arXiv subjects

Srijita Kundu

Publications and source records attributed to Srijita Kundu.

At least 19 recordsLinked to original sources

arXiv2026

An exponential separation between entanglement-assisted and unassisted one-way quantum communication

A longstanding question in quantum communication complexity is whether some task can be accomplished with a small amount of communication in the presence of entanglement, yet require much more quantum communication in the absence of entanglement. Separations of this nature were previously known for relational problems and, in the simultaneous message passing model, for partial functions. But it has remained unresolved whether any such separation exists for a total Boolean function. We resolve this question with an exponential separation in the one-way setting: we exhibit a family of total Boolean functions $f_n\colon \{0,1\}^n \times \{0,1\}^n \to \{0,1\}$ that can be computed with $O(\log n)$ bits of one-way classical communication given prior entanglement, but that require $Ω(n^{1/3})$ qubits of one-way quantum communication without entanglement. Our function is a special case of the subgroup membership problem, first studied in the communication setting by Aaronson, Le Gall, Russell, and Tani.

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arXiv2026

Flexible rigidity: Compiling generic trusted-preparation protocols into sequential device-independent protocols

We give a generic compiler for turning a wide class of device-dependent protocols with trusted state preparation into sequential device-independent protocols. In order for our compiler to apply, the trusted-preparation protocol needs to satisfy certain minimal conditions: having an entanglement-based realization in the first place, and the entanglement-based realization corresponding to the optimal strategy of any non-local game that satisfies a fairly weak rigidity condition. We apply our generic compiler to give sequential device-independent protocols for uncloneable encryption, copy-protection of point functions, and blind randomness expansion. Our technical contribution is a new class of rigidity theorems based on Rényi divergences, with flexible cryptographic applications. They allow our compiler to achieve a constant rate (i.e., the ratio of trusted states prepared to device uses), while tolerating a constant level of noise per device usage. This overcomes a fundamental scaling obstacle faced by previous rigidity theorems for trace distance or fidelity. For the generic sequential case, our proof is based on the sharp-divergence chain rule by Fawzi and Fawzi (2021), which suffices for a constant but fairly low rate. In the special case when the devices retain no memory, we improve the rates by deriving a novel subadditivity property for a modified channel sandwiched divergence, which may be of independent interest. Finally, as a prospect for future improvements, we also prove a chain rule for the iterated-mean divergences from Brown, Fawzi and Fawzi (2021).

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arXiv2026

Non-local games and communication complexity with noisy entanglement

We study the impact of noise on the theories of quantum nonlocality and entanglement-assisted communication complexity. We consider non-local games and entanglement-assisted communication complexity in a model where Alice and Bob may share arbitrarily many noisy EPR pairs. We study four noise models: depolarizing noise, unital noise, biased reset noise, and erasure noise. Our results are as follows: 1. We upper bound the value of the CHSH game under all these noise models in terms of the noise parameter, without any assumptions on the measurements used in the strategy. 2. We prove a parallel repetition theorem for general non-local games under all noise models except biased reset noise; we prove an improved parallel repetition theorem for unique games. Our parallel repetition rate is smaller than the quantum parallel repetition rate for CHSH in a nontrivial noise regime. 3. Using our unique-game parallel repetition theorem and a relation defined by the CHSH game, we prove a separation between communication complexity with noisy vs noiseless entanglement. This implies an $Ω(n)$ two-way communication lower bound for distilling $n$ EPR pairs from noisy EPR pairs, in the same nontrivial noise regime. 4. We show that any interactive entanglement-assisted communication protocol can be simulated by an SMP communication protocol with noisy shared randomness, with an exponential blowup in communication. This generalizes a known result on the simulation of noiseless shared randomness with noisy shared randomness. 5. We show a polynomial lower bound on the number of copies of noisy EPR pairs required to compute the Equality function with constant communication, under all four noise models. The previous result gives a matching upper bound, and moreover, this answers an open question in the literature on whether logarithmically many noisy shared bits suffice for communication.

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arXiv2026

Non-Standard Oracles for Bounded-Error Complexity Classes

In recent years, the quantum oracle model introduced by Aaronson and Kuperberg (2007) has found a lot of use in showing oracle separations between complexity classes and cryptographic primitives. It is generally assumed that proof techniques that do not relativize with respect to quantum oracles will also not relativize with respect to classical oracles. Aaronson (2009) showed that this is not the case by showing a complexity class containment that relativizes with respect to classical oracles but not with quantum oracles. However, their result only works for zero-error quantum complexity classes and they leave open the problem for bounded-error complexity classes. We show that there is a quantum oracle problem that is contained in the class QMA, but not in a class we call polyQCPH. However, with respect to classical oracles, QMA is contained in polyQCPH, because polyQCPH is equal to PSPACE with respect to classical oracles. Our result works for polyQCPH, which is a bounded-error complexity class, thus it resolves the open problem from Aaronson (2009). We also show that the same separation holds relative to a distributional oracle, which is a model introduced by Natarajan and Nirkhe (2024). We believe our findings show the need for some caution when using these non-standard oracle models, particularly when showing separations between quantum and classical resources.

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arXiv2026

Near-optimal entanglement-communication tradeoffs for remote state preparation

We study the following task: Alice is given a classical description of a rank-$k$ projector $P$ on $\mathbb{C}^d$, and Alice and Bob want to prepare the quantum state $P/k$ on Bob's side using shared entanglement and classical communication. The general form of this task is known as remote state preparation (RSP). We give nearly-matching lower and upper bounds for the entanglement cost and communication cost for RSP of the states $P/k$. Ours are the first nearly matching upper and lower bounds for RSP of mixed states, and in the special case of pure states, our lower bound outperforms the best previously known lower bound. Our results show that any pure entangled state that can be used to do RSP of these states with $o(d)$ bits of communication, can distill $\log d$ ebits of entanglement, and conversely, any state that can distill $\log d$ ebits of entanglement can be used to do RSP of these states efficiently. As applications of our results, we rederive a previously-known incompressibility result for states of the form $P/k$, and give a new entanglement-assisted communication protocol for the equality function that uses $\frac{1}{2}\log n + O(1)$ many ebits, and $O(1)$ communication.

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arXiv2026

Quantum information advantage based on Bell inequalities

Recently, Kretschmer et al. [KGD+25] presented an experimental demonstration of a proposed quantum information advantage protocol. We present an alternate proposal based on a relation derived from parallel-repeated CHSH games. Our memory measure is based on an information measure and is different from [KGD+25], where they count the number of qubits. Our proposal has an efficient verifier and a noise-robust quantum prover which is arguably much more efficient compared to [KGD+25].

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arXiv2025

Are uncloneable proof and advice states strictly necessary?

Yes, we show that they are. We initiate the study of languages that necessarily need uncloneable quantum proofs and advice. We define strictly uncloneable versions of the classes QMA, BQP/qpoly and FEQP/qpoly (which is the class of relational problems solvable exactly with polynomial-sized quantum advice). Strictly uncloneable QMA is defined to be the class of languages in QMA that only have uncloneable proofs, i.e., given any family of candidate proof states, a polynomial-time cloning algorithm cannot act on it to produce states that are jointly usable by $k$ separate polynomial-time verifiers, for arbitrary polynomial $k$. This is a stronger notion of uncloneable proofs and advice than those considered in previous works, which only required the existence of a single family of proof or advice states that are uncloneable. We show that in the quantum oracle model, there exist languages in strictly uncloneable QMA and strictly uncloneable BQP/qpoly. The language in strictly uncloneable QMA also gives a quantum oracle separation between QMA and the class cloneableQMA introduced by Nehoran and Zhandry (2024). We also show without using any oracles that the language, used by Aaronson, Buhrman and Kretschmer (2024) to separate FEQP/qpoly and FBQP/poly, is in strictly uncloneable FEQP/qpoly.

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arXiv2025

Does there exist a quantum fingerprinting protocol without coherent measurements?

Buhrman, Cleve, Watrous, and de Wolf (PRL 2001) discovered the quantum fingerprinting protocol, which is the quantum SMP protocol with $O(\log n)$ qubits communication for the equality problem. In the protocol, Alice and Bob create some quantum fingerprints of their inputs, and the referee conducts the SWAP tests for the quantum fingerprints. Since $Ω(\sqrt{n})$ bits communication is required with the classical SMP scheme for the equality problem first shown by Newman and Szegedy (STOC 1996), there exists an exponential quantum advantage in the amount of communication. In this paper, we consider a setting in which the referee can do only incoherent measurements rather than coherent measurements including the SWAP tests. We first show that, in the case of one-way LOCC measurements, $Ω(\sqrt{n})$ qubits communication is required. To prove the result, we derive a new method to replace quantum messages by classical messages and consider a reduction to the optimal lower bound in the hybrid SMP model where one message is quantum and the other is classical, which was first shown by Klauck and Podder (MFCS 2014). Our method uses the result of Oszmaniec, Guerini, Wittek, and Acín (PRL 2017), who showed that general POVM measurements can be simulated by randomized projective measurements with small ancilla qubits, and Newman's theorem. We further investigate the setting of quantum SMP protocols with two-way LOCC measurements, and derive a lower bound against some restricted two-way LOCC measurements. To prove it, we revisit the technique to replace quantum messages by classical deterministic messages introduced by Aaronson (ToC 2005) and generalized by Gavinsky, Regev, and de Wolf (CJTCS 2008), and show that, using the deterministic message, the referee can simulate the two-way LOCC measurements.

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arXiv2024

Device-independent uncloneable encryption

Uncloneable encryption, first introduced by Broadbent and Lord (TQC 2020) is a quantum encryption scheme in which a quantum ciphertext cannot be distributed between two non-communicating parties such that, given access to the decryption key, both parties cannot learn the underlying plaintext. In this work, we introduce a variant of uncloneable encryption in which several possible decryption keys can decrypt a particular encryption, and the security requirement is that two parties who receive independently generated decryption keys cannot both learn the underlying ciphertext. We show that this variant of uncloneable encryption can be achieved device-independently, i.e., without trusting the quantum states and measurements used in the scheme, and that this variant works just as well as the original definition in constructing quantum money. Moreover, we show that a simple modification of our scheme yields a single-decryptor encryption scheme, which was a related notion introduced by Georgiou and Zhandry. In particular, the resulting single-decryptor encryption scheme achieves device-independent security with respect to a standard definition of security against random plaintexts. Finally, we derive an "extractor" result for a two-adversary scenario, which in particular yields a single-decryptor encryption scheme for single bit-messages that achieves perfect anti-piracy security without needing the quantum random oracle model.

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arXiv2024

Separations in query complexity for total search problems

We study the query complexity analogue of the class TFNP of total search problems. We give a way to convert partial functions to total search problems under certain settings; we also give a way to convert search problems back into partial functions. As an application, we give new separations for degree-like measures. We give an exponential separation between quantum query complexity and approximate degree for a total search problem. We also give an exponential separation between approximate degree and the positive quantum adversary for a total search problem. We then strengthen the former separation to upper bound a larger measure: the two-sided approximate non-negative degree, also called the conical junta degree. This measure is often larger than quantum query complexity and even a separation from randomized query complexity was not known. We extend our results to communication complexity, and obtain an exponential separation between quantum information complexity and the relaxed partition bound for a total search problem. Even a weaker separation between randomized communication complexity and the relaxed partition bound was not known for total search problems (or even for partial functions). Most of our separations for total search problems can be converted to separations for partial functions. Using this, we reprove the recent exponential separation between quantum query complexity and approximate degree for a partial function by Ambainis and Belovs (2023), among other new results.

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arXiv2024

On the Power of Quantum Distributed Proofs

Quantum nondeterministic distributed computing was recently introduced as dQMA (distributed quantum Merlin-Arthur) protocols by Fraigniaud, Le Gall, Nishimura and Paz (ITCS 2021). In dQMA protocols, with the help of quantum proofs and local communication, nodes on a network verify a global property of the network. Fraigniaud et al. showed that, when the network size is small, there exists an exponential separation in proof size between distributed classical and quantum verification protocols, for the equality problem, where the verifiers check if all the data owned by a subset of them are identical. In this paper, we further investigate and characterize the power of the dQMA protocols for various decision problems. First, we give a more efficient dQMA protocol for the equality problem with a simpler analysis. This is done by adding a symmetrization step on each node and exploiting properties of the permutation test, which is a generalization of the SWAP test. We also show a quantum advantage for the equality problem on path networks still persists even when the network size is large, by considering ``relay points'' between extreme nodes. Second, we show that even in a general network, there exist efficient dQMA protocols for the ranking verification problem, the Hamming distance problem, and more problems that derive from efficient quantum one-way communication protocols. Third, in a line network, we construct an efficient dQMA protocol for a problem that has an efficient two-party QMA communication protocol. Finally, we obtain the first lower bounds on the proof and communication cost of dQMA protocols. To prove a lower bound on the equality problem, we show any dQMA protocol with an entangled proof between nodes can be simulated with a dQMA protocol with a separable proof between nodes by using a QMA communication-complete problem introduced by Raz and Shpilka (CCC 2004).

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arXiv2024

Oracle separation of QMA and QCMA with bounded adaptivity

We give an oracle separation between QMA and QCMA for quantum algorithms that have bounded adaptivity in their oracle queries; that is, the number of rounds of oracle calls is small, though each round may involve polynomially many queries in parallel. Our oracle construction is a simplified version of the construction used recently by Li, Liu, Pelecanos, and Yamakawa (2023), who showed an oracle separation between QMA and QCMA when the quantum algorithms are only allowed to access the oracle classically. To prove our results, we introduce a property of relations called \emph{slipperiness}, which may be useful for getting a fully general classical oracle separation between QMA and QCMA.

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arXiv2023

On the Hardness of the Minimum Distance Problem of Quantum Codes

We study the hardness of the problem of finding the distance of quantum error-correcting codes. The analogous problem for classical codes is known to be NP-hard, even in approximate form. For quantum codes, various problems related to decoding are known to be NP-hard, but the hardness of the distance problem has not been studied before. In this work, we show that finding the minimum distance of stabilizer quantum codes exactly or approximately is NP-hard. This result is obtained by reducing the classical minimum distance problem to the quantum problem, using the CWS framework for quantum codes, which constructs a quantum code using a classical code and a graph. A main technical tool used for our result is a lower bound on the so-called graph state distance of 4-cycle free graphs. In particular, we show that for a 4-cycle free graph $G$, its graph state distance is either $δ$ or $δ+1$, where $δ$ is the minimum vertex degree of $G$. Due to a well-known reduction from stabilizer codes to CSS codes, our results also imply that finding the minimum distance of CSS codes is also NP-hard.

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arXiv2023

Composably secure device-independent encryption with certified deletion

We study the task of encryption with certified deletion (ECD) introduced by Broadbent and Islam (2020), but in a device-independent setting: we show that it is possible to achieve this task even when the honest parties do not trust their quantum devices. Moreover, we define security for the ECD task in a composable manner and show that our ECD protocol satisfies conditions that lead to composable security. Our protocol is based on device-independent quantum key distribution (DIQKD), and in particular the parallel DIQKD protocol based on the magic square non-local game, given by Jain, Miller and Shi (2020). To achieve certified deletion, we use a property of the magic square game observed by Fu and Miller (2018), namely that a two-round variant of the game can be used to certify deletion of a single random bit. In order to achieve certified deletion security for arbitrarily long messages from this property, we prove a parallel repetition theorem for two-round non-local games, which may be of independent interest.

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arXiv2023

A direct product theorem for quantum communication complexity with applications to device-independent cryptography

We give a direct product theorem for the entanglement-assisted interactive quantum communication complexity of an $l$-player predicate $\mathsf{V}$. In particular we show that for a distribution $p$ that is product across the input sets of the $l$ players, the success probability of any entanglement-assisted quantum communication protocol for computing $n$ copies of $\mathsf{V}$, whose communication is $o(\log(\mathrm{eff}^*(\mathsf{V},p))\cdot n)$, goes down exponentially in $n$. Here $\mathrm{eff}^*(\mathsf{V}, p)$ is a distributional version of the quantum efficiency or partition bound introduced by Laplante, Lerays and Roland (2014), which is a lower bound on the distributional quantum communication complexity of computing a single copy of $\mathsf{V}$ with respect to $p$. Applying our direct product theorem for small communication and techniques related to $\mathrm{eff}^*$, we show that it is possible to do device-independent (DI) quantum cryptography without the assumption that devices do not leak any information. First, we analyze the parallel DI quantum key distribution protocol given by Jain, Miller and Shi (2020), and show that when the protocol is carried out with devices that are compatible with $n$ copies of the Magic Square game, it is possible to extract $Ω(n)$ bits of key from it, even in the presence of $O(n)$ bits of leakage. Second, we show that it is possible to do sequential versions of the Jain, Miller and Shi protocol, which give a better key rate for QKD with leakage, and let us do sequential DI randomness expansion with leakage (it is not known how to do parallel DI randomness expansion even without leakage). Third, we show that proofs of quantumness with two entangled provers are resistant to leakage, i.e., classical players who communicate $O(n)$ bits with each other cannot convince the verifier that they share entanglement.

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arXiv2022

A device-independent protocol for XOR oblivious transfer

Oblivious transfer is a cryptographic primitive where Alice has two bits and Bob wishes to learn some function of them. Ideally, Alice should not learn Bob's desired function choice and Bob should not learn any more than what is logically implied by the function value. While decent quantum protocols for this task are known, many become completely insecure if an adversary were to control the quantum devices used in the implementation of the protocol. In this work we give a fully device-independent quantum protocol for XOR oblivious transfer.

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arXiv2020

On Query-to-Communication Lifting for Adversary Bounds

We investigate query-to-communication lifting theorems for models related to the quantum adversary bounds. Our results are as follows: 1. We show that the classical adversary bound lifts to a lower bound on randomized communication complexity with a constant-sized gadget. We also show that the classical adversary bound is a strictly stronger lower bound technique than the previously-lifted measure known as critical block sensitivity, making our lifting theorem one of the strongest lifting theorems for randomized communication complexity using a constant-sized gadget. 2. Turning to quantum models, we show a connection between lifting theorems for quantum adversary bounds and secure 2-party quantum computation in a certain "honest-but-curious" model. Under the assumption that such secure 2-party computation is impossible, we show that a simplified version of the positive-weight adversary bound lifts to a quantum communication lower bound using a constant-sized gadget. We also give an unconditional lifting theorem which lower bounds bounded-round quantum communication protocols. 3. Finally, we give some new results in query complexity. We show that the classical adversary and the positive-weight quantum adversary are quadratically related. We also show that the positive-weight quantum adversary is never larger than the square of the approximate degree. Both relations hold even for partial functions.

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arXiv2020

A Direct Product Theorem for One-Way Quantum Communication

We prove a direct product theorem for the one-way entanglement-assisted quantum communication complexity of a general relation $f\subseteq\mathcal{X}\times\mathcal{Y}\times\mathcal{Z}$. For any $\varepsilon, ζ> 0$ and any $k\geq1$, we show that \[ \mathrm{Q}^1_{1-(1-\varepsilon)^{Ω(ζ^6k/\log|\mathcal{Z}|)}}(f^k) = Ω\left(k\left(ζ^5\cdot\mathrm{Q}^1_{\varepsilon + 12ζ}(f) - \log\log(1/ζ)\right)\right),\] where $\mathrm{Q}^1_{\varepsilon}(f)$ represents the one-way entanglement-assisted quantum communication complexity of $f$ with worst-case error $\varepsilon$ and $f^k$ denotes $k$ parallel instances of $f$. As far as we are aware, this is the first direct product theorem for quantum communication. Our techniques are inspired by the parallel repetition theorems for the entangled value of two-player non-local games, under product distributions due to Jain, Pereszlényi and Yao, and under anchored distributions due to Bavarian, Vidick and Yuen, as well as message-compression for quantum protocols due to Jain, Radhakrishnan and Sen. Our techniques also work for entangled non-local games which have input distributions anchored on any one side. In particular, we show that for any game $G = (q, \mathcal{X}\times\mathcal{Y}, \mathcal{A}\times\mathcal{B}, \mathsf{V})$ where $q$ is a distribution on $\mathcal{X}\times\mathcal{Y}$ anchored on any one side with anchoring probability $ζ$, then \[ ω^*(G^k) = \left(1 - (1-ω^*(G))^5\right)^{Ω\left(\frac{ζ^2 k}{\log(|\mathcal{A}|\cdot|\mathcal{B}|)}\right)}\] where $ω^*(G)$ represents the entangled value of the game $G$. This is a generalization of the result of Bavarian, Vidick and Yuen, who proved a parallel repetition theorem for games anchored on both sides, and potentially a simplification of their proof.

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