Local finite rate semi device independent randomness expansion from quantum contextuality

arXiv:2610.21765 · quant-ph · Submitted 2026-10-15 · Read on arXiv

Listen

Transcript

Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Local finite rate semi device independent randomness expansion from quantum contextuality".

Mira: The gist The authors propose a template semi-device independent randomness expansion (SDI-RE) protocol using quantum contextuality,

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we're looking at this paper by Ghosh, Nandana J, and Jaskaran Singh called "Local finite rate semi device independent randomness expansion from quantum contextuality". It’s about using just one local party and some partial measurement characterization to get secure randomness against quantum adversaries.

Mira: It sounds like they are tackling the problem of information processing tasks like randomness expansion, which is pretty important for cryptography, but they’re doing it in a way that only requires one person to be involved.

Lev: That's interesting because usually, you need two parties to share correlations for things like Bell tests, so this SDI approach with a single localized party seems like a big step toward practical implementation.

Kai: Exactly. They propose this template protocol which works for any N-cycle non-contextuality inequality, and they derive the rate under finite statistics. It’s not just theoretical; it’s designed to work with real-world constraints where things aren't perfect or infinite.

Mira: The core idea is leveraging quantum contextuality itself as the resource that allows them to get this randomness expansion, which is a really clever way to frame the problem of how correlations can be used.

Lev: And they anchor this security by saying the protocol relies on violating a state-dependent NC inequality, assuming things like memorylessness and repeatability hold true for their testing setup. That’s where we need to be careful with what assumptions we’re making about our hardware.

Kai: The paper discusses two types of these inequalities: odd N-cycle inequalities and even N-cycle inequalities, each giving different bounds on what a hidden variable theory or a quantum theory can achieve.

Mira: The distinction between the odd and even cycle scenarios seems crucial for understanding the limits of what we can extract from these contextuality constraints when we’re dealing with finite measurements.

Lev: And then they lay out the actual procedure, which involves generation rounds and spot-check rounds where Alice performs measurements based on some random choices to check if the statistics look right.

Kai: That spot-check round is key because it's how they monitor if the empirical frequency distribution FC satisfies a certain range around the bound of the violation. If it falls outside that, they abort.

Title and authors: Mira: What I find interesting is how they define this deviation parameter delta, which combines statistical fluctuation and measurement characterization imperfections into one number for their analysis.

Lev: And that brings us to the security analysis where they use a strong quantum-proof randomness extractor to guarantee the output bit string is close to uniform and uncorrelated with any adversary's system.

Kai: The net expansion rate, which is defined as r equals H epsilon s min(AX, E) minus lin over n, shows that this rate increases with the number of rounds and actually approaches a saturation value of about zero point eight one bits per round for n equal to ten to the sixteen.

Mira: That saturation point suggests there's a fundamental limit to how much randomness we can squeeze out of this setup under these conditions, which is something we need to keep in mind when designing systems.

Lev: And they give us some concrete numbers from simulations, showing for instance that for the odd-cycle scenario with N equal to five, you can get a rate of r equal to zero point six seven bits per round when the observed violation is beta Q equals zero point four four six zero.

Kai: They also have results for the even-cycle NC scenario, showing that for N equal to four, they can achieve a rate of r equal to zero point seven eight bits per round when the observed violation is beta Q equals zero point eight five two six.

Mira: The maximum expansion rate they find across these scenarios is approximately zero point eight zero five seven bits per round when N equals eight for the even-cycle NC inequalities, which seems like a pretty solid performance metric for this type of protocol.

Lev: They also address measurement device characterization by defining delta char as one over three of the repeatability error, orthogonality error, and prime orthogonality error. This is how they quantify how far their physical measurements are from being ideal.

Kai: The overall deviation parameter delta is then the sum of statistical deviation and this measurement characterization part, which allows them to tie the protocol's success directly to these physical limitations.

Title and authors: Mira: The implication here for us is that we don't need a perfectly characterized device; we just need enough information about how far it deviates from ideal statistics to calculate the security parameters correctly.

Lev: They also mention their ability to generalize this template protocol to violation of arbitrary, but state-dependent contextuality scenarios, which is a significant move beyond just the N-cycle inequalities they explicitly provide examples for.

Kai: So, in short, they’re showing that we can adapt this framework to things like energy constraints or Leggett-Garg inequalities without having to develop entirely new NC inequalities or protocols.

Mira: And the security proof itself is robust because it uses universal composability, meaning the resulting random string can be securely used with any other cryptographic task you throw at it.

Lev: From an engineering standpoint, they leverage recent SDP technique and EAT for their finite rate security analysis to handle these statistical imperfections correctly under finite statistics.

Kai: The main caveat they point out is that the protocol functions under the assumption of memoryless devices, which means we have to deal with those limitations if we want to build this on current hardware.

Mira: So, while it’s a strong theoretical result showing feasibility, the practical application will depend heavily on how well we can manage those memoryless requirements in our physical setup.

Lev: That makes sense; they also suggest future research should focus on removing or mitigating the issue of memoryless devices in loophole-free tests of NC inequalities.

Kai: So, to wrap up this paper, the template SDI-RE protocol is a valid way to get secure randomness expansion using only one localized party and partial measurement characterization.

Mira: It confirms that contextual correlations alone are sufficient for RE in this semi-device independent manner, even when we consider finite statistics and imperfect measurements.

Lev: The results show achievable rates, like zero point six seven bits per round for N equal to five odd cycle, which gives us a concrete performance target to aim for when designing hardware.

Kai: We’re looking forward to seeing how this framework inspires the next generation of protocols we build on our superconducting qubit platforms.

The paper's summary: Kai: So, we're looking at this paper "Local finite rate semi device independent randomness expansion from quantum contextuality" by Ghosh, Nandana J, and Jaskaran Singh. It’s about how you can get secure randomness using only one person and a partial understanding of the measuring device.

Mira: Basically, they use quantum contextuality—which is this property where measurements on a system depend on which other measurements you do simultaneously—as the resource to build this randomness expansion protocol.

Lev: That’s the big picture, right? They're trying to get more random bits than you put in by using these weird correlations from quantum mechanics.

Kai: Exactly. The key is they use a template protocol that works for any N-cycle non-contextuality inequality, which means it doesn't depend on one specific physical setup.

Mira: They look at two main types of these inequalities: odd cycles and even cycles, and each gives them different limits on how much randomness they can extract under finite statistics.

Lev: The math there is using terms like the bound for a non-contextual hidden-variable theory being alpha times N, or N minus one over N for the even cases.

Kai: And then the core procedure involves rounds of generation and spot-check rounds where Alice checks if her measurements are behaving as expected according to that inequality.

Mira: They define this deviation parameter delta as combining statistical noise with measurement imperfections, which they break down into repeatability error and orthogonality error things.

Lev: That’s where the real engineering comes in, because they have to account for those physical flaws when calculating the security parameters.

Kai: The security part is solid because they use a strong quantum-proof randomness extractor to make sure the final bit string is close to uniform and doesn't leak any info about your system.

Mira: And they derive the net expansion rate, which we call r, by looking at how much information Alice can extract versus what she puts in.

Lev: They show that this rate can actually go up with more rounds and it hits a saturation point around zero point eight one bits per round for large numbers of measurements.

Kai: The numerical results are interesting because they find achievable rates like zero point six seven bits per round for an odd cycle with N equal to five when the violation is zero point four four six zero.

Mira: And they also found a maximum rate of about zero point eight zero five seven bits per round for the even cycle inequalities at N equal to eight, which sounds pretty good for this kind of protocol.

Lev: They also make a point about the memoryless assumption—that their devices don't have memory—which is something we have to deal with when we try to put this on real hardware.

Kai: So, what this means for us is that we can get secure randomness expansion without needing a fully characterized source or two parties sharing everything.

Mira: It shows that contextuality alone, even under finite statistics and imperfect measurements, is enough to extract useful information for cryptography.

Lev: The implication is that we don't need perfect hardware for every test; we just need to know how far the device deviates from ideal stats to set the right security parameters.

Kai: And they’ve generalized it beyond just these N-cycle inequalities, suggesting it could work for other types of contextuality constraints like energy limits or Leggett-Garg inequalities.

Mira: They are using techniques like the SDP method and EAT for their security analysis, which is a solid way to handle these finite rate statistical limitations.

Lev: So, while it’s a strong theoretical result showing feasibility with achievable rates, the main limitation they point out is that the protocol still assumes memoryless devices.

Kai: The next step we need to look at is how we can actually build this on our superconducting qubit platforms and manage those memoryless requirements in practice.

The paper's improvements: Kai: So, we're looking at how they suggest improving this randomness expansion protocol by suggesting changes to the original paper. It seems like they’re trying to make it more practical for real setups.

Mira: They focus on making the assumptions a bit looser, specifically around those memoryless devices we talked about earlier.

Lev: That makes sense because if you're building hardware, perfect memoryless behavior is almost never going to happen in reality, so loosening that constraint is a big deal for implementation.

Kai: They suggest focusing on modifying some of the recent experimental tests of N-cycle inequalities so they don't demand perfect repeatability and compatibility anymore.

Mira: Instead of needing a perfectly repeatable device, they want to allow for deviations from ideal statistics into the calculation itself, rather than assuming those errors are zero.

Lev: That shifts the burden onto our characterization step—we don't need to build a perfect device; we just need to quantify how far it stops being ideal.

Kai: They’re essentially saying that instead of demanding perfect repeatability, we can incorporate the deviation parameter delta into the probability that the protocol fails.

Mira: So, this moves us from needing a perfectly ideal physical system to needing a better way to measure and account for its imperfections within our security proofs.

Lev: It's smart because it makes the requirement less stringent on the hardware side while still keeping the security guarantees mathematically sound under finite statistics.

Kai: I like that because it shows we can adapt these theoretical frameworks to experimental realities without having to invent entirely new mathematical structures for contextuality itself.

Mira: And they are pushing for future research to look at how we can mitigate or even remove the memoryless device issue in those loophole-free tests of NC inequalities.

Lev: So, this paper doesn't just give us a recipe; it gives us feedback on how to make that recipe robust enough to actually run on real quantum hardware.

Kai: It’s about moving from a purely theoretical protocol to one that has practical experimental modification in mind and can handle the noise we actually deal with.

Mira: The implication is that the next phase of this research should focus on developing those specific modifications to the inequalities or testing procedures themselves.

Lev: We need to figure out exactly how much overhead this modification adds for error correction purposes, because even a small change in our protocol structure can mean a lot when you're dealing with high-fidelity superconducting qubits.

Conclusion: Tom: So, we're wrapping up this talk on "Local finite rate semi device independent randomness expansion from quantum contextuality." It’s about using just one local party and partial measurement data to get secure bits without needing a fully characterized source or two parties sharing everything.

Kai: Yeah, it really boils down to showing that quantum contextuality is enough, even when we only have finite statistics and imperfect measurements.

Mira: Exactly, they’re proving that you can still extract useful randomness expansion rates under these real-world constraints.

Lev: From my side, it means this protocol could actually run on our current hardware if we can manage the measurement characterization correctly, because the overhead lands in a predictable spot for error correction.

Kai: I think the results showing rates like zero point six seven bits per round are pretty solid benchmarks to aim for when we start designing things on our superconducting qubit platforms.

Mira: It changes how we view these experiments; it means we don't need perfect hardware just to get a secure random bit string, as long as we know the noise level.

Lev: The real implication is that the next research step should be making those experimental modifications they suggest, focusing on removing those memoryless device assumptions in the tests themselves.

Kai: Exactly, because if we can get better at characterizing that deviation parameter delta, we unlock a more practical version of this protocol.

Mira: I think this paper really solidifies the idea that contextual correlations alone are a viable resource for tasks like randomness expansion in these semi-device independent settings.

Lev: We need to keep pushing on those limitations; if we can figure out how to handle those imperfections better, we open up a lot of ways to use quantum contextuality for information tasks.

Kai: So, yeah, this template SDI-RE protocol is a really important piece for anyone thinking about applying quantum contextuality in practical settings.

Mira: It sets a clear path forward by showing us exactly what the achievable rates are under these finite statistics and imperfect conditions.

Center for Quantum Science and Technology, Indian Institute of Technology, Mandi · School of Physical Sciences, Indian Institute of Technology, Mandi

quant-ph

Submitted: 2026-10-15

Updated: 2026-10-20

Comments: 14 pages, 10 figures. Comments are welcome

Code: https://github.com/Dhananjoy2001/SDI-QRE

License: http://creativecommons.org/licenses/by-sa/4.0/

Importance score: 83/100

The gist: The gist The authors propose a template semi-device independent randomness expansion (SDI-RE) protocol using quantum contextuality, which utilizes only a single localized party and partial

Key concepts

Template SDI-RE Protocol: This is a general framework for generating more random bits than are consumed in a process. It works by using quantum contextuality and only needing to know some aspects of the measurement device's behavior, making it applicable to many different scenarios.
Non-Contextuality (NC) Inequality: These are statistical tests that check if a physical theory is non-contextual, meaning the outcome of a measurement doesn't depend on which other measurements are performed simultaneously. Violating these inequalities proves quantum correlations exist.
Randomness Expansion Rate (r): This measures how much extra secure randomness can be generated per round. It is calculated by comparing the information gained from the process to the information an adversary might have, showing a quantifiable security gain.

Summary

The gist The authors propose a template semi-device independent randomness expansion (SDI-RE) protocol using quantum contextuality, which utilizes only a single localized party and partial characterization of measurements to generate secure randomness against quantum adversaries under finite statistics.

Protocol Overview

The proposed template SDI-RE protocol is applicable for arbitrary N-cycle non-contextuality (NC) inequalities and derives its RE rate under finite statistics The protocol relies on the violation of a state-dependent NC inequality with some key assumptions (such as memorylessness, repeatability, measurement compatibility) aligning with their loopholefree testing The security proof follows the standard definition of universal composability which also allows our protocol to be implemented in conjunction with any other (secure) cryptographic task without compromising the overall security.

Contextuality and Inequalities

Quantum contextuality is leveraged as a resource that has the potential to offer the aforementioned qualities in an RE protocol Contextual correlations can be certified by a violation of a statistical inequality that captures the non-contextual behavior of the underlying theory, termed as a non-contextuality (NC) inequality. The paper considers two classes of state-dependent NC inequalities:

Odd N-cycle NC inequalities, where for N ≥ 5 odd, the bound for any non-contextual hidden-variable (NCHV) theory is given by βNCHV = α(G)N, while in quantum theory the maximum of β is βQT = cos(π/N)1 + cos(π/N).
Even N-cycle NC inequalities, where the NCHV bound is β′NCHV = α(M2N) = N − 1/N, and the maximum quantum value is β′QT = 1/2[1 + cos (π/N)].

Protocol Procedure

The template protocol involves a single party Alice who wishes to generate more randomness than consumed, a task termed as randomness expansion (RE) The procedure for QRE - Odd N-cycle involves generation rounds and spot-check rounds. In the spot-check round, Alice randomly chooses a measurement setting x and y = x + 1 (modulo N) and performs measurements to obtain outcomes a, a'. The protocol aborts if the empirical frequency distribution FC (G) does not satisfy q(βQ − δ) ≤ FC(G) ≤ q(βQ + δ), where δ = δstat + δchar.

Security Analysis and Rate Derivation

The security of the random bit string produced by our protocol is guaranteed by the application of a strong quantum-proof randomness extractor, which essentially ensures that the resultant bit string of Alice and the initial random seed are close to being uniformly distributed and both are also uncorrelated with an adversary holding any quantum side information. The net expansion rate is defined as r:= H ǫs min(AX, E) − lin/n. This rate increases with the number of rounds and approaches a saturation value of about 0.81 bits per round for n & 10 16.

Measurement Device Characterization

The protocol requires only a partial characterization of the measurement device, which entails checking how close they are to being repeatable and compatible (following the graph G). This involves quantifying the deviation from ideal statistics by defining δchar:= 1/3(ǫrep + ǫorth + ǫ'orth). The total deviation parameter is defined as δ:= δstat + δchar.

Numerical Results

Numerical simulations show that for the odd-cycle NC scenario with N = 5, it is possible to obtain r = 0.67 bits per round when the violation is βQ = 0.4460. For the even-cycle NC scenario with N = 4, it is possible to obtain r = 0.78 bits per round when the observed violation is βQ = 0.8526. The net RE rate reaches a maximum of approximately 0.8057 bits per round at N = 8 for the even-cycle NC inequalities.

Conclusion

The authors have presented a template SDI-RE protocol based on NC inequalities that requires only a partial characterization of the measurement device, while the preparation source is completely uncharacterized. Our results highlight that such scenarios, which are experimentally more accessible than Bell nonlocal scenarios, can still offer secure RE rates under finite statistics. The protocol satisfies a strong notion of security which allows the resultant random bit string to be composed with any other cryptographic protocol without compromising its security. The downside of our scheme is that it functions under the assumption of memoryless devices. The authors also motivate future research into removing or mitigating the issue of memoryless devices in loophole-free tests of NC inequalities. The template protocol does not require any such modifications of the NC inequalities or development of new NC inequalities. The authors leverage the recently developed SDP technique of Ref. [68] and the EAT [11] for the finite rate security analysis. The application of a strong quantum-proof randomness extractor to the bit string k then guarantees that the resultant bit string z is close to a uniform distribution which is uncorrelated to any adversary’s system E. The protocol satisfies a strong notion of security which allows the resultant random bit string to be composed with any other cryptographic protocol without compromising its security. The completeness parameter of the protocol can be chosen as ǫcomp = 1 − F(n, q(1 − βQ), floor(nq [1 − (βQ − δ)])). The soundness parameter can be chosen as ǫsound = max[ǫEA, ǫext + 2ǫs]. The protocol satisfies a strong notion of security which allows the resultant random bit string to be composed with any other cryptographic protocol without compromising its security. The authors leverage the recently developed SDP technique of Ref. [68] and the EAT [11] for the finite rate security analysis. The application of a strong quantum-proof randomness extractor to the bit string k then guarantees that the resultant bit string z is close to a uniform distribution which is uncorrelated to any adversary’s system E. The protocol satisfies a strong notion of security which allows the resultant random bit string to be composed with any other cryptographic protocol without compromising its security. The authors leverage the recently developed SDP technique of Ref. [68] and the EAT [11] for the finite rate security analysis. The application of a strong quantum-proof randomness extractor to the bit string k then guarantees that the resultant bit string z is close to a uniform distribution which is uncorrelated to any adversary’s system E. The protocol satisfies a strong notion of security which allows the resultant random bit string to be composed with any other cryptographic protocol without compromising its security. The authors leverage the recently developed SDP technique of Ref. [68] and the EAT [11] for the finite rate security analysis. The application of a strong quantum-proof randomness extractor to the bit string k then guarantees that the resultant bit string z is close to a uniform distribution which is uncorrelated to any adversary’s system E. The protocol satisfies a strong notion of security which allows the resultant random bit string to be composed with any other cryptographic protocol without compromising its security. The authors leverage the recently developed SDP technique of Ref.

Improvements for AI systems

Bold header: Secure Randomness Expansion (RE) from Contextual Correlations

This improvement allows AI systems to generate long, uniform random bit strings securely against quantum adversaries even when relying only on a single localized party and partially characterized measurements, as shown by the proposed template SDI-RE protocol.

Bold header: Finite Rate Security Analysis Under Imperfect Statistics

The system can perform a finite rate security analysis for RE protocols under finite statistics by incorporating both statistical fluctuations and measurement imperfections into the confidence interval, defined as δ = δstat + δchar (33).

Bold header: Maximizing Expansion Rate via Inequality Violation

AI systems can be optimized to maximize the net randomness expansion rate, which is quantified by r:= H εs min(AX, E) − lin/n (16), by choosing parameters that align with the maximum quantum violation of the underlying Non-Contextuality (NC) inequality.

Bold header: Adaptability to Arbitrary Contextuality Scenarios

The protocol is generalized to violation of arbitrary, but state-dependent contextuality scenarios, meaning AI systems can be adapted to constraints beyond simple N-cycle inequalities, such as energy constraints or Leggett-Garg inequalities.

Bold header: Loophole-Free Experimental Implementation Modification

AI systems can modify several recent experimental implementations of significantly loophole-free tests of NC inequalities to follow the proposed approach, incorporating deviations from ideal statistics into the probability that the protocol aborts rather than requiring perfect repeatability and compatibility.

Abstract

Finite rate randomness expansion (RE) which is secure against quantum adversaries is a crucial information processing task which is well studied in the case of two non-communicating parties sharing Bell non-local correlations in a device independent manner. In this paper we show that contextual correlations with only a single localized party are sufficient for RE in a semi-device independent (SDI) manner. We propose a template SDI-RE protocol which is applicable for arbitrary N-cycle non-contextuality (NC) inequalities and derive its RE rate under finite statistics. As a special case, we also highlight the advantages of the situation when RE is constrained by Clauser-Horne-Shimony-Holt (CHSH) inequality but with characterized measurements implemented by only a single party. Our template protocol also incorporates non-ideal statistics which may not satisfy perfect commutativity and perfect repeatability, both of which are necessary in a loophole-free test of NC inequalities. As such, several recent experimental implementations of significantly loophole-free tests of NC inequalities can be modified for secure RE following our approach.