Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

Sharma, Kunal; Wilde, Mark M.; Adhikari, Sushovit; Takeoka, Masahiro

doi:10.1088/1367-2630/aac11a

Cited by 64 publications

(82 citation statements)

References 114 publications

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“…Lemma 7 (Eq. (5.1) of [18]). Gaussian loss channel can be decomposed into a bosonic pure-loss channel followed by a quantum-limited amplification…”

Section: B Synthesis and Decomposition Of Gaussian Channelsmentioning

confidence: 96%

“…Since coherent information of the bosonic pure-loss channel is additive, its quantum capacity is known [13][14][15] (see [16] for the general formalism of energy-constrained quantum capacity, and our Theorem 9 for a pedagogical self-contained derivation of energy-constrained quantum capacity of bosonic pure-loss channels). For general Gaussian loss channels with added thermal noise, a lower bound of quantum capacity can be obtained by evaluating oneshot coherent information of the channel [13], and several upper bounds are obtained by using, e.g., data-processing inequality [13,[17][18][19].…”

Section: Introductionmentioning

confidence: 99%

“…In section II, we review and summarize key properties of Gaussian loss, amplification and random displacement channels, which will be used in later sections. In section III, we provide an improved upper bound of quantum capacity of the Gaussian loss channel, both in energy-constrained and unconstrained cases by introducing a slight modification of an earlier result in [18] (Theorems 10, 11 and 12; see also Eq. (42) for an improved upper bound of Gaussian random displacement channel capacity).…”

Section: Introductionmentioning

confidence: 99%

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Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Noh

Albert

Jiang

2019

IEEE Trans. Inform. Theory

158

146

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Gaussian loss channels are of particular importance since they model realistic optical communication channels. Except for special cases, quantum capacity of Gaussian loss channels is not yet known completely. In this paper, we provide improved upper bounds of Gaussian loss channel capacity, both in the energy-constrained and unconstrained scenarios. We briefly review the Gottesman-Kitaev-Preskill (GKP) codes and discuss their experimental implementation. We then prove, in the energy-unconstrained case, that the GKP codes achieve the quantum capacity of Gaussian loss channels up to at most a constant gap from the improved upper bound. In the energy-constrained case, we formulate a biconvex encoding and decoding optimization problem to maximize the entanglement fidelity. The biconvex optimization is solved by an alternating semidefinite programming (SDP) method and we report that, starting from random initial codes, our numerical optimization yields GKP codes as the optimal encoding in a practically relevant regime. arXiv:1801.07271v2 [quant-ph]

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“…Lemma 7 (Eq. (5.1) of [18]). Gaussian loss channel can be decomposed into a bosonic pure-loss channel followed by a quantum-limited amplification…”

Section: B Synthesis and Decomposition Of Gaussian Channelsmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Noh

Albert

Jiang

2019

IEEE Trans. Inform. Theory

158

146

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“…The family of generalized divergences discussed earlier (see also [49]), along with other methods to extend divergences [25], provide only necessary conditions for the existence of a superchannel that converts one pair of channels to another. We now focus on yet another family of channel divergences that provides both necessary and sufficient conditions for the existence of such a superchannel.…”

Section: Comparison Of Channels With the Extended Conditional Minementioning

confidence: 99%

Comparison of Quantum Channels by Superchannels

Gour

2019

IEEE Trans. Inform. Theory

123

156

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We extend the definition of the conditional minentropy from bipartite quantum states to bipartite quantum channels. We show that many of the properties of the conditional min-entropy carry over to the extended version, including an operational interpretation as a guessing probability when one of the subsystems is classical. We then show that the extended conditional min-entropy can be used to fully characterize when two bipartite quantum channels are related to each other via a superchannel (also known as supermap or a comb) that is acting on one of the subsystems. This relation is a preorder that extends the definition of "quantum majorization" from bipartite states to bipartite channels, and can also be characterized with semidefinite programming. As a special case, our characterization provides necessary and sufficient conditions for when a set of quantum channels is related to another set of channels via a single superchannel. We discuss the applications of our results to channel discrimination, and to resource theories of quantum processes. Along the way we study channel divergences, entropy functions of quantum channels, and noise models of superchannels, including random unitary superchannels, and doubly-stochastic superchannels. For the latter we give a physical meaning as being completely-uniformity preserving.

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“…As discussed in [61,63], a generalized divergence possesses the direct-sum property on classical-quantum states if the following equality holds:…”

Section: Ramentioning

confidence: 99%

Quantifying the magic of quantum channels

2019

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Keywords: resource theory of magic quantum channels, completely positive-Wigner-preserving quantum operations, thauma of a quantum channel, distillable magic, classical simulation of noisy quantum circuits Abstract To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum channels to characterize and quantify the quantum 'magic' or non-stabilizerness of noisy quantum circuits. For qudit quantum computing with odd dimension d, it is known that quantum states with non-negative Wigner function can be efficiently simulated classically. First, inspired by this observation, we introduce a resource theory based on completely positive-Wigner-preserving quantum operations as free operations, and we show that they can be efficiently simulated via a classical algorithm. Second, we introduce two efficiently computable magic measures for quantum channels, called the mana and thauma of a quantum channel. As applications, we show that these measures not only provide fundamental limits on the distillable magic of quantum channels, but they also lead to lower bounds for the task of synthesizing non-Clifford gates. Third, we propose a classical algorithm for simulating noisy quantum circuits, whose sample complexity can be quantified by the mana of a quantum channel. We further show that this algorithm can outperform another approach for simulating noisy quantum circuits, based on channel robustness. Finally, we explore the threshold of non-stabilizerness for basic quantum circuits under depolarizing noise.states also motivates the resource theory of magic states [15][16][17][18][19][20], where the free operations are the SOs and the free states are the stabilizer states (abbreviated as 'Stab'). On the other hand, since a key step of fault-tolerant quantum computing is to implement non-SOs, a natural and fundamental problem is to quantify the nonstabilizerness or 'magic' of quantum operations. As we are at the stage of noisy intermediate-scale quantum (NISQ) technology, a resource theory of magic for noisy quantum operations is desirable both to exploit the power and to identify the limitations of NISQ devices in fault-tolerant quantum computation (FTQC). Overview of resultsIn this paper, we develop a framework for the resource theory of magic quantum channels, based on qudit systems with odd prime dimension d. Related work on this topic has appeared recently [21], but the set of free operations that we take in our resource theory is larger, given by the completely positive-Wigner-preserving (CPWP) perations as we detail below. We note here that d-level FTQC based on qudits with prime d is of considerable interest for both theoretical and practical purposes [22][23][24][25][26].Our paper is structured as follows.• In section 2, we first review the stabilizer formalism [4] and the discrete Wigner function [27][28][29]. We further review various magic m...

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Bounding the energy-constrained quantum and private capacities of phase-insensitive bosonic Gaussian channels

Cited by 64 publications

References 114 publications

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Quantum Capacity Bounds of Gaussian Thermal Loss Channels and Achievable Rates With Gottesman-Kitaev-Preskill Codes

Comparison of Quantum Channels by Superchannels

Quantifying the magic of quantum channels

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