We ask where the qg description of a qubit, and its companions [1], is useful for cryptography. Post-quantum cryptography (lattice-based key encapsulation such as ML-KEM [2]) is classical and has no place for it. Quantum cryptography does, because its raw data are qg values. (i) In BB84 [3] over a qubit channel with relaxation, the sum of the received polar biases is a T1 witness. Natural relaxation raises it, while intercept-resend adds symmetric errors that leave it unchanged. A likelihood-ratio monitor built on it detects intercept-resend as well as the standard QBER monitor, but raises no false alarms when the memory’s T1 degrades, where the QBER monitor fires in 48–100% of windows. By construction it misses an attacker who mimics T1, which the QBER monitor catches, so the two are complementary and neither changes the secret-key rate. With finite keys [4] the diagnosis comes free from the error-corrected block: at key bits it attributes every block correctly, including a small attack hidden under drift. (ii) For a qubit random-number generator with a trusted measurement, the certified min-entropy is , independent of . The usual output-bias estimate is unsafe whenever the state is mixed: it certifies 0.97 bits per shot where 0.015 are private. A qg estimate from -rotation test rounds is safe in every run, and a readout calibration recovers 10–50% more certified bits. On IonQ trapped-ion noise models, with an environment ion that learns the output, the naive estimate stays near 1 bit while the qg estimate remains safe and captures 82–90% of the private randomness. All results are simulations, reproduced by scripts and pinned by regression tests.
We ask where the qg description of a qubit, and its companions [1], is useful for cryptography. Post-quantum cryptography (lattice-based key encapsulation such as ML-KEM [2]) is classical and has no place for it. Quantum cryptography does, because its raw data are qg values. (i) In BB84 [3] over a qubit channel with relaxation, the sum of the received polar biases is a T1 witness. Natural relaxation raises it, while intercept-resend adds symmetric errors that leave it unchanged. A likelihood-ratio monitor built on it detects intercept-resend as well as the standard QBER monitor, but raises no false alarms when the memory’s T1 degrades, where the QBER monitor fires in 48–100% of windows. By construction it misses an attacker who mimics T1, which the QBER monitor catches, so the two are complementary and neither changes the secret-key rate. With finite keys [4] the diagnosis comes free from the error-corrected block: at key bits it attributes every block correctly, including a small attack hidden under drift. (ii) For a qubit random-number generator with a trusted measurement, the certified min-entropy is , independent of . The usual output-bias estimate is unsafe whenever the state is mixed: it certifies 0.97 bits per shot where 0.015 are private. A qg estimate from -rotation test rounds is safe in every run, and a readout calibration recovers 10–50% more certified bits. On IonQ trapped-ion noise models, with an environment ion that learns the output, the naive estimate stays near 1 bit while the qg estimate remains safe and captures 82–90% of the private randomness. All results are simulations, reproduced by scripts and pinned by regression tests.
In the qg framework [1] a qubit is described by its polar bias . When a circuit conserves a Hamming weight, the average of over the register is fixed in advance: for excitations on qubits. This one number is a reference-free witness of noise that changes the conserved quantity, and its shot-level version is the known symmetry-verification filter [2], [3]. We measure when the witness and the filter help, and when they do not, on six problems with classical controls and on four molecules for the rotated-basis extension, using calibration-based and vendor noise models. (i) On H the filter lowers the energy error from 18 to 5.5 mHa, below Hartree–Fock (20.3 mHa), and it stays below Hartree–Fock along the dissociation curve. (ii) Across noise channels the witness predicts the outcome: it moves under T1 and the filter removes 94–95% of the error for free, while under dephasing it stays at its ideal value and the filter does nothing. Zero-noise extrapolation is complementary and fails on idle decoherence; the combination reaches mHa. (iii) With separate spin-up and spin-down witnesses, a second filter pays off only when a spin-leak witness is nonzero. Qubit routing on a heavy-hex device creates such leak in 1D Hubbard dynamics. (iv) In QAOA with an “exactly ” constraint, the filter doubles the success probability of the constraint-preserving ansatz. Penalty QAOA at depth does not beat a random feasible guess, and a greedy algorithm beats all quantum variants. (v) The witness relies on calibrated readout. A heralded sweep separates thermal population from asymmetric readout error, which the standard calibration conflates, and gives an unbiased effective temperature ( mK) together with and . (vi) On IonQ’s trapped-ion noise models the filter doubles the constraint-preserving QAOA success and halves the H error in every run, while zero-noise extrapolation, which must fold native gates because CX folding is undone by the compiler, is nearly unbiased but too noisy at the 2000-shot limit. (vii) Beyond symmetries, every stabilizer expectation of the repetition and Leung codes is a power of one single-qubit qg, so the syndromes track noise drift for free and choose between codes by the rule . (viii) Z-basis filtering cannot reach Hamiltonian terms measured in rotated bases, which hold most of the LiH error. Parity and mod 4 checks on two ancillas do reach them: they cut the LiH error (below Hartree–Fock on a generic model, on IonQ’s forte-1 model) and approach the full number-projection ceiling up to 12 qubits (H, HO, H). That ceiling shrinks with depth, because number-conserving errors grow. Coherent over-rotation of the entangling gate passes through native-gate ZNE untouched, while the filter removes 94% of it. We also report where the method stops: Hubbard circuits beyond 190 two-qubit gates, where the witness correctly reports unital scrambling. No result is a quantum advantage over classical computation. Every number is reproduced by a script and pinned by a regression test.
Quantum Key Distribution (QKD) provides information-theoretic security by exploiting the principles of quantum mechanics. Among QKD protocols, the BB84 scheme remains the most widely adopted for both theoretical research and practical implementation. A critical parameter determining the reliability and security of BB84 is the Quantum Bit Error Rate (QBER), which quantifies errors in the sifted key arising from channel noise or potential eavesdropping. This paper presents a systematic review and analysis of QBER within the BB84 protocol, examining its calculation, statistical estimation methods, and role in detecting eavesdropping activity. Simulation results, corroborated by reported experimental observations, reveal a near-linear relationship between eavesdropping intensity and QBER, with values approaching 25% under full intercept-resend attacks. Four confidence interval estimation methods, Wald, Wilson, Clopper-Pearson, and Hoeffding's inequality, are compared for robust QBER analysis in finite-key scenarios. Protocol enhancements, including decoy-state methods, hybrid cryptographic models, and quantum-resistant authentication, are discussed as mechanisms to mitigate errors and strengthen resilience across fiber, free-space, underwater, and satellite QKD systems. Open challenges in distinguishing noise-induced errors from malicious eavesdropping, and the role of adaptive error correction and machine-learning-assisted QBER estimation in future quantum networks, are identified as key directions for further research.
As quantum computing threatens classical cryptography like RSA via Shor's algorithm, Quantum Key Distribution (QKD)—especially BB84—offers physics-based security. BB84 leverages quantum principles: Heisenberg Uncertainty, No-Cloning Theorem, and superposition, shifting from math complexity to unbreakable physical laws using polarized photons for key exchange. The protocol detects eavesdropping through Quantum Bit Error Rate (QBER), showing 25% errors in Intercept-Resend attacks. Key challenges like Photon Number Splitting (PNS) attacks are addressed via decoy states. Compared to B92 and E91, BB84 balances feasibility and security best. Despite issues like signal loss, BB84 provides provably secure communication, restoring trust in a post-quantum world.
Quantum computers have the potential to break the public-key cryptosystems widely used in key exchange and digital signature applications. To address this issue, quantum key distribution (QKD) offers a robust countermeasure against quantum computer attacks. Among various QKD schemes, BB84 is the most widely used and studied. However, BB84 implementations are inherently imperfect, resulting in quantum bit error rates (QBERs) even in the absence of eavesdroppers. Distinguishing between QBERs caused by eavesdropping and QBERs due to channel imperfections is fundamentally infeasible. In this context, this paper proposes and examines a practical method for detecting eavesdropping via partial intercept-and-resend attacks in the BB84 protocol. A key feature of the proposed method is its consideration of quantum system noise. The efficacy of this method is assessed by employing the Quantum Solver library in conjunction with backend simulators inspired by real quantum machines that model quantum system noise. The simulation outcomes demonstrate the method’s capacity to accurately estimate the eavesdropper’s interception density in the presence of system noise. Moreover, the results indicate that the estimation accuracy of the eavesdropper’s interception density in the presence of system noise is dependent on both the actual interception density value and the key length.
The Qang () framework [1] expresses single-qubit rotations through two measurement-level quantities, the polar bias and the outcome entropy . We report results obtained with the open-source reference implementation qang. First, the two metrics are linked by an exact, branch-free identity, , which holds for any single-qubit state. Consequently, any new multi-qubit information must come from the joint outcome distribution. We name the resulting Z-basis total correlation and give its bounds and its scope: it is not an entanglement measure. Second, we identify exact blind spots: graph-state entanglement and readout-only dephasing are invisible to every Z-diagonal statistic, and qg-space updates cannot reach optima outside because of the range. On H unsigned qg updates recover none of the correlation energy. Keeping the sign of as a branch label removes this limit and reaches the FCI energy, but the best signed update reduces to -space descent, so qg coordinates bring no optimization gain. Third, we study a pole-damped gradient step whose damping schedule is . On a 300-landscape benchmark, H, and a 4-qubit LiH Hamiltonian with a mixed ansatz, it trades 3–20 more iterations at well-tuned learning rates for convergence where plain gradient descent diverges. Fourth, as a benchmark, tracks heavy output probability () and needs no calibration, unlike linear XEB. However, it is not monotonic under amplitude damping: under device-calibrated noise with added idle relaxation it falls below its own noiseless value. Pairing with the register-averaged removes the ambiguity in 23 of 24 circuits tested. A summary section lists fifty-two follow-up studies (QML encoding, control quantization, noise-type detection, circuit knitting, chemistry, error mitigation, thermal states, error correction, Hubbard dynamics, constrained QAOA, qubit characterization, syndrome tracking, coherence, few-shot estimation, IonQ noise models, shot-noise propagation, neural quantum states, coherent gate errors, symmetry checks in rotated bases, Heisenberg-chain dynamics, classical shadows, noisy Grover search, GHZ metrology, circuit-level surface codes, a lattice gauge theory, and the choice between filter and ZNE by shot budget), each with its classical or standard control; for the qg quantities, direct measurement is 3–41 cheaper than classical shadows, and the per-qubit reading loses to the outcome histogram when the answer is a bitstring; the symmetry-witness results are developed in a companion paper. Every number is reproduced by a script and pinned by a regression test in the public repository.