Multilevel Polarization for Quantum Channels

• URL: http://arxiv.org/abs/2006.12652v2
• Date: Sun, 21 Mar 2021 23:53:10 GMT
• Title: Multilevel Polarization for Quantum Channels
• Authors: Ashutosh Goswami, Mehdi Mhalla, Valentin Savin
• Abstract summary: We consider the quantum polar code construction using the same channel combining and splitting procedure as in [1], but with a fixed two-qubit Clifford unitary. For the family of Pauli channels, we show that polarization happens in multi-levels, where synthesized quantum virtual channels tend to become completely noisy, half-noisy, or noiseless. We present a quantum polar code exploiting the multilevel nature of polarization, and provide an efficient decoding for this code.
• Score: 5.607676459156789
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, a purely quantum version of polar codes has been proposed in [1] based on a quantum channel combining and splitting procedure, where a randomly chosen two-qubit Clifford unitary acts as channel combining operation. Here, we consider the quantum polar code construction using the same channel combining and splitting procedure as in [1], but with a fixed two-qubit Clifford unitary. For the family of Pauli channels, we show that polarization happens in multi-levels, where synthesized quantum virtual channels tend to become completely noisy, half-noisy, or noiseless. Further, we present a quantum polar code exploiting the multilevel nature of polarization, and provide an efficient decoding for this code. We show that half-noisy channels can be frozen by fixing their inputs in either the amplitude or the phase basis, which allows reducing the number of preshared EPR pairs compared to the construction in [1]. We provide an upper bound on the number of preshared EPR pairs, which is an equality in the case of the quantum erasure channel. To improve the speed of polarization, we propose an alternative construction, which again polarizes in multi-levels, and the previous upper bound on the number of preshared EPR pairs also holds. For a quantum erasure channel, we confirm by numerical analysis that the multilevel polarization happens relatively faster for the alternative construction.

Related papers

• Resolvability of classical-quantum channels [54.825573549226924]
  We study the resolvability of classical-quantum channels in two settings, for the channel output generated from the worst input, and form the fixed independent and identically distributed (i.i.d.) input. For the fixed-input setting, while the direct part follows from the known quantum soft covering result, we exploit the recent alternative quantum Sanov theorem to solve the strong converse.
  arXiv  Detail & Related papers  (2024-10-22T05:18:43Z)
• The multimode conditional quantum Entropy Power Inequality and the squashed entanglement of the extreme multimode bosonic Gaussian channels [53.253900735220796]
  Inequality determines the minimum conditional von Neumann entropy of the output of the most general linear mixing of bosonic quantum modes. Bosonic quantum systems constitute the mathematical model for the electromagnetic radiation in the quantum regime.
  arXiv  Detail & Related papers  (2024-10-18T13:59:50Z)
• Towards an All-Silicon QKD Transmitter Sourced by a Ge-on-Si Light Emitter [1.8823998908501027]
  We demonstrate a novel quantum key distribution transmitter based on polarization-encoded BB84 protocol. We experimentally prove that the Ge-on-Si light source can accommodate for quantum key generation by accomplishing raw-key rates of 2.15 kbit/s at a quantum bit error ratio of 7.71% at a symbol rate of 1 GHz. Our results prove the feasibility of a fully-integrated silicon quantum key distribution transmitter, including its light source, for possible short-reach applications in zero-trust intra-datacenter environments.
  arXiv  Detail & Related papers  (2024-03-20T11:04:00Z)
• Normal quantum channels and Markovian correlated two-qubit quantum errors [77.34726150561087]
  We study general normally'' distributed random unitary transformations. On the one hand, a normal distribution induces a unital quantum channel. On the other hand, the diffusive random walk defines a unital quantum process.
  arXiv  Detail & Related papers  (2023-07-25T15:33:28Z)
• Quantum soft-covering lemma with applications to rate-distortion coding, resolvability and identification via quantum channels [7.874708385247353]
  We prove a one-shot quantum covering lemma in terms of smooth min-entropies. We provide new upper bounds on the unrestricted and simultaneous identification capacities of quantum channels.
  arXiv  Detail & Related papers  (2023-06-21T17:53:22Z)
• Quantum emulation of the transient dynamics in the multistate Landau-Zener model [50.591267188664666]
  We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity. Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
  arXiv  Detail & Related papers  (2022-11-26T15:04:11Z)
• Quantum-inspired optimization for wavelength assignment [51.55491037321065]
  We propose and develop a quantum-inspired algorithm for solving the wavelength assignment problem. Our results pave the way to the use of quantum-inspired algorithms for practical problems in telecommunications.
  arXiv  Detail & Related papers  (2022-11-01T07:52:47Z)
• Channel Polarization of Two-dimensional-input Quantum Symmetric Channels [2.7913769926470082]
  In this paper, we define a class of quantum channels called quantum symmetric channels. Under the similar channel combining and splitting process as in the classical channel polarization, the maximum single letter coherent information of the coordinate channels will polarize.
  arXiv  Detail & Related papers  (2021-11-10T03:29:12Z)
• Coherent control and distinguishability of quantum channels via PBS-diagrams [59.94347858883343]
  We introduce a graphical language for coherent control of general quantum channels inspired by practical quantum optical setups involving polarising beam splitters (PBS) We characterise the observational equivalence of purified channels in various coherent-control contexts, paving the way towards a faithful representation of quantum channels under coherent control.
  arXiv  Detail & Related papers  (2021-03-02T22:56:25Z)
• Quantum Polarization of Qudit Channels [5.607676459156789]
  We provide a generalization of quantum polar codes to quantum channels with qudit-input. We show how to decode the proposed quantum polar codes on Pauli qudit channels.
  arXiv  Detail & Related papers  (2021-01-25T15:58:37Z)
• Belief Propagation with Quantum Messages for Quantum-Enhanced Classical Communications [10.881273953303268]
  In space-based laser communications, the mean photon number per received optical pulse is much smaller than one. There is a large gap between communications capacity achievable with a receiver that performs individual pulse-by-pulse detection, and the quantum-optimal "joint-detection receiver" We show that a BPQM-receiver might attain the Holevo capacity of this BPSK-modulated pure-loss channel.
  arXiv  Detail & Related papers  (2020-03-09T18:44:34Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.