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Security in a prepare-and-measure quantum key distribution protocol when the receiver uses weak values to guess the sender's bits

Rajendra Singh Bhati

TL;DR

This work investigates whether weak values for mixed states can enhance security in a prepare-and-measure QKD protocol. It derives a generalized weak-value expression via the TSVF and constructs a QKD scheme where Bob uses weak-value–based state discrimination, then analyzes security under the weak measurement approximation (WMA) and without it. Under WMA, the protocol superficially appears to tolerate arbitrarily high depolarizing noise, suggesting an advantage over standard six-state QKD; however, a full security calculation without WMA shows no real improvement, with the secret fraction remaining bounded similarly to the six-state protocol. The results caution against relying on weak-value–driven discrimination in mixed-state QKD and highlight that apparent gains from WMA can be artifacts of higher-order terms being neglected, inviting careful scrutiny of TSVF-based security claims.

Abstract

The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be abstract properties of systems describing a complete picture between successive measurements in the two-state vector formalism (TSVF). The remarkable achievements of the weak value formalism in experimental quantum mechanics have persuaded most quantum physicists that it is impeccable. However, we explore a scenario where the formalism of weak values for mixed states is employed in a quantum communication protocol, but discover that it generates inaccurate outcomes. This reinforces our previous conclusion that the weak values may not be elements of the reality of weak measurements, contrary to what the proponents of weak values proposed.

Security in a prepare-and-measure quantum key distribution protocol when the receiver uses weak values to guess the sender's bits

TL;DR

This work investigates whether weak values for mixed states can enhance security in a prepare-and-measure QKD protocol. It derives a generalized weak-value expression via the TSVF and constructs a QKD scheme where Bob uses weak-value–based state discrimination, then analyzes security under the weak measurement approximation (WMA) and without it. Under WMA, the protocol superficially appears to tolerate arbitrarily high depolarizing noise, suggesting an advantage over standard six-state QKD; however, a full security calculation without WMA shows no real improvement, with the secret fraction remaining bounded similarly to the six-state protocol. The results caution against relying on weak-value–driven discrimination in mixed-state QKD and highlight that apparent gains from WMA can be artifacts of higher-order terms being neglected, inviting careful scrutiny of TSVF-based security claims.

Abstract

The weak values and weak measurement formalism were initially limited to pure states, which were later extended to mixed states, leading to intriguing applications in quantum information processing tasks. Weak values are considered to be abstract properties of systems describing a complete picture between successive measurements in the two-state vector formalism (TSVF). The remarkable achievements of the weak value formalism in experimental quantum mechanics have persuaded most quantum physicists that it is impeccable. However, we explore a scenario where the formalism of weak values for mixed states is employed in a quantum communication protocol, but discover that it generates inaccurate outcomes. This reinforces our previous conclusion that the weak values may not be elements of the reality of weak measurements, contrary to what the proponents of weak values proposed.

Paper Structure

This paper contains 8 sections, 52 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Weak values and weak measurements
  3. State discrimination using weak values
  4. QKD Protocol using weak values
  5. Security definition
  6. Security analysis with weak measurement approximation
  7. Security analysis without weak measurement approximation
  8. Discussion and conclusions

Figures (3)

  • Figure 1: $P_{err}$ is plotted as a function of $\alpha$ for $\epsilon/\delta^2=0.1$
  • Figure 2: Secrete key fraction according to weak measurement approximation. The secret fraction is plotted as a function of depolarizing noise $\eta$ for (a) $\gamma=0.1$ and (b) $\gamma=0.2$.
  • Figure 3: Secrete key fraction calculated without assuming the weak measurement approximation. The secret fraction is plotted as a function of depolarizing noise $\eta$ for (a) $\gamma=0.1$ and (b) $\gamma=0.2$, note that plots for $\alpha=20,25,30,35$ are coinciding.