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arxiv: 2605.29717 · v1 · pith:3GN6KHBAnew · submitted 2026-05-28 · 🪐 quant-ph

Discrete and Continuous Wigner Functions in Open Quantum Systems: Non-Markovian and Thermodynamic Effects

Jai Lalita This is my paper

Pith reviewed 2026-06-29 06:49 UTC · model grok-4.3

classification 🪐 quant-ph
keywords negative quantum statesdiscrete Wigner functionsnon-Markovian noisequantum teleportationCHSH violationFisher informationBell statessuperconducting qubits
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The pith

Negative quantum states from phase-space operators resist non-Markovian noise better than Bell states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper examines how negative quantum states identified through discrete Wigner functions maintain non-classical features under realistic noise, focusing on non-Markovian random-telegraph and amplitude-damping channels. It shows that states derived from phase-space point operators preserve entanglement, coherence, and teleportation fidelity more effectively than Bell states, and that weak measurement with reversal can further protect these properties. These states are prepared and verified on superconducting hardware for use in a teleportation scheme, where they also yield stronger CHSH violation and Fisher information. A sympathetic reader would care because this points to practical alternatives for quantum tasks when noise includes memory effects that standard entangled states handle poorly.

Core claim

The thesis establishes that certain negative quantum states generated from phase-space point operators in the discrete Wigner function framework exhibit greater resilience than Bell states under non-Markovian noise, preserving higher entanglement, achieving stronger maximal CHSH violation, and delivering better Fisher information, while also supporting improved teleportation performance when protected by weak measurement and reversal; these states are realized experimentally on IBM superconducting devices with high-fidelity state tomography.

What carries the argument

Discrete Wigner functions that define negative quantum states from phase-space point operators, which characterize non-classicality and track its evolution under open-system channels.

If this is right

  • These negative states can function as improved resources for quantum teleportation in environments with memory-bearing noise.
  • Weak measurement and reversal strategies increase their quantum correlations and reduce fidelity loss compared to unprotected evolution.
  • They enable higher maximal CHSH violation and Fisher information than Bell states under the same non-Markovian channels.
  • Preparation on superconducting hardware demonstrates that the states remain usable for quantum information tasks after realistic noise exposure.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the advantage holds across other non-Markovian models, the states could serve as drop-in replacements for Bell pairs in quantum networks exposed to memory effects.
  • The thermodynamic aspects noted in the title suggest possible links between Wigner negativity and heat dissipation that could be tested in continuous-variable extensions.
  • Verification on additional hardware platforms would clarify whether the observed resilience is device-specific or general to the state construction.

Load-bearing premise

The random-telegraph and amplitude-damping models accurately represent the dominant noise processes in the IBM superconducting device.

What would settle it

An experiment on the IBM device in which the negative states fail to show higher entanglement preservation or CHSH values than Bell states under the device's actual noise would falsify the resilience claim.

Figures

Figures reproduced from arXiv: 2605.29717 by Jai Lalita.

Figure 3.4
Figure 3.4. Figure 3.4: 1: Variation of discrete Wigner negativity for a qubit, qutrit, and two-qubit systems, non-Markovian RTN with time. For 𝛾 = 0.001 and 𝑏 = 0.05. 3.5 DWFS OF MAXIMALLY NEGATIVE QUANTUM STATES UNDER NOISY CHAN‐ NELS In this section, we calculate the DWFs for single-qubit, single-qutrit, and two-qubit systems, using the formalism given in chapter 2, Sec. 2.1.5. We then identify the DWFs for the first negativ… view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: 2: Variation of discrete Wigner negativity for a qubit, qutrit, and two-qubit systems under non-Markovian AD noise with time. For 𝛾 = 50, 𝑔 = 0.01. 0 100 200 300 400 500 t 0.10 0.05 0.00 0.05 0.10 0.15 0.20 Mana Qutrit- NS1 state under NMAD Qutrit- NS2 state under NMAD Qutrit- NS1 state under NMRTN Qutrit- NS2 state under NMRTN [PITH_FULL_IMAGE:figures/full_fig_p056_3_4.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 1: Lines and striations of the 2 × 2 phase space. AMPLITUDE DAMPING NOISE The evolution of a single-qubit system DWFs under the (non)-Markovian AD noise using the Bloch vector representation, given above in Sec. 3.5.1, with Eq. (2.41) and Eq. (2.19) detailed in 35 [PITH_FULL_IMAGE:figures/full_fig_p057_3_5.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 2 and [PITH_FULL_IMAGE:figures/full_fig_p058_3_5.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 3: Variation of DWFs corresponding to the qubit’s |𝑁𝑆1 ⟩ state (for 𝑎1 = 0.50, 𝑎2 = 0.56, and 𝑎3 = −0.66), under Markovian AD noise (for 𝛾 = 0.01, 𝑔 = 1) with time. RANDOM TELEGRAPH NOISE To determine the DWFs of a single-qubit quantum system under the action of (non)-Markovian RTN channel, we employ the Bloch vector representation of single-qubit systems given in Sec. 3.5.1 with Eq. (2.45) and Eq. (2.19… view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 4: Variation of DWFs corresponding to the qubit’s |𝑁𝑆1 ⟩ state (when 𝑎1 = 0.50, 𝑎2 = 0.56 and 𝑎3 = −0.66), under non-Markovian RTN (for 𝛾 = 0.001, 𝑏 = 0.05) with time. W1,1 W1,2 W2,1 W2,2 0 100 200 300 400 500 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 t DWFs [PITH_FULL_IMAGE:figures/full_fig_p060_3_5.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 6: Lines and striations of the 3 × 3 phase space. AMPLITUDE DAMPING NOISE To study the behavior of single-qutrit DWFs under the (non)-Markovian AD channel, we use its dynamical map Eqs. (2.43) and (2.19) (elaborated earlier in chapter 2) for a particular association of MUBs given in TABLE 4.3.2. For the qutrit’s |𝑁𝑆1 ⟩ state, [PITH_FULL_IMAGE:figures/full_fig_p061_3_5.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 7: Variation of DWFs corresponding to the the qutrit’s |𝑁𝑆1 ⟩ state (for 𝑛1 = 0, 𝑛2 = 0, 𝑛3 = −0.5, 𝑛4 = 0, 𝑛5 = 0, 𝑛6 = 0.4, 𝑛7 = 0.7, 𝑛8 = −0.3), under non-Markovian AD (for 𝛾 = 50, 𝑔 = 0.01) with time. RANDOM TELEGRAPH NOISE The DWFs of the single-qutrit system under (non)-Markovian RTN channel are determined by first calculating its dynamical form ℰ 𝑅𝑇 𝑁(𝜌) (discussed in Sec. 2.7.3) using the Bloch v… view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 8: Variation of DWFs corresponding to the qutrit’s |𝑁𝑆1 ⟩ state (when 𝑛1 = 0, 𝑛2 = 0, 𝑛3 = −0.5, 𝑛4 = 0, 𝑛5 = 0, 𝑛6 = 0.4, 𝑛7 = 0.7, 𝑛8 = −0.3), under (non)-Markovian RTN (for 𝛾 = 0.001, 𝑏 = 0.05) with time. 3.5.3 TWO‐QUBIT The discrete phase space for two-qubit systems is defined on a 4 × 4 array. The Galois field, 𝔽4 = {0, 1, 𝜔, 𝜔2}, is used to label the points in this discrete phase space. There are f… view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 9: Lines and striations of the 4 × 4 phase space. AMPLITUDE DAMPING NOISE Using the dynamical form of the non-Markovian AD channel given in Eq. (2.44) and Eq. (2.19) for a par￾ticular association of MUBs given in TABLE 3.5.3, we can study the variation of DWFs of a two-qubit system with time under the action of non-Markovian AD noise [PITH_FULL_IMAGE:figures/full_fig_p064_3_5.png] view at source ↗
Figure 3.5
Figure 3.5. Figure 3.5: 10: Variation of DWFs corresponding to the two-qubit’s |𝑁𝑆1 ⟩ state (𝑎1 = 0.14, 𝑎2 = 0.14, 𝑎3 = 0.61, 𝑠1 = 0.44, 𝑠2 = −0.44, 𝑠3 = 0.14, 𝑡11 = 0.61, 𝑡12 = 0.14, 𝑡13 = −0.44, 𝑡21 = −0.14, 𝑡22 = −0.61, 𝑡23 = −0.44, 𝑡31 = 0.61, 𝑡32 = −0.61 and, 𝑡33 = 0.44), under (non)-Markovian AD (for 𝛾 = 50, 𝑔 = 0.01) with time. 0.2 0.1 0.0 0.1 W1, 1 W1, 2, W2, 2 W1, 3, W3, 3 W1, 4, W4, 4 W2, 1 0 20 40 60 80 100 0.2 0.1 0… view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: 1: Variation of quantum coherence for the two-qubit’s |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩ states, and Bell state under non-Markovian RTN noise with time. For 𝛾 = 0.001 and 𝑏 = 0.05. 0 100 200 300 400 500 t 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Quantum coherence Bell state Two-qubit- NS1 state Two-qubit- NS2 state Two-qubit- NS3 state [PITH_FULL_IMAGE:figures/full_fig_p067_3_6.png] view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: 3: Concurrence variation for the two-qubit’s |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩ states, and Bell state under Markovian RTN noise with time. For 𝛾 = 1 and 𝑏 = 0.07. 3.7 TELEPORTATION FIDELITY VARIATION USING DWFS UNDER DIFFERENT NOISY CHANNELS Quantum teleportation uses two-qubit entangled states as a resource, and the teleportation fidelity [Horodecki et al., 1996] is determined as 𝐹(𝜌𝐴𝐵) = 1 2 (1 + 𝑁𝐹 (𝜌𝐴𝐵) 3 ) , (… view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: 4: Concurrence variation for the two-qubit’s |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩ states, and Bell state under Markovian AD noise with time. For 𝛾 = 0.01, 𝑔 = 1. 0 100 200 300 400 500 t 0.0 0.2 0.4 0.6 0.8 1.0 Concurrence Bell state Two-qubit- NS1 state Two-qubit- NS2 state Two-qubit- NS3 state [PITH_FULL_IMAGE:figures/full_fig_p069_3_6.png] view at source ↗
Figure 3.6
Figure 3.6. Figure 3.6: 6: Concurrence variation for the two-qubit’s |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩ states, and Bell state under non-Markovian AD noise with time. For 𝛾 = 1, 𝑔 = 0.005. 𝑡11 =1 − 2 (𝑊1,1 + 𝑊1,2 + 𝑊1,3 + 𝑊1,4 + 𝑊4,1 + 𝑊4,2 + 𝑊4,3 + 𝑊4,4) , 𝑡12 =1 − 2 (𝑊1,2 + 𝑊1,4 + 𝑊2,1 + 𝑊2,3 + 𝑊3,1 + 𝑊3,3 + 𝑊4,2 + 𝑊4,4) , 𝑡13 =1 − 2 (𝑊1,2 + 𝑊1,4 + 𝑊2,2 + 𝑊2,4 + 𝑊3,1 + 𝑊3,3 + 𝑊4,1 + 𝑊4,3) , 𝑡21 =1 − 2 (𝑊1,1 + 𝑊1,2 + 𝑊2,3 + 𝑊2,4 + 𝑊3,3 + … view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: 1: Variation of teleportation fidelity for the two-qubit’s |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩ states, and Bell state under Markovian RTN noise with time. For 𝛾 = 1 and 𝑏 = 0.07. 0 100 200 300 400 500 t 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 Teleportation fidelity Bell state 1st Negative state 2nd Negative state 3rd Negative state [PITH_FULL_IMAGE:figures/full_fig_p071_3_7.png] view at source ↗
Figure 3.7
Figure 3.7. Figure 3.7: 3: Variation of teleportation fidelity for the two-qubit’s |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩ states, and Bell state under non-Markovian RTN noise with time. For 𝛾 = 0.001 and 𝑏 = 0.05. 0 100 200 300 400 500 t 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 Teleportation fidelity Bell state Two-qubit- NS1 state Two-qubit- NS2 state Two-qubit- NS3 state [PITH_FULL_IMAGE:figures/full_fig_p072_3_7.png] view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: 1: Schematic diagram for protecting quantum correlations of negative quantum states and Bell state using weak measurement (𝑀WM) and quantum measurement reversal (𝑀QMR). 4.2 MODEL This section presents the physical model for protecting quantum correlations and universal quan￾tum teleportation protocol requirements of two-qubit quantum states using weak measurement and quantum measurement reversal in the n… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 1: Variation of concurrence of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non-Markovian AD channel without WM and QMR in subplot (a), and with WM and QMR in subplot (b) with time. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁𝑆2 ⟩ (𝑝 = 0.05, 𝑞 = 0.74), for |𝑁𝑆′ 3 ⟩ (𝑝 = 0.05, 𝑞 = 0.05), and for Bell state (𝑝 = 0.01, 𝑞 = 0.01). The non-Markovian AD channel parameters are 𝑔 = 0.01 and 𝛾 = 5. 0 10 20 30 … view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 3(a) shows the variation of discord of two-qubit |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and the Bell state under non-Markovian AD noise without WM and QMR. The variation of discord of |𝑁𝑆′ 3 ⟩ state is similar to the Bell state under non-Markovian AD noise. Also, these states have the highest discord values among all the considered states. The variation of discord under the non-Markovian AD noise with WM and QMR of t… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 4: Variation of discord of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non-Markovian RTN channel without WM and QMR in subplot (a), and with WM and QMR in subplot (b) with time. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁𝑆2 ⟩ (𝑝 = 0.05, 𝑞 = 0.74), for |𝑁𝑆′ 3 ⟩ (𝑝 = 0.05, 𝑞 = 0.05), and for Bell state (𝑝 = 0.01, 𝑞 = 0.01). The non-Markovian RTN channel parameters are 𝑏 = 0.05 and 𝛾 = 0.001. 4.3.4 STE… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 5: Variation of two (three)-measurement steering of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non-Markovian AD channel with time. Here, subplots (a) and (c) represent the two￾measurement and three-measurement steering without WM and QMR, and subplots (b) and (d) represent the two-measurement and three-measurement steering with WM and QMR, respec￾tively. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁𝑆… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 6: Variation of two (three)-measurement steering of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non-Markovian RTN channel with time. Here, subplots (a) and (b) represent the two￾measurement and three-measurement steering without WM and QMR, and subplots (b) and (d) represent the two-measurement and three-measurement steering with WM and QMR, respec￾tively. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 7: Variation of maximal average fidelity of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non-Markovian AD channel without WM and QMR in subplot (a), and with WM and QMR in subplot (b) with time. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁𝑆2 ⟩ (𝑝 = 0.05, 𝑞 = 0.74), for |𝑁𝑆′ 3 ⟩ (𝑝 = 0.05, 𝑞 = 0.05), and for Bell state (𝑝 = 0.01, 𝑞 = 0.01). The non-Markovian AD channel parameters are 𝑔 = 0.01 and 𝛾 = 5… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 8: Variation of maximal average fidelity of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non-Markovian RTN channel without WM and QMR in subplot (a), and with WM and QMR in subplot (b) with time. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁𝑆2 ⟩ (𝑝 = 0.05, 𝑞 = 0.74), for |𝑁𝑆′ 3 ⟩ (𝑝 = 0.05, 𝑞 = 0.05), and for Bell state (𝑝 = 0.01, 𝑞 = 0.01). The non-Markovian RTN channel parameters are 𝑏 = 0.05 and 𝛾 =… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 9: Variation of fidelity deviation of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non￾Markovian AD channel without WM and QMR in subplot (a), and with WM and QMR in subplot (b) with time. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁𝑆2 ⟩ (𝑝 = 0.05, 𝑞 = 0.74), for |𝑁𝑆′ 3 ⟩ (𝑝 = 0.05, 𝑞 = 0.05), and for Bell state (𝑝 = 0.01, 𝑞 = 0.01). The non-Markovian AD channel parameters are 𝑔 = 0.01 and 𝛾 = 5. UNDE… view at source ↗
Figure 4.3
Figure 4.3. Figure 4.3: 10: Variation of fidelity deviation of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non￾Markovian RTN channel without WM and QMR in subplot (a), and with WM and QMR in subplot (b) with time. Here, for |𝑁𝑆1 ⟩ (𝑝 = 0.17, 𝑞 = 0.54), for |𝑁𝑆2 ⟩ (𝑝 = 0.05, 𝑞 = 0.74), for |𝑁𝑆′ 3 ⟩ (𝑝 = 0.05, 𝑞 = 0.05), and for Bell state (𝑝 = 0.01, 𝑞 = 0.01). The non-Markovian RTN channel parameters are 𝑏 = 0.05 and 𝛾 = 0.00… view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: 1: Variation of concurrence of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state under non-Markovian AD channel with WM and QMR in subplots (a), (b), (c), and (d). In subplot (a) 𝑝 = 0.17, 𝑞 = 0.54 for all states, in subplot (b) 𝑝 = 0.05, 𝑞 = 0.74 for all states, in subplot (c) 𝑝 = 0.05, 𝑞 = 0.05 for all states, and in subplot (d) 𝑝 = 0.01, 𝑞 = 0.01 for all states. The non-Markovian AD channel parameters are 𝑔 = … view at source ↗
Figure 4.4
Figure 4.4. Figure 4.4: 2: Variation of success probability of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆′ 3 ⟩, and Bell state (𝐵𝑆) under non-Markovian AD and RTN channels in subplots (a) and (b), respectively. Here, the figures are depicted for WM strength (𝑝) and QMR strength (𝑞) at time 𝑡 = 10. The non-Markovian AD and RTN channel parameters are (𝑔 = 0.01, 𝛾 = 5) and (𝑏 = 0.05, 𝛾 = 0.001), respectively. states, making it an ideal state for UQT. Al… view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: 0: Quantum circuits to generate the two-qubit |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩, and |𝑁𝑆′ 3 ⟩ states from the |00⟩ state using 𝐻, 𝑅𝑥 , 𝑅𝑧 , and 𝐶𝑍 gates are shown in subfigures (a), (b), (c), and (d) respectively. Here, 𝑞0 and 𝑞1 represent the qubits in the |00⟩ state. 5.2.3 QUANTUM STATE TOMOGRAPHY AND ERROR MITIGATION ON IBM DEVICES Tomography is a technique used to construct an image of a hidden object by analyz… view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: 1: The city plot for the |𝑁𝑆2 ⟩ state displays the absolute difference between the compo￾nents of the original 𝜌𝑁𝑆2 and the 𝑁𝑆 ̃𝜌 2 obtained after performing a state tomography experiment on the real IBM quantum computer ibm_brisbane for 8192 times. Quantum States Circuit depth Circuit complexity Schmidt Rank Fidelity State Tomography Mitigated State Tomography On simulator (AerSimulator) On IBM quantum … view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: 2: The city plot for the |𝑁𝑆2 ⟩ state displays the absolute difference between the compo￾nents of the original 𝜌𝑁𝑆2 and the 𝑁𝑆 ̃𝜌 2 obtained after performing a mitigated state tomography experiment on the real IBM quantum computer ibm_brisbane for 8192 times. This is known as mitigated state tomography. We carry out the mitigated state tomography for the nega￾tive quantum states and the Bell state on the… view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: 0: Variation of (1 − 𝐹) for |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩, and |𝜙+⟩ Bell state with depolarizing error probability 𝑝 (a) without any error correction and (b) after implementing Shor’s error cor￾rection [PITH_FULL_IMAGE:figures/full_fig_p099_5_3.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: 1: Variation of fidelity of |𝑁𝑆1 ⟩, |𝑁𝑆2 ⟩, |𝑁𝑆3 ⟩ and |𝜙+⟩ Bell state with time (a) under non-Markovian RTN for 𝑏 = 0.05 and 𝛾 𝑅𝑇 𝑁 = 0.001, (b) under non-Markovian AD for 𝑔 = 0.01 and 𝛾 𝐴𝐷 = 5. The variation of fidelity 𝐹, between the original state and the state after applying the non-Markovian noise, of two-qubit negative quantum states and the Bell state under non-Markovian RTN and AD noise is illus… view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: 2: Variation of 𝜁|𝑁𝑆1 ⟩ and 𝜁|𝑁𝑆2 ⟩ with respect to time under non-Markovian AD for 𝑔 = 0.01 and 𝛾 𝐴𝐷 = 5. 5.3.4 CHSH INEQUALITY VIOLATION: NONLOCALITY UNDER NOISE The optimal violation of the Clauser-Horne-Shimony-Holt (CHSH) inequality constitutes a fundamental benchmark for detecting the quantum nonlocality of a general two-qubit state. Given a two-qubit density matrix 𝜌, the maximal CHSH violation is… view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: 3: The temporal variation of 𝜂|𝑁𝑆2 ⟩ , specifically the ratio 𝑆𝑚𝑎𝑥|𝑁𝑆2 ⟩/𝑆𝑚𝑎𝑥|𝜙+⟩ under non￾Markovian AD channel with WM and QMR for |𝑁𝑆2 ⟩ (𝑝 = 0.05, 𝑞 = 0.74), and for Bell |𝜙+⟩ state (𝑝 = 0.05, 𝑞 = 0.05). The non-Markovian AD channel parameters are 𝑔 = 0.01 and 𝛾 𝐴𝐷 = 5. Further, a detailed methodology and comprehensive analysis for identifying optimal states, among the Bell states and two-qubit negat… view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: 1 [PITH_FULL_IMAGE:figures/full_fig_p110_6_2.png] view at source ↗
Figure 6.2
Figure 6.2. Figure 6.2: 2: Schematic representation of Scheme B, where system qubits 𝑠1 and 𝑠2 interact with two independent streams of ancillae 𝑎 𝐿 𝑛 and 𝑎 𝑅 𝑛 , respectively. In this diagram, black lines indicate Heisenberg-type interactions between the system qubits as well as between each system qubit and its corresponding ancilla. The red line represents a partial swap interaction occurring between successive ancillae in t… view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: 1: The evolution of the trace distance and non-Markovianity measure (𝒩) between the Bell states |𝜙+⟩ and |𝜙−⟩ is analyzed using the scheme A as a function of the number of collisions (𝑛) in subplots (𝑎) and (𝑏), respectively. In this analysis, the parameters are set as follows: 𝜔𝑠1 = 𝜔𝑠2 = 𝜔𝑎𝑅𝑛 = 1, 𝑔𝑠2𝑎𝑅𝑛 = 0.85, 𝑔𝑠1𝑠2 = 0.95, Δ𝑡 = 0.5 and 𝛽𝑎𝑅𝑛 = 1. For Markovian dynamics, intra-ancilla interaction stre… view at source ↗
Figure 6.3
Figure 6.3. Figure 6.3: 2: The evolution of the trace distance in the upper panels (a, b) and non-Markovianity measure (𝒩) in the lower panels (c, d) between the Bell states |𝜙+⟩ and |𝜙−⟩ is analyzed using the scheme B as a function of the number of collisions (𝑛). In this analysis, the parameters are set as follows: 𝜔𝑠1 = 𝜔𝑠2 = 𝜔𝑎𝐿 𝑛 = 𝜔𝑎𝑅𝑛 = 1, 𝑔𝑠2𝑎𝑅𝑛 = 𝑔𝑠1𝑎𝐿 𝑛 = 0.85, 𝑔𝑠1𝑠2 = 0.95, Δ𝑡 = 0.5. In subplot (a) and (c) 𝛽𝑎𝐿 𝑛 = 𝛽𝑎… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: 1: Variation of the Wigner function of the |𝑁𝑆′ 3 ⟩, and Bell |𝜙+⟩ states using the scheme A with the number of collisions. Here 𝜃1 = 𝜃2 = 𝜋/2, 𝜙1 = 𝜙2 = 𝜋/6, 𝜔𝑠1 = 𝜔𝑠2 = 𝜔𝑎𝑅𝑛 = 1, 𝑔𝑠2𝑎𝑅𝑛 = 0.85, 𝑔𝑠1𝑠2 = 0.95, Δ𝑡 = 0.08 and 𝛽𝑎𝑅𝑛 = 1. Subplot (a) is for Markovian dynamics when Θ = 0, and subplot (b) is for non-Markovian dynamics when Θ = 0.95 × 𝜋/2. et al., 2015]. The Wigner function is also normalized su… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: 2: Variation of the Wigner function of the |𝑁𝑆′ 3 ⟩, and Bell |𝜙+⟩ states using the scheme B with the number of collisions. In this analysis, the parameters are set as follows: 𝜃1 = 𝜃2 = 𝜋/2, 𝜙1 = 𝜙2 = 𝜋/6, 𝜔𝑠1 = 𝜔𝑠2 = 𝜔𝑎𝐿 𝑛 = 𝜔𝑎𝑅𝑛 = 1, 𝑔𝑠2𝑎𝑅𝑛 = 𝑔𝑠1𝑎𝐿 𝑛 = 0.85, 𝑔𝑠1𝑠2 = 0.95, Δ𝑡 = 0.08. In subplot (a) and (b) 𝛽𝑎𝐿 𝑛 = 𝛽𝑎𝑅𝑛 = 1, and in subplot (c) and (d) 𝛽𝑎𝐿 𝑛 = 1, 𝛽𝑎𝑅𝑛 = 4. For Markovian dynamics, intra-a… view at source ↗
Figure 6.4
Figure 6.4. Figure 6.4: 3: Variation of the non-classical volume of the |𝑁𝑆′ 3 ⟩, and Bell |𝜙+⟩ states with the number of collisions using scheme A. Here 𝜔𝑠1 = 𝜔𝑠2 = 𝜔𝑎𝑅𝑛 = 1, 𝑔𝑠2𝑎𝑅𝑛 = 0.85, 𝑔𝑠1𝑠2 = 0.95, Δ𝑡 = 0.08 and 𝛽𝑎𝑅𝑛 = 1. Subplot (a) is for Markovian dynamics when Θ = 0, and subplot (b) is for non-Markovian dynamics when Θ = 0.95 × 𝜋/2. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 (a) Markovian case, a L n = a R n |NS 0 3 state Bell | + … view at source ↗
Figure 6.5
Figure 6.5. Figure 6.5: 1: Variation of the concurrence of the |00⟩, |01⟩, |10⟩ and |11⟩ states using the scheme A with the number of collisions. Here 𝜔𝑠1 = 𝜔𝑠2 = 𝜔𝑎𝑅𝑛 = 1, 𝑔𝑠2𝑎𝑅𝑛 = 0.85, 𝑔𝑠1𝑠2 = 0.95, Δ𝑡 = 0.08 and 𝛽𝑎𝑅𝑛 = 1. Subplot (a) is for Markovian dynamics when Θ = 0, and subplot (b) is for non￾Markovian dynamics when Θ = 0.95 × 𝜋/2. 0.0 0.2 0.4 0.6 0.8 (a) Markovian case, a L n = a R n |00 state |01 state |10 state |11 … view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: 1: Evolution of fidelity between the two-qubit system’s steady state and the Gibbs state corresponding to the two-qubit system Hamiltonian and Hamiltonian of mean force in subplots (a) and (b), respectively, under scheme B within the context of Markovian (Θ = 0) and non￾Markovian dynamics (Θ = 0.95𝜋/2) with the temperature of ancillae. Here, the temperature of ancillae, i.e., 𝑇𝑎𝐿 𝑛 = 1/𝛽𝑎𝐿 𝑛 , 𝑇𝑎𝑅𝑛 = 1/𝛽… view at source ↗
Figure 6.6
Figure 6.6. Figure 6.6: 2: Evolution of fidelity between the each system’s qubit individual steady state and the Gibbs state corresponding to its bare Hamiltonian with the temperature of ancillae, i.e., 𝑇𝑎𝐿 𝑛 = 1/𝛽𝑎𝐿 𝑛 , and 𝑇𝑎𝑅𝑛 = 1/𝛽𝑎𝑅𝑛 , under scheme B within the context of Markovian (Θ = 0) and non￾Markovian dynamics (Θ = 0.95𝜋/2). Here 𝑇𝑎𝐿 𝑛 = 𝑇𝑎𝑅𝑛 = 𝑇𝑎 . The parameters are set as follows: in subplots (a) and (b) 𝜔𝑠1 = 𝜔𝑠2… view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: 1: This diagram illustrates a single-qubit collision model in which the system qubit, de￾noted as 𝑆, interacts with a sequence of ancilla qubits 𝑅𝑛. The spiral lines represent a Heisenberg￾type interaction between the system qubit 𝑆 and the ancillae. In contrast, the double-sided ar￾rowed straight lines indicate a partial-swap interaction between successive ancilla qubits. where 𝑟 ′ 𝑥 , 𝑟′ 𝑦 , 𝑟′ 𝑧 are t… view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: 2: Variation of non-classical volume (𝛿), von-Neumann entropy (𝑆) in subplot (𝑎), and entropy production (Σ), ergotropy (𝒲) in subplot (𝑏) with the number of collisions of the single￾qubit maximally negative quantum state using a non-Markovian collision model. The parameters are: 𝜔𝑠 = 1.5, 𝜔𝑅 = 1, 𝛽 = 50, 𝑔𝑆𝑅 = 0.5, Θ = 0.98𝜋 2 and 𝜏 = 0.5. site relation between entropy production and ergotropy, demonstr… view at source ↗
Figure 7.3
Figure 7.3. Figure 7.3: 3: Variation of non-classical volume (𝛿), von-Neumann entropy (𝑆) in subplot (𝑎), and entropy production (Σ), ergotropy (𝒲) in subplot (𝑏) with time using the central spin model of the single-qubit maximally negative quantum state. The parameters are: 𝜔0 = 1.5, 𝜔 = 1, 𝛽 = 100, 𝜖 ′ = 0.5 and 𝑁 = 50. The reduced dynamics of the central spin is then obtained by tracing out the bath degrees of freedom as 𝜌 ′… view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: 1: Variation of non-classical volume (𝛿), von-Neumann entropy (𝑆) in subplot (𝑎), and entropy production (Σ), ergotropy (𝒲) in subplot (𝑏) with time of the single-qubit maximally negative quantum state under the NMAD channel. The parameters are: 𝜔0 = 10, 𝜆 = 0.05 and 𝛾0 = 50. evolution, while 𝜆 > 2𝛾0 gives time-dependent Markovian dynamics, and 𝜆 ≫ 𝛾0 reduces to the standard time-independent amplitude da… view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: 2: Variation of non-classical volume (𝛿), von-Neumann entropy (𝑆) in subplot (𝑎), and entropy production (Σ), ergotropy (𝒲) in subplot (𝑏) with time of the one-qubit maximally nega￾tive quantum state. The evolution is governed by the Markovian generalized amplitude damping master equation. The parameters are: 𝜔0 = 1.5, 𝛽 = 1, and 𝑔 = 0.05. 2021]. The Hamiltonian of the Jaynes-Cummings model is 𝐻JC = 𝜔0 2… view at source ↗
Figure 7.4
Figure 7.4. Figure 7.4: 3: Variation of non-classical volume (𝛿), von-Neumann entropy (𝑆) in subplot (𝑎), and entropy production (Σ), ergotropy (𝒲) in subplot (𝑏) with time of the one-qubit maximally neg￾ative quantum state using the Jaynes-Cummings model. The parameters are: 𝜔0 = 1.5, 𝜔𝑐 = 1, 𝛽 = 3, 𝑔 = 0.5, and 𝜏 = 0.5. more work to be extracted. Despite this universal structure, notable distinctions emerged depending on the … view at source ↗
read the original abstract

The central aim of the thesis is to examine how non-classical resources in finite-dimensional quantum systems can be identified, characterized, and protected for practical use in the presence of realistic noise. Using the discrete Wigner functions (DWFs) framework, we introduce negative quantum states and examine how their Wigner negativity, mana, coherence, and teleportation fidelity evolve under unital and non-unital channels, with particular attention to non-Markovian random-telegraph and amplitude-damping dynamics. We also analyze protection strategies based on weak measurement and quantum measurement reversal, showing that these methods can enhance quantum correlations, reduce fidelity deviation, and improve teleportation performance for two-qubit negative states in memory-bearing environments. Moreover, we demonstrate that certain negative states, derived from phase-space point operators, exhibit greater resilience than Bell states in measures of entanglement under non-Markovian noise. Further, this thesis focuses on developing and implementing quantum circuits for generating these states on superconducting hardware and realizing them for the first time on IBM's ibm-Brisbane device. Their preparation is verified using quantum state tomography, demonstrating high fidelity under realistic noise conditions. We propose a teleportation scheme that leverages one of the two-qubit negative quantum states as a resource. Moreover, these two-qubit negative quantum states are also found to perform better than the Bell states for maximal CHSH violation and Fisher information in noisy conditions. We believe that these negative quantum states have the potential to be used in place of the traditional Bell states in scenarios where non-Markovian errors are prevalent. (continued in the PDF)

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Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

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Summary. The manuscript examines negative quantum states defined through discrete Wigner functions in open quantum systems. It analyzes their Wigner negativity, mana, coherence, and teleportation fidelity under unital and non-unital channels, with emphasis on non-Markovian random-telegraph and amplitude-damping dynamics. Protection via weak measurement and reversal is studied. The central claims are that certain phase-space-point-operator-derived negative states exhibit greater entanglement resilience than Bell states under these channels, superior maximal CHSH violation and Fisher information in noise, and that they were prepared and tomographically verified on ibm-Brisbane hardware, with a proposed teleportation scheme using one such state.

Significance. If the resilience advantage and hardware results hold after proper model calibration, the work would identify concrete alternatives to Bell states for non-Markovian environments in superconducting platforms, with potential impact on entanglement distribution and metrology tasks. The explicit hardware implementation and tomography verification constitute a concrete strength.

major comments (1)
  1. [Abstract; hardware implementation and simulation sections] The load-bearing claim that negative states derived from phase-space point operators exhibit greater resilience than Bell states (and superior CHSH/Fisher performance) under non-Markovian noise rests on simulations with random-telegraph and amplitude-damping channels. No section describes calibration of the model parameters (switching rate, correlation time, damping strength) to measured ibm-Brisbane quantities such as T1/T2 spectra, cross-talk, or non-Markovian signatures. Without this mapping, the reported advantage does not demonstrably transfer to the hardware regime invoked in the abstract and conclusion.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the single major comment below and will revise the manuscript accordingly to clarify the distinction between phenomenological simulations and hardware results.

read point-by-point responses

  1. Referee: [Abstract; hardware implementation and simulation sections] The load-bearing claim that negative states derived from phase-space point operators exhibit greater resilience than Bell states (and superior CHSH/Fisher performance) under non-Markovian noise rests on simulations with random-telegraph and amplitude-damping channels. No section describes calibration of the model parameters (switching rate, correlation time, damping strength) to measured ibm-Brisbane quantities such as T1/T2 spectra, cross-talk, or non-Markovian signatures. Without this mapping, the reported advantage does not demonstrably transfer to the hardware regime invoked in the abstract and conclusion.

    Authors: We agree that the manuscript does not provide explicit calibration of the random-telegraph switching rates or amplitude-damping strengths to ibm-Brisbane T1/T2 spectra, cross-talk, or measured non-Markovian signatures. The simulations use standard phenomenological models with parameters selected to illustrate non-Markovian memory effects in general, while the hardware section reports only state preparation and tomography on ibm-Brisbane, independent of the dynamical evolution. In the revised version we will add a dedicated paragraph in the simulation section (and a clarifying sentence in the abstract) stating that the reported resilience advantage applies to the chosen model channels and that quantitative mapping to the specific device would require additional calibration experiments, which lie outside the present scope. This revision will remove any implication that the advantage has been directly verified on the hardware. revision: yes

Circularity Check

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No circularity in derivation chain

full rationale

The provided abstract and thesis summary describe introduction of negative states via discrete Wigner functions, their evolution under chosen non-Markovian channel models, and hardware verification on ibm-Brisbane via tomography. No equations, fitting procedures, or self-citations are exhibited that would reduce any resilience, CHSH, or Fisher-information claims to the inputs by construction. The channel simulations and experimental preparation are presented as separate steps, with the former used to compute metrics and the latter to confirm realizability; this structure remains self-contained against external benchmarks without load-bearing circular reductions.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review supplies no explicit free parameters, axioms, or invented entities; the central claims rest on standard quantum channel models and the definition of discrete Wigner functions from prior literature.

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