement assistance could retain superadditivity by continuity arguments. If the classical capacity is additive, it is unknown if superadditivity can still be developed with limited entanglement assistance. We show this is possible, by providing an example. We construct a channel for which the classical capacity is additive, but that with limited entanglement assistance can be superadditive. This shows entanglement plays a weird role in communication, and we still understand very little about it. DOI: 10.1103/PhysRevLett.119.040503 In Shannon's classical information theory [1], a classical (memoryless) channel is a probabilistic map from input states to output states. This has been extended to the quantum world. A (memoryless) quantum channel is a time-invariant completely positive trace preserving (CPTP) linear map from input quantum states to output quantum states [2]. A classical channel can only transmit classical information, and the maximum communication rate is fully characterized by its capacity. A quantum channel can be used to transmit not only classical information but also quantum information. Hence, there are different types of capacity, such as classical capacity C for classical communication [3,4] and quantum capacity Q for quantum communication [5][6][7].Since quantum channels transmit quantum states, and quantum states can be entangled with other parties, it is natural to ask if entanglement can assist the communication. This was first considered by Bennett et al., who showed that unlimited preshared entanglement could improve the classical capacity of a noisy channel [8,9]. Shor examined the case where only finite preshared entanglement is available and obtained a trade-off curve that illustrates how the optimal rate of classical communication depends on the amount of entanglement assistance (CE trade-off) [10]. One can also consider how entanglement (E), classical communication (C), or quantum communication (Q) can trade-off against each other as resources. The trade-off capacity of almost any two resources was studied by Devetak et al. [11,12], such as entanglement-assisted quantum capacity (QE trade-off). Subsequently, the triple resource (CQE) trade-off capacity was also characterized [13][14][15].However, almost all the capacity formulas above are given by regularized expressions. They are difficult to evaluate because they require an optimization over an infinite number of channel uses, which is typically intractable. The existence of this regularization is because entanglement acr...

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Section: Conclusion-our Work Unveils the Complications In Characteriz...mentioning

confidence: 91%

Superadditivity of the Classical Capacity with Limited Entanglement Assistance

Zhu¹,

Zhuang²

2017

Phys. Rev. Lett.

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“…To begin with, the Shannon capacity has been generalized to the Holevo-Schumacher-Westmoreland (HSW) classical capacity [3][4][5]. Quantum effects such as entanglement have also enabled nonclassical phenomena in communication, such as superadditivity [6][7][8][9][10][11] and capacity-boost from entanglementassistance (EA) [12][13][14][15][16][17][18][19][20][21]. Moreover, reliable transmission of quantum information is possible, established by the Lloyd-Shor-Devetak quantum capacity theorem [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Entanglement-assisted multiple-access channels: capacity regions and protocol designs

Shi

Hsieh

Guha

et al. 2021

Quantum Information and Measurement VI 2021

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We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss multiple-access channel and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance, therefore also larger than the Yen-Shapiro rate-region of Gaussian encoding or coherent-state encoding. When the senders have transmitters of equal low brightness, we also numerically find that the two-mode squeezed vacuum source is optimal at a corner rate point. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rate. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.

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“…With the development of quantum source generation and detection, quantum effects, such as the uncertainty principle, squeezing and entanglement, become relevant in characterizing the capacity of optical channels. For example, entanglement can sometimes lead to the superadditivity phenomena [1][2][3][4][5][6], where the communication capacity is increased due to entanglement between inputs among multiple channel uses. While an increased capacity is beneficial in practice, the evaluation of channel capacities becomes challenging as it requires an optimization of the joint input over an arbitrary number of channel uses.…”

Section: Introductionmentioning

confidence: 99%

Computable limits of optical multiple-access communications

Shi,

Zhuang

2021

Preprint

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Communication rates over quantum channels can be boosted by entanglement, via superadditivity phenomena or entanglement assistance. Superadditivity refers to the capacity improvement from entangling inputs across multiple channel uses. Nevertheless, when unlimited entanglement assistance is available, the entanglement between channel uses becomes unnecessary-the entanglementassisted (EA) capacity of a single-sender and single-receiver channel is additive. We generalize the additivity of EA capacity to general multiple-access channels (MACs) for the total communication rate. Furthermore, for optical communication modelled as phase-insensitive bosonic Gaussian MACs, we prove that the optimal total rate is achieved by Gaussian entanglement and therefore can be efficiently evaluated. To benchmark entanglement's advantage, we propose computable outer bounds for the capacity region without entanglement assistance. Finally, we formulate an EA version of minimum entropy conjecture, which leads to the additivity of the capacity region of phaseinsensitive bosonic Gaussian MACs if it is true. The computable limits confirm entanglement's boosts in optical multiple-access communications.

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Superadditivity in Trade-Off Capacities of Quantum Channels

Cited by 19 publications

References 31 publications

Superadditivity of the Classical Capacity with Limited Entanglement Assistance

Superadditivity of the Classical Capacity with Limited Entanglement Assistance

Entanglement-assisted multiple-access channels: capacity regions and protocol designs

Computable limits of optical multiple-access communications

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