arXiv subjects

Devashish Tupkary

Publications and source records attributed to Devashish Tupkary.

17 recordsLinked to original sources

arXiv2026

Experimental quantum cryptography with single photons and imperfect devices

Quantum key distribution (QKD) allows for provably secure key distribution between two trusted parties. Because the security and performance of QKD protocols rely on devices that behave according to specific assumptions, idealized or inaccurate assumptions about device behavior can introduce security loopholes. Real devices can never be perfectly characterized, and their performance metrics are always subject to certain error margins, which must be accounted for in a rigorous theoretical analysis. Only recently have rigorous finite-size results allowed for imperfect characterizations of devices (where device parameter have uncertainty margins) - an advance yet to be considered in experimental implementations of the BB84 protocol. In this work, we prove the security and analyze the performance of an implementation of the BB84 protocol using single photons generated by a semiconductor quantum dot light source in combination with dynamic polarization-state encoding. We consider the presence of incompletely characterized devices by accounting for imperfections in the single-photon source (in terms of finite g(2)(0)) as well as the receiver (non-ideal beam-splitters, finite detector efficiencies, and dark counts), all with error margins. The resulting protocol implementation shows competitive performance, paving the way towards practical and loop-hole free implementations of QKD.

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arXiv2026

Rigorous Security Proofs for Practical Quantum Key Distribution

This thesis is concerned with rigorous security analyses of practical Quantum Key Distribution (QKD) protocols, using a variety of modern proof techniques. The main results are as follows. First, we establish a security proof for variable-length QKD protocols against IID collective attacks, and extend this result to coherent attacks using the postselection technique. In doing so, we resolve a long-standing flaw in the application of the postselection technique to QKD, thereby placing it on a rigorous mathematical footing. Second, we develop a method to bound phase error rates in entropic uncertainty relation-based and phase error rate-based proofs, using only the observed statistics of the protocol, even when detectors are imperfect and only approximately characterized. This removes a key assumption of identical detector behaviour and enables these techniques to be applied in realistic settings. Third, we present a very general security analysis based on the marginal-constrained entropy accumulation theorem. The resulting framework can be readily adapted to practical imperfections and side channels, and is suitable for certification efforts. Finally, we show that the security of QKD protocols under realistic authentication assumptions can be reduced to the standard idealized setting, where authentication is assumed to behave honestly, with only minor protocol modifications. A distinctive feature of this thesis is its unified presentation of several major QKD security proof frameworks using consistent protocol descriptions and notation. Consequently, this thesis is intended not only as a collection of new technical results, but also as a useful reference for understanding rigorous security analysis in quantum key distribution.

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arXiv2026

Semidefinite programming for understanding the limitations of Lindblad equations

Lindbladian quantum master equations (LEs) are the most popular descriptions for quantum systems weakly coupled to baths. But, recent works have established that in many situations such Markovian descriptions are fundamentally limited: they cannot simultaneously capture populations and coherences even to the leading-order in system-bath couplings. This can cause violation of fundamental properties like thermalization and continuity equations associated with local conservation laws, even when such properties are expected in the actual setting. This begs the question: given a physical situation, how do we know if there exists an LE that describes it to a desired accuracy? Here we show that, for both equilibrium and non-equilibrium steady states (NESS), this question can be succinctly formulated as a semidefinite program (SDP), a convex optimization technique. If a solution to the SDP can be found to a desired accuracy, then an LE description is possible for the chosen setting. If not, no LE description is fundamentally attainable, showing that a consistent Markovian treatment is impossible even at weak system-bath coupling for that particular setting. Considering few qubit isotropic XXZ-type models coupled to multiple baths, we find that in most parameter regimes, LE description giving accurate populations and coherences to leading-order is unattainable, leading to rigorous no-go results. However, in some cases, LE description having correct populations but inaccurate coherences, and satisfying local conservation laws, is possible over some of the parameter regimes. Our work highlights the power of semidefinite programming in the analysis of physically consistent LEs, thereby, in understanding the limits of Markovian descriptions at weak system-bath couplings.

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arXiv2026

Authentication in Security Proofs for Quantum Key Distribution

Quantum Key Distribution (QKD) protocols rely on authenticated classical communication. Typical QKD security proofs are carried out in an idealized setting where authentication is assumed to behave honestly: it never aborts, and all classical messages are delivered faithfully with their original timing preserved. Authenticated channels that can be constructed in practice have different properties. Most critically, such channels may abort asymmetrically, such that only the receiving party may detect an authentication failure while the sending party remains unaware. Furthermore, an adversary may delay, reorder, or block classical messages. This discrepancy renders the standard QKD security definition and existing QKD security proofs invalid in the practical authentication setting. In this work we resolve this issue. Our main result is a reduction theorem showing that, under mild and easily satisfied protocol conditions, any QKD protocol proven secure under the honest authentication setting remains secure under a practical authentication setting. This result allows all existing QKD proofs to be retroactively lifted to the practical authentication setting with a minor protocol tweak.

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arXiv2026

A rigorous and complete security proof of decoy-state BB84 quantum key distribution

We present a rigorous and complete security proof of the decoy-state BB84 quantum key distribution (QKD) protocol. Our analysis aims to achieve a high standard of mathematical rigour and completeness, thereby providing the necessary foundation for certification and standardization efforts. Beyond establishing the security of a specific protocol, this work develops a general and modular framework that can be readily adapted to a broad class of QKD protocols, including both prepare-and-measure and entanglement-based variants. Our framework unifies all major ingredients required for the analysis of realistic QKD protocols, including the analysis of classical authentication and classical processing, source-replacement schemes, finite-size analysis, source maps, squashing maps, and decoy-state techniques. In doing so, this work consolidates a diverse range of techniques scattered across the QKD literature into a unified formalism, representing a general and rigorous treatment of QKD security. Finally, it outlines a clear path towards incorporating practical imperfections within the same framework, thereby laying the groundwork for addressing implementation security in future analysis.

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arXiv2025

Phase error estimation for passive detection setups with imperfections and memory effects

We develop a generic framework to bound the phase error rate for quantum key distribution protocols using passive detection setups with imperfections and memory effects. This framework can be used in proof techniques based on the entropic uncertainty relation or phase error correction, to prove security in the finite-size regime against coherent attacks. Our framework can incorporate on-the-fly announcements of click/no-click outcomes on Bob's side. In the case of imperfections without memory effects, it can be combined with proofs addressing source imperfections in a modular manner. We apply our framework to compute key rates for the decoy-state BB84 protocol, when the beam splitting ratio, the detection efficiency, and dark counts of the detectors are only known to be within some ranges. We also compute key rates in the presence of memory effects in the detectors. In this case, our results allow for protocols to be run at higher repetition rates, resulting in a significant improvement in the secure key generation rate.

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arXiv2025

Security of quantum key distribution with source and detector imperfections through phase-error estimation

Quantum key distribution promises information-theoretic security, but practical implementations face vulnerabilities due to device imperfections. Existing security proofs typically address source and detector imperfections separately and cannot be directly combined, while the few attempts to handle both simultaneously have assumed idealized scenarios with infinitely many protocol rounds, which is insufficient to certify the security of real-world systems. Here, we close this gap by introducing a modular lifting theorem that extends any (present or future) phase-error-based security proof for BB84-type protocols to incorporate detector efficiency mismatches. By applying this theorem to a state-of-the-art analysis for source imperfections, we obtain the first finite-key security proof against general coherent attacks that simultaneously addresses both source and detector imperfections.

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arXiv2025

Imperfect detectors for adversarial tasks with applications to quantum key distribution

Security analyses in quantum key distribution (QKD) and other adversarial quantum tasks often assume perfect device models. However, real-world implementations often deviate from these models. Thus, it is important to develop security proofs that account for such deviations from ideality. In this work, we extend the idea of squashing maps to develop a general framework for analysing imperfect threshold detectors, treating uncharacterised device parameters such as dark counts and detection efficiencies as adversarially controlled within some ranges. This approach enables a rigorous worst-case analysis with exactly characterised devices, ensuring security proofs remain valid under realistic conditions. Our results strengthen the connection between theoretical security and practical implementations by introducing a flexible framework for integrating detector imperfections into adversarial quantum protocols.

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arXiv2025

Security proofs for practical QKD: variations, techniques, gaps, and limitations

We review the current status of security proofs for practical decoy-state Quantum Key Distribution using the BB84 protocol, focusing on optical implementations with weak coherent pulses and threshold photodetectors. The primary aim of this review is to highlight gaps in the existing literature. Such gaps may arise, for instance, from mismatches between detailed protocol specifications and proof technique elements, reliance on earlier results based on different assumptions, or protocol choices that overlook real world requirements. While substantial progress has been made, our overview draws attention to the details that still demand careful attention.

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arXiv2025

Improved finite-size effects in QKD protocols with applications to decoy-state QKD

We present a finite-size security proof for generic quantum key distribution protocols against independent and identically distributed collective attacks and extend it to coherent attacks using the postselection technique. This work introduces two significant improvements over previous results. First, we achieve tighter finite-size key rates by employing refined concentration inequalities in the acceptance testing phase. Second, we improve second-order correction terms in the key rate expression, by reducing them to scale with the number of sifted rounds rather than the total number of protocol rounds. We apply these advancements to compute finite-size key rates for a qubit and decoy-state BB84 protocol, accommodating arbitrary protocol parameters. Finally, we extend our finite-size security proof to coherent attacks and variable-length protocols and present our results for the decoy-state 4-6 protocol incorporating imperfections such as unequal intensity settings.

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arXiv2024

Phase error rate estimation in QKD with imperfect detectors

We present a finite-size security proof of the decoy-state BB84 QKD protocol against coherent attacks, using entropic uncertainty relations, for imperfect detectors. We apply this result to the case of detectors with imperfectly characterized basis-efficiency mismatch. Our proof works by obtaining a suitable bound on the phase error rate, without requiring any new modifications to the protocol steps or hardware. It is applicable to imperfectly characterized detectors, and only requires the maximum relative difference in detection efficiencies and dark count rates of the detectors to be characterized. Moreover, our proof allows Eve to choose detector efficiencies and dark count rates in their allowed ranges in each round, thereby addressing an important problem of detector side channels. We prove security in the variable-length framework, where users are allowed to adaptively determine the length of key to be produced, and number of bits to be used for error-correction, based on observations made during the protocol. We quantitatively demonstrate the effect of basis-efficiency mismatch by applying our results to the decoy-state BB84 protocol.

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arXiv2024

A consolidated and accessible security proof for finite-size decoy-state quantum key distribution

In recent years, quantum key distribution (QKD) has evolved from a scientific research field to a commercially available security solution, supported by mathematically formulated security proofs. However, since the knowledge required for a full understanding of a security proof is scattered across numerous publications, it has proven difficult to gain a comprehensive understanding of all steps involved in the process and their limitations without considerable effort and attention to detail. Our paper aims to address this issue by providing a rigorous and comprehensive security proof for the finite-size 1-decoy and 2-decoy BB84 protocols against coherent attacks within Renner's entropic uncertainty relation framework. We resolve important technical flaws found in previous works regarding the fixed-length treatment of protocols and the careful handling of acceptance testing. To this end, we provide various technical arguments, including an analysis accounting for the important distinction of the 1-decoy protocol where statistics are computed after error correction, along with a slight improvement of the secure-key length. We also explicitly clarify the aspect of conditioning on events, addressing a technical detail often overlooked and essential for rigorous proofs. We extensively consolidate and unify concepts from many works, thoroughly discussing the underlying assumptions and resolving technical inconsistencies. Therefore, our contribution represents a significant advancement towards a broader and deeper understanding of QKD security proofs.

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arXiv2024

Security Proof for Variable-Length Quantum Key Distribution

We present a security proof for variable-length QKD in the Renner framework against IID collective attacks. Our proof can be lifted to coherent attacks using the postselection technique. Our first main result is a theorem to convert a series of security proofs for fixed-length protocols satisfying certain conditions to a security proof for a variable-length protocol. This conversion requires no new calculations, does not require any changes to the final key lengths or the amount of error-correction information, and at most doubles the security parameter. Our second main result is the description and security proof of a more general class of variable-length QKD protocols, which does not require characterizing the honest behaviour of the channel connecting the users before the execution of the QKD protocol. Instead, these protocols adaptively determine the length of the final key, and the amount of information to be used for error-correction, based upon the observations made during the protocol. We apply these results to the qubit BB84 protocol, and show that variable-length implementations lead to higher expected key rates than the fixed-length implementations.

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arXiv2024

Postselection technique for optical Quantum Key Distribution with improved de Finetti reductions

The postselection technique is an important proof technique for proving the security of quantum key distribution protocols against coherent attacks. In this work, we go through multiple steps to rigorously apply the postselection technique to optical quantum key distribution protocols. First, we place the postselection technique on a rigorous mathematical foundation by fixing a technical flaw in the original postselection paper. Second, we extend the applicability of the postselection technique to prepare-and-measure protocols by using a de Finetti reduction with a fixed marginal. Third, we show how the postselection technique can be used for decoy-state protocols by tagging the source. Finally, we extend the applicability of the postselection technique to realistic optical setups by developing a new variant of the flag-state squasher. We also improve existing de Finetti reductions, which reduce the effect of using the postselection technique on the key rate. These improvements can be more generally applied to other quantum information processing tasks. As an example to demonstrate the applicability of our work, we apply our results to the time-bin encoded three-state protocol. We observe that the postselection technique performs better than all other known proof techniques against coherent attacks.

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arXiv2024

Searching for Lindbladians obeying local conservation laws and showing thermalization

We investigate the possibility of a Markovian quantum master equation (QME) that consistently describes a finite-dimensional system, a part of which is weakly coupled to a thermal bath. In order to preserve complete positivity and trace, such a QME must be of Lindblad form. For physical consistency, it should additionally preserve local conservation laws and be able to show thermalization. We search of Lindblad equations satisfying these additional criteria. First, we show that the microscopically derived Bloch-Redfield equation (RE) violates complete positivity unless in extremely special cases. We then prove that imposing complete positivity and demanding preservation of local conservation laws enforces the Lindblad operators and the lamb-shift Hamiltonian to be `local', i.e, to be supported only on the part of the system directly coupled to the bath. We then cast the problem of finding `local' Lindblad QME which can show thermalization into a semidefinite program (SDP). We call this the thermalization optimization problem (TOP). For given system parameters and temperature, the solution of the TOP conclusively shows whether the desired type of QME is possible up to a given precision. Whenever possible, it also outputs a form for such a QME. For a XXZ chain of few qubits, fixing a reasonably high precision, we find that such a QME is impossible over a considerably wide parameter regime when only the first qubit is coupled to the bath. Remarkably, we find that when the first two qubits are attached to the bath, such a QME becomes possible over much of the same paramater regime, including a wide range of temperatures.

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arXiv2023

Using Cascade in Quantum Key Distribution

We point out a critical flaw in the analysis of Quantum Key Distribution (QKD) protocols that employ the two-way error correction protocol Cascade. Specifically, this flaw stems from an incom-plete consideration of all two-way communication that occurs during the Cascade protocol. We present a straightforward and elegant alternative approach that addresses this flaw and produces valid key rates. We exemplify our new approach by comparing its key rates with those generated using older, incorrect approaches, for Qubit BB84 and Decoy-State BB84 protocols. We show that in many practically relevant situations, our rectified approach produces the same key rate as older, incorrect approaches. However, in other scenarios, our approach produces valid key rates that are lower, highlighting the importance of properly accounting for all two-way communication during Cascade.

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arXiv2022

Fundamental limitations in Lindblad descriptions of systems weakly coupled to baths

It is very common in the literature to write down a Markovian quantum master equation in Lindblad form to describe a system with multiple degrees of freedom and weakly connected to multiple thermal baths which can, in general, be at different temperatures and chemical potentials. However, the microscopically derived quantum master equation up to leading order in system-bath coupling is of the so-called Redfield form which is known to not preserve complete positivity in most cases. Additional approximations to the Redfield equation are required to obtain a Lindblad form. We lay down some fundamental requirements for any further approximations to Redfield equation, which, if violated, leads to physical inconsistencies like inaccuracies in the leading order populations and coherences in the energy eigenbasis, violation of thermalization, violation of local conservation laws at the non-equilibrium steady state (NESS). We argue that one or more of these conditions will generically be violated in all the weak system-bath-coupling Lindblad descriptions existing in literature to our knowledge. As an example, we study the recently derived Universal Lindblad Equation (ULE) and use these conditions to show violation of local conservation laws due to inaccurate coherences but accurate populations in energy eigenbasis. Finally, we exemplify our analytical results numerically in an interacting open quantum spin system.

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