Gentle quantum leakage is proposed as a measure of information leakage to arbitrary eavesdroppers that aim to avoid detection. Gentle (also sometimes referred to as weak or non-demolition) measurements are used to encode the desire of the eavesdropper to evade detection. The gentle quantum leakage meets important axioms proposed for measures of information leakage including positivity, independence, and unitary invariance. Global depolarizing noise, an important family of physical noise in quantum devices, is shown to reduce gentle quantum leakage (and hence can be used as a mechanism to ensure privacy or security). A lower bound for the gentle quantum leakage based on asymmetric approximate cloning is presented. This lower bound relates information leakage to mutual incompatibility of quantum states. A numerical example, based on the encoding in the celebrated BB84 quantum key distribution algorithm, is used to demonstrate the results.
Gentle quantum leakage is proposed as a measure of information leakage to arbitrary eavesdroppers that aim to avoid detection. Gentle (also sometimes referred to as weak or non-demolition) measurements are used to encode the desire of the eavesdropper to evade detection. The gentle quantum leakage meets important axioms proposed for measures of information leakage including positivity, independence, and unitary invariance. Global depolarizing noise, an important family of physical noise in quantum devices, is shown to reduce gentle quantum leakage (and hence can be used as a mechanism to ensure privacy or security). A lower bound for the gentle quantum leakage based on asymmetric approximate cloning is presented. This lower bound relates information leakage to mutual incompatibility of quantum states. A numerical example, based on the encoding in the celebrated BB84 quantum key distribution algorithm, is used to demonstrate the results.
Barycentric and pairwise quantum Renyi leakages are proposed as two measures of information leakage for privacy and security analysis in quantum computing and communication systems. These quantities both require minimal assumptions on the eavesdropper, i.e., they do not make any assumptions on the eavesdropper's attack strategy or the statistical prior on the secret or private classical data encoded in the quantum system. They also satisfy important properties of positivity, independence, post-processing inequality, and unitary invariance. The barycentric quantum Renyi leakage can be computed by solving a semi-definite program and the pairwise quantum Renyi leakage possesses an explicit formula. The barycentric and pairwise quantum Renyi leakages form upper bounds on the maximal quantum leakage, the sandwiched quantum α-mutual information, the accessible information, and the Holevo's information. Furthermore, differentially-private quantum channels are shown to bound these measures of information leakage. Global and local depolarizing channels, that are common models of noise in quantum computing and communication, restrict private or secure information leakage. Finally, a privacy-utility trade-off formula in quantum machine learning using variational circuits is developed. The privacy guarantees can only be strengthened, i.e., information leakage can only be reduced, if the performance degradation grows larger and vice versa.
An alternative measure of information leakage for quantum encoding of classical data is defined. An adversary can access a single copy of the state of a quantum system that encodes some classical data and is interested in correctly guessing a general randomized or deterministic function of the data (e.g., a specific feature or attribute of the data in quantum machine learning) that is unknown to the security analyst. The resulting measure of information leakage, referred to as maximal quantum leakage, is the multiplicative increase of the probability of correctly guessing any function of the classical data upon observing measurements of the quantum state. Maximal quantum leakage is shown to satisfy the postprocessing inequality (i.e., applying a quantum channel reduces information leakage) and independence property (i.e., leakage is zero if the quantum state is independent of the classical data), which are fundamental properties required for privacy and security analysis. It also bounds accessible information. Effects of global and local depolarizing noise models on the maximal quantum leakage are established.
Every quantum key distribution (QKD) protocol must limit the information available outside the users' laboratories. In device-independent QKD this is essentially the only assumption made on the devices. In a prepare-and-measure setting it cannot be imposed strictly, since the sender's device must emit a signal that depends on her private input. The natural replacement, and a minimal one, is a leakage bound: a bound on how much information about the input leaves the sender's laboratory, through the intended signal or through any side channel. We ask how far this unavoidable requirement can replace a detailed model of the source. We show that this single bound, quantified by the probability of guessing the input from everything the source emits, suffices to prove security against collective attacks. In our analysis, nothing is assumed about the precise form of the emitted states, their dimension, energy or purity, nor about the receiver's measurement device, beyond the standard requirement that it does not leak Bob's data. The standard B92 and BB84 protocols do not certify any key under this minimal leakage bound assumption. But closely related protocols can and, in the ideal limit, achieve one secret bit per key round. For noisy implementations, we compute key rates using semidefinite programming relaxations. Our best protocols tolerate visibilities down to 0.84, corresponding to an 8% quantum bit error rate, compared with the 11% threshold of standard device-dependent BB84.
Barycentric and pairwise quantum Rényi leakages are proposed as two measures of information leakage for privacy and security analysis in quantum computing and communication systems. These quantities both require minimal assumptions on the eavesdropper, i.e. they do not make any assumptions on the eavesdropper’s attack strategy or the statistical prior on the secret or private classical data encoded in the quantum system. They also satisfy important properties of positivity, independence, post-processing inequality and unitary invariance. The barycentric quantum Rényi leakage can be computed by solving a semi-definite program; the pairwise quantum Rényi leakage possesses an explicit formula. The barycentric and pairwise quantum Rényi leakages form upper bounds on the maximal quantum leakage, the sandwiched quantum α -mutual information, the accessible information and the Holevo’s information. Furthermore, differentially private quantum channels are shown to bound these measures of information leakage. Global and local depolarizing channels, that are common models of noise in quantum computing and communication, restrict private or secure information leakage. Finally, a privacy-utility trade-off formula in quantum machine learning using variational circuits is developed. The privacy guarantees can only be strengthened, i.e. information leakage can only be reduced, if the performance degradation grows larger and vice versa .
We study the task of estimating a d−dimensional quantum state ρ under the constraint that the measurement is α−gentle. Such measurements M do not collapse the state; they issue both a random variable RM=ω containing statistical information and a post-measurement state ρM→ω such that ∥ρM→ω−ρ∥Tr≤α. We describe gentle measurements and their connection to quantum differential privacy.
Our results show that the optimal minimax estimation rate in Frobenius norm is of order d3/(nα2), instead of d2/n for general measurements. Moreover, for rank r states with r≤d we prove that the optimal minimax rate is rd2/(nα2), instead of rd/n. Very surprisingly, the loss for gentleness d/α2 scales with the ambient dimension of the Hilbert space, rather than the number of parameters rd, typically seen in classical differential privacy.
We propose optimal gentle measurements and indicate how they can be physically implemented using an ancillary state and a CNOT gate to entangle it with the initial state. We notice that the resulting random variable has a likelihood that satisfies local differential privacy. Lower bounds are proven through a new quantum information-theoretic inequality applied to well chosen families of states in the manifold of (small-rank) quantum states.
Abstract Quantum Key Distribution (QKD) is widely marketed as an unconditionally secure framework, shielded by the quantum mechanical postulate that any measurement of an unknown state inevitably disturbs the system and alerts legitimate parties to eavesdropping. In this paper, we demonstrate that this assumption represents a critical overgeneralization. By deploying Quantum Non-Demolition (QND) measurement techniques alongside state synchronization, an adversary can extract state information without triggering the wave-function collapse or state disturbance predicted by classical interpretations of von Neumann measurements. We establish that the security of current quantum cryptographic protocols relies on a restrictive dogma rather than a universal physical boundary, exposing a fundamental architectural flaw in quantum communication security. Key Takeaways & Core Concepts Refutation of the "Disturbance Axiom": Challenges the foundational assumption of QKD protocols (such as BB84) that information extraction inherently requires physical perturbation of the transmitted quantum state. QND Eavesdropping Mechanism: Outlines a theoretical State Synchronization Attack where an adversary uses Quantum Non-Demolition probes to weakly couple with carrier signals, reading state data without introducing a detectable Quantum Bit Error Rate (QBER). Logical Invalidation: Uses formal Aristotelian deductive logic to demonstrate that the existence of non-disturbing (QND) measurement classes serves as a single counterexample that falsifies claims of "unconditional physical security." Systemic Cryptographic Impact: Re-evaluates quantum physical-layer security, arguing that 0% error rate reporting does not guarantee an uncompromised channel and pushing for rewritten security bounds that