arXiv subjects

Alexander Streltsov

Publications and source records attributed to Alexander Streltsov.

At least 19 recordsLinked to original sources

arXiv2026

PPT Entanglement with Correlated Catalysis: Monotones and Irreversibility

Quantum catalysts can overcome otherwise impossible quantum state transformations without being consumed, and allowing them to become correlated with the output makes this assistance substantially more powerful. This raises a fundamental question for entanglement theory: which limitations on state manipulation remain when such correlated catalysts are freely available? We answer this question in the positive-partial-transpose (PPT) resource theory, which allows a substantially broader class of operations than local operations and classical communication (LOCC). We identify general conditions under which regularized relative-entropy measures become strongly superadditive, and use them to construct monotones that constrain correlated catalytic PPT transformations without any knowledge of the catalyst. In particular, we prove that the regularized PPT relative entropy is fully additive and strongly superadditive, resolving an open problem in entanglement theory. Most importantly, these constraints show that even arbitrary correlated catalysts cannot restore asymptotic reversibility: for an explicit state, the optimal entanglement distillation rate remains strictly smaller than the entanglement cost. Thus, substantial catalytic assistance does not remove some of the fundamental limitations of mixed-state entanglement manipulation.

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arXiv2026

Entanglement battery and entanglement catalyst in local state discrimination problems

In this work, we study the limitations and advantages of using entanglement battery and entanglement catalyst in local state discrimination problems. We consider both cases of such tools, i.e., exact and approximate cases. We show that to distinguish any set of orthogonal pure bipartite entangled states perfectly under local operations and classical communication using an (exact) entanglement battery or an (exact) entanglement catalyst, it is necessary to consider that the cardinality of the set must be smaller than the total dimension of the given Hilbert space. Then, we construct a nontrivial case where an exact entanglement battery can provide huge advantage. We also construct other nontrivial cases where exact or approximate entanglement battery or entanglement catalyst can be useful. In fact, we find that the approximate tools are particularly useful in the local discrimination of certain sets which can be derived from many-copy indistinguishable ensembles.

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arXiv2026

Witness robustness: An operational quantifier of measurement resources via free state discrimination

We introduce the witness robustness of quantum measurements, a resource quantifier whose admissible noise consists of tuples of free-state witnesses rather than physical measurements. We establish its operational interpretation: it quantifies the maximal advantage that a measurement can provide over free measurements in discriminating an ensemble composed entirely of free states. Unlike the standard and generalized robustnesses, the witness robustness is not faithful in general, reflecting the fact that a resourceful measurement need not be useful when only free states can be prepared. We identify conditions under which faithfulness is recovered and show that, in resource theories admitting a resource-destroying map, the witness robustness vanishes for every measurement. We also establish fundamental properties, including convexity and monotonicity. Finally, we derive analytical results for projective measurements in single-qubit magic and for binary pure-state projective measurements in the two-qubit PPT entanglement theory.

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arXiv2026

Quantum Resources and Performance in the Initialization-Free Bernstein-Vazirani Algorithm

Naseri et al. [Phys. Rev. A 106, 062429 (2022); arXiv:2205.13610] studied which quantum resources in initial states are essential for the probabilistic Bernstein-Vazirani (BV) algorithm, defining its performance as the optimal average success probability over all measurements. In this work, we consider a variant of BV algorithm, which is called the initialization-free (IF) BV algorithm, in which an arbitrary ancilla state as the oracle register is allowed, to improve the performance. We derive an explicit formula for the performance of the probabilistic IF-BV algorithm and obtain a necessary and sufficient condition for an initial state to achieve maximal performance. We further prove that, under a suitable ordering assumption on the coefficients of the initial state, the probabilistic IF-BV algorithm outperforms the standard probabilistic BV algorithm.

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arXiv2026

Resourcefulness without Resource: Geometric Origins and Robustness

A prevailing intuition holds that quantum protocols using only free states confer no operational advantage. This intuition is contradicted by free-state discrimination gaps in which restricted measurements fail to optimally distinguish even orthogonal free states. Known instances include nonlocality without entanglement and, more recently, nonstabilizerness without magic. We trace these examples to a single convex-geometric mechanism: whenever the set of free measurements is closed, convex, and strict subset the set of all measurements, and the free states is a convex set with an interior, a gap-witnessing ensemble can be drawn entirely from the free states. The resulting gap is operationally rigid: no finite-dimensional assistance -- catalyst or quantum memory -- can asymptotically improve the discrimination rate beyond the single-shot restricted limit. By contrast, non-free ensembles admit memory-assisted attacks that fully erase the gap, exposing a sharp operational asymmetry between free and resource-carrying ensembles.

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arXiv2026

Asymptotic Limits of Entanglement Transmission

Reliable distribution of quantum entanglement over long distances is a central challenge in quantum information science, fundamentally limited by decoherence in noisy communication channels. In this work, we investigate the asymptotic limits of entanglement distribution across homogeneous linear repeater chains with arbitrary intermediate LOCC processing. We establish a strict dichotomy: the asymptotic preservation of entanglement over arbitrarily long distances is possible if and only if the underlying quantum channel admits a correctable subspace. For channels lacking such a subspace, we prove that the transmitted state converges exponentially fast to the set of separable states, rendering standard LOCC filtering insufficient. To counteract this exponential degradation, we analyze ``networks'' employing parallel channel uses per link. We derive a fundamental lower bound on the required number of parallel channel uses per elementary link, proving that for broad classes of channels without a correctable subspace, the number of parallel channels per link must scale at least logarithmically with the number of intermediate stations to sustain a non-zero amount of entanglement. This provides a code-independent bound for the number of physical links for the considered homogeneous one-way architecture. For depolarizing noise below the corresponding coding threshold, the logarithmic lower bound is achievable.

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arXiv2026

Advantage of flexible catalysis for entanglement and quantum thermodynamics

Understanding the fundamental limits of state convertibility is crucial for establishing the boundaries of quantum information processing and thermodynamic efficiency. While auxiliary systems, catalysts, can facilitate otherwise impossible transformations, standard catalysis rigidly requires the auxiliary system to return to its exact initial state. In this work, we investigate the power of flexible catalysis, where the catalyst evolves through a cycle of states, restoring its initial configuration only after a finite number of steps. Focusing on the regime of fixed, finite dimensions, we analyze the capabilities of flexible catalysis within the resource theories of entanglement and quantum thermodynamics. In the context of entanglement, we derive conditions limiting flexible catalysts, yet show that flexible catalysis can be strictly more powerful than same-dimensional standard catalysis: it enables deterministic transformations achievable by no standard catalyst of the same dimension, and it strictly increases the success probability of stochastic local operations and classical communication. A similar deterministic advantage arises in quantum thermodynamics, where flexible catalysis enables state transformations that are impossible with any standard catalyst of fixed dimension and Hamiltonian but become achievable via flexible catalysis.

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arXiv2025

ENTCALC: Toolkit for calculating geometric entanglement in multipartite quantum systems

We present entcalc, a Python and MATLAB package for estimating the geometric entanglement of multipartite quantum states. The package operates as follows: given a multipartite quantum state as input, it outputs an estimate of its geometric entanglement. For pure states, it computes the geometric entanglement together with an estimation error. For mixed states, it provides both lower and upper bounds on the geometric entanglement, thereby identifying an interval in which the true value lies. We provide several methods to compute the lower bound, enabling users to balance accuracy against computational cost. We apply entcalc to several representative examples, including for $3\otimes3$ PPT entangled states, mixtures of GHZ and W states, thermal states of selected three-qubit spin chains, and noisy GHZ and W states. We observe signatures of quantum phase transitions by quantifying entanglement in spin chains. We also demonstrate that entanglement between non-neighbouring sites can be activated by tuning the external magnetic field. In all tested cases, the gap between the lower and upper bounds is found to be very small, indicating that entcalc provides highly accurate estimates of the geometric entanglement for these states.

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arXiv2025

Robustness of quantum data hiding against entangled catalysts and memory

Quantum data hiding stores classical information in bipartite quantum states that are, in principle, perfectly distinguishable, yet remain almost indistinguishable without access to a quantum communication channel. Here, we investigate whether this limitation can be overcome when the communicating parties are assisted by additional quantum resources. We develop a general framework for state discrimination that unifies catalytic and memory-assisted local discrimination protocols and analyze their power to reveal hidden information. We prove that when the hiding states are separable, neither entangled catalysts nor quantum memory can increase the optimal discrimination probability, establishing the robustness of separable data-hiding schemes. In contrast, for some entangled states, a reusable quantum memory turns locally indistinguishable states into ones that can be discriminated almost perfectly. Our results delineate the fundamental limits of catalytic and memory-assisted state discrimination and identify separable encodings as a robust strategy for quantum data hiding.

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arXiv2025

Optimality of universal conclusive entanglement concentration protocols

Entanglement concentration is essential for quantum technologies, yet rigorous bounds on the success probability for universal protocols (those requiring no prior knowledge about the input state) have remained underexplored. We establish such fundamental limits for conclusive protocols distilling a perfect Bell state from pure two-qubit states by deriving the optimal success probability starting with two copies of a state with known Schmidt basis and four copies of a state with unknown Schmidt basis, using concatenated two-qubit operations. We prove that a known protocol achieves these bounds, confirming its optimality. Crucially, universality imposes an inherent efficiency trade-off, yielding an average success probability of just 2/105 over Haar measure.

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arXiv2025

Optimizing entanglement distribution via noisy quantum channels

Entanglement distribution is a crucial problem in quantum information science, owing to the essential role that entanglement plays in enabling advanced quantum protocols, including quantum teleportation and quantum cryptography. We investigate strategies for distributing quantum entanglement between two distant parties through noisy quantum channels. Specifically, we compare two configurations: one where the entanglement source is placed at the midpoint of the communication line, and another where it is located at one end. For certain families of qubit channels we show analytically that the midpoint strategy is optimal. Based on extensive numerical analysis, we conjecture that this strategy is generally optimal for all qubit channels. Focusing on the midpoint configuration, we develop semidefinite programming (SDP) techniques to assess whether entanglement can be successfully distributed through the network, and to quantify the amount of entanglement that can be distributed in the process. In many relevant cases the SDP formulation reliably captures the maximal amount of entanglement which can be distributed, if entanglement is quantified using the negativity. We analyze several channel models and demonstrate that, for various combinations of amplitude damping and depolarizing noise, entanglement distribution is only possible with weakly entangled input states. Excessive entanglement in the input state can hinder the channel's ability to establish entanglement. Our findings have implications for optimizing entanglement distribution in realistic quantum communication networks.

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arXiv2024

Geometric monotones of violations of quantum realism

Quantum realism, as introduced by Bilobran and Angelo [EPL 112, 40005 (2015)], states that projective measurements in quantum systems establish the reality of physical properties, even in the absence of a revealed outcome. This framework provides a nuanced perspective on the distinction between classical and quantum notions of realism, emphasizing the contextuality and complementarity inherent to quantum systems. While prior works have quantified violations of quantum realism (VQR) using measures based on entropic distances, here we extend the theoretical framework to geometric distances. Building on an informational approach, we derive geometric monotones of VQR using trace distance, Hilbert-Schmidt distance, Schatten $p$-distances, Bures, and Hellinger distances. We identify Bures and Hellinger distances as uniquely satisfying all minimal criteria for a bona fide VQR monotone. Remarkably, these distances can be expressed in terms of symmetric R\'enyi and Sandwiched R\'enyi divergences, aligning geometric and entropic approaches. Our findings suggest that the realism-information relation implies a deep connection between geometric and entropic frameworks, with only those geometric distances expressible as entropic quantities qualifying as valid monotones of VQR. This work highlights the theoretical and practical advantages of geometric distances, particularly in contexts where computational simplicity or symmetry is important.

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arXiv2024

Second Law of Entanglement Manipulation with Entanglement Battery

A central question since the beginning of quantum information science is how two distant parties can convert one entangled state into another. It has been conjectured that such conversions could be executed reversibly in an asymptotic regime, mirroring the reversible nature of Carnot cycles in classical thermodynamics. While a conclusive proof of this conjecture has been missing so far, earlier studies have excluded reversible entanglement manipulation in various settings. In this work, we show that arbitrary mixed state entanglement transformations can be made reversible under local operations and classical communication, when assisted by an entanglement battery--an auxiliary quantum system that stores and supplies entanglement in a way that ensures no net entanglement is lost. In particular, the rate of transformation in the asymptotic limit can be quantitatively expressed as a ratio of entanglement present within the quantum states involved. Our setting allows to consider different entanglement quantifiers which give rise to unique principles governing state transformations, effectively constituting diverse manifestations of a ``second law'' of entanglement manipulation. These findings resolve a long-standing open question on the reversible manipulation of entangled states and are also applicable to multipartite entanglement and other quantum resource theories, including quantum thermodynamics.

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arXiv2024

Coherence generation with Hamiltonians

We explore methods to generate quantum coherence through unitary evolutions, by introducing and studying the coherence generating capacity of Hamiltonians. This quantity is defined as the maximum derivative of coherence that can be achieved by a Hamiltonian. By adopting the relative entropy of coherence as our figure of merit, we evaluate the maximal coherence generating capacity with the constraint of a bounded Hilbert-Schmidt norm for the Hamiltonian. Our investigation yields closed-form expressions for both Hamiltonians and quantum states that induce the maximal derivative of coherence under these conditions. Specifically, for qubit systems, we solve this problem comprehensively for any given Hamiltonian, identifying the quantum states that lead to the largest coherence derivative induced by the Hamiltonian. Our investigation enables a precise identification of conditions under which quantum coherence is optimally enhanced, offering valuable insights for the manipulation and control of quantum coherence in quantum systems.

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arXiv2023

Local Purity Distillation in Quantum Systems: Exploring the Complementarity Between Purity and Entanglement

Quantum thermodynamics and quantum entanglement represent two pivotal quantum resource theories with significant relevance in quantum information science. Despite their importance, the intricate relationship between these two theories is still not fully understood. Here, we delve into the interplay between entanglement and thermodynamics, particularly in the context of local cooling processes. We introduce and develop the framework of Gibbs-preserving local operations and classical communication. Within this framework, we explore strategies enabling remote parties to effectively cool their local systems to the ground state. Our analysis is centered on scenarios where only a single copy of a quantum state is accessible, with the ideal performance defined by the highest possible fidelity to the ground state achievable under these constraints. We focus on systems with fully degenerate local Hamiltonians, where local cooling aligns with the extraction of local purity. In this context, we establish a powerful link between the efficiency of local purity extraction and the degree of entanglement present in the system, a concept we define as purity-entanglement complementarity. Moreover, we demonstrate that in many pertinent scenarios, the optimal performance can be precisely determined through semidefinite programming techniques. Our findings open doors to various practical applications, including techniques for entanglement detection and estimation. We demonstrate this by evaluating the amount of entanglement for a class of bound entangled states.

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arXiv2023

Quantum advantage in a unified scenario and secure detection of resources

Quantum resources may provide advantage over their classical counterparts. We say this as quantum advantage. Here we consider a single communication task to study different approaches of observing quantum advantage. We say this setting as a unified scenario. In our task, there are three parties - the Manager, Alice, and Bob. The Manager sends a value of a random variable to Alice and at the same time Bob receives some partial information regarding that value. Initially, neither Alice nor Bob knows the input of the other, received from the Manager. The goal of the task is achieved if and only if the value of the random variable, sent to Alice by the Manager, is identified by Bob with success probability greater than half all the time. Here non-zero error probability is allowed. However, to help Bob, Alice sends a limited amount of classical or quantum information to him (cbit or qubit). We show that the goal of the task can be achieved when Alice sends a qubit. On the other hand, a cbit communication is not sufficient for achieving the goal. Thus, it establishes quantum advantage. We further show that the optimal success probability in the overall process for a qubit communication can be higher than the optimal success probability for a cbit communication. In fact, this success probability is higher for qubit communication even if along with cbit communication Alice and Bob share randomness. Clearly, it demonstrates a more prominent non-classical feature. Actually, we obtain higher success probability compared to other tasks. This also suggests the experiment friendly nature of our task. We then connect our task with semi-device-independence and show how our task can be useful to detect quantumness of a communication in a secure way. With increasing dimension of the random variable, to achieve the goal, the separation between the quantum and the classical communication also increases.

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arXiv2023

Coherence manipulation in asymmetry and thermodynamics

In the classical regime, thermodynamic state transformations are governed by the free energy. This is also called as the second law of thermodynamics. Previous works showed that, access to a catalytic system allows us to restore the second law in the quantum regime when we ignore coherence. However, in the quantum regime, coherence and free energy are two independent resources. Therefore, coherence places additional non-trivial restrictions on the the state transformations, that remains elusive. In order to close this gap, we isolate and study the nature of coherence, i.e., we assume access to a source of free energy. We show that allowing catalysis along with a source of free energy allows us to amplify any quantum coherence present in the quantum state arbitrarily. Additionally, any correlations between the system and the catalyst can be suppressed arbitrarily. Therefore, our results provide a key step in formulating a fully general law of quantum thermodynamics.

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arXiv2023

Multipartite entanglement theory with entanglement-nonincreasing operations

A key problem in quantum information science is to determine optimal protocols for the interconversion of entangled states shared between remote parties. While for two parties a large number of results in this direction is available, the multipartite setting still remains a major challenge. In this article, this problem is addressed by extending the resource theory of entanglement for multipartite systems beyond the standard framework of local operations and classical communication. Specifically, we consider transformations capable of introducing a small, controllable increase of entanglement of a state, with the requirement that the increase can be made arbitrarily small. We demonstrate that in this adjusted framework, the transformation rates between multipartite states are fundamentally dictated by the bipartite entanglement entropies of the respective quantum states. Remarkably, this approach allows the reduction of tripartite entanglement to its bipartite analog, indicating that every pure tripartite state can be reversibly synthesized from a suitable number of singlets distributed between pairs of parties.

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