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Lecture notes in mathematics

An open problem in quantum shot noise

Gerhard C. Hegerfeldt

Published Jan 1, 1990• 0 citations
Publisher
DOI
10.1007/bfb0085511

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Open Quantum Theory of Shot Noise in Dissipative Chiral Transport

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We develop an open quantum theory for shot-noise dynamics in dissipative chiral transport. By mapping a system under consideration onto a quantum circuit, we show that current noise is governed by two competing factors: the average occupancy distribution and particle-number fluctuations. With energy fully relaxed, shot noise is strongly suppressed, reflecting the stacking of electrons into lower energy states due to dissipation. This process quenches the partition noise from partially occupied levels, and finally isolates the residual noise protected by strong $U(1)$ symmetry. Moreover, selectively heating the source against the bath uncovers the underlying competition between the noise contributions from the occupancy distribution and those from the particle-number fluctuations. It triggers a sign reversal in inter-channel correlation noise, a signature masked by seemingly identical single-channel thermal noises. We propose an inversion scheme to experimentally reconstruct the hidden occupancy distribution directly from measurable noise cumulants.

cond-mat.mes-hallCross-listedarXiv:2605.14263•May 15, 2026
The bosonic quantum channels have recently attracted a growing interest, motivated by the hope that they open a tractable approach to the generally hard problem of evaluating quantum channel capacities. These studies, however, have always been restricted to memoryless channels. Here, it is shown that the classical capacity of a bosonic Gaussian channel with memory can be significantly enhanced if entangled symbols are used instead of product symbols. For example, the capacity of a photonic channel with 70%-correlated thermal noise of one-third the shot noise is enhanced by about 11% when using 3.8-dB entangled light with a modulation variance equal to the shot noise.
Abstract The shot-noise unit (SNU) is a crucial factor for the practical security of a continuous-variable quantum key distribution system. In the most widely used experimental scheme, the SNU should be calibrated first and acts as a constant during the key distribution. However, the SNU of a practical system is dependent on the various parameters of the local oscillator (LO), which can be controlled by the eavesdropper in the open channel. In this paper, we report a quantum hacking method to control the practical SNU by using the limited compensation rate of the polarization compensation. Since the compensation is only based on of the polarization measurement results of part of LO pulses, the polarization of other unmeasured pulses may not be compensated correctly, which can be utilized by the eavesdropper to control the practical SNU. The simulation and experiment results indicate that the practical SNU can be controlled by the eavesdropper. Thus, the eavesdropper can use the fact that the practical SNU is no longer equals to the calibrated one to control the excess noise and final key rate.
The shot-noise unit (SNU) is a crucial factor for the practical security of a continuous-variable quantum key distribution system. In the most widely used experimental scheme, the SNU should be calibrated first and used as a constant during key distribution. Because the measurement result of quadrature is normalized with the calibration SNU but scaled with practical SNU, which could open loopholes for the eavesdropper to intercept the secret key. In this paper, we report a quantum hacking method to control the practical SNU by using the limited compensation rate for polarization drift. Since the polarization of local oscillator pulses is partially measured, the attack is implemented by manipulating the polarization of the local oscillator pulses without measurement when the system is running. The simulation and experiment results indicate that the practical SNU can be manipulated by the eavesdropper. By making the difference between the calibration and the practical SNU, the excess noise estimated by Alice and Bob could always be lower than the practice which is introduced by the eavesdropper and the distributed keys are not secure.
We develop an open quantum theory for shot-noise dynamics in dissipative chiral transport. By mapping a system under consideration onto a quantum circuit, we show that current noise is governed by two competing factors: the average occupancy distribution and particle-number fluctuations. With energy fully relaxed, shot noise is strongly suppressed, reflecting the stacking of electrons into lower energy states due to dissipation. This process quenches the partition noise from partially occupied levels, and finally isolates the residual noise protected by strong U(1)U(1)U(1) symmetry. Moreover, selectively heating the source against the bath uncovers the underlying competition between the noise contributions from the occupancy distribution and those from the particle-number fluctuations. It triggers a sign reversal in inter-channel correlation noise, a signature masked by seemingly identical single-channel thermal noises. We propose an inversion scheme to experimentally reconstruct the hidden occupancy distribution directly from measurable noise cumulants.