arXiv subjects

Saronath Halder

Publications and source records attributed to Saronath Halder.

At least 19 recordsLinked to original sources

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

Incompleteness is necessary for activation of nonlocality without entanglement

A set of orthogonal product states is said to exhibit "quantum nonlocality without entanglement" if it is locally indistinguishable, i.e. no sequence of local operations and classical communication (LOCC) can perfectly discriminate the states. Building on this foundational idea, recent studies have highlighted the phenomenon of "genuine activation of hidden nonlocality", where a set of initially distinguishable orthogonal states becomes locally indistinguishable through orthogonality-preserving LOCC transformations. In this letter, we establish that any complete orthogonal product basis that is initially locally distinguishable remains so under all orthogonality-preserving local projective measurements, thereby ruling out activation via orthogonality-preserving local projective measurements and classical communication. We further introduce and formalise the notions of "strongly local sets", namely locally distinguishable sets that remain non-activable under all bipartitions. Interestingly, the study of "local activability" of distinguishable sets is useful to characterise the boundary between LOCC distinguishability and its irreversible loss in multipartite systems. Our results provide a rigorous structural understanding of local-to-nonlocal transitions in quantum state discrimination.

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arXiv2026

Entanglement of minimal dimension and a class of local state discrimination problems

In this work, we construct small sets of bipartite orthogonal pure states that cannot be perfectly distinguished by local operations and classical communication (LOCC). We mention that not all the states within the constructed sets are necessarily entangled. However, such a set contains at least one entangled state which cannot be conclusively identified by LOCC (with nonzero probability). Then, we show that the states of any such set can be perfectly distinguished by LOCC using a minimal-dimensional entangled resource state. Clearly, here the entangled resource state provides an advantage irrespective of the dimension of the given set. Using this result, we also prove that any pure entangled state is useful as a resource to distinguish the states of any present set unambiguously with nonzero probability under LOCC. These sets exist in all two-qudit Hilbert spaces. Furthermore, it is possible to decrease the average entanglement content of such a set or to increase the cardinality of the set without changing certain properties of the same.

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arXiv2026

Protocols for sharing genuine multipartite entanglement by employing copies of biseparable states

Sharing genuine multipartite entanglement by considering collective use of copies of biseparable states, which are entangled across all bipartitions but lack genuine multipartite entanglement at the single-copy level, plays a central role in several quantum information processing protocols, and has been referred as genuine multipartite entanglement activation. We present a protocol for three-qutrit systems showing that two copies of rank-two biseparable states, entangled across every bipartition, are sufficient to generate a genuinely multipartite entangled state with nonzero probability. This contrasts with the three-qubit scenario where many copies of biseparable states might be required for sharing genuine multipartite entanglement. We subsequently generalize our protocols to the case of an arbitrary number of parties. Interestingly, the proposed construction naturally leads to the activation of genuinely nonlocal correlations, yielding a result that is stronger than genuine multipartite entanglement activation alone.

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arXiv2025

Paradox-free classical non-causality and unambiguous non-locality without entanglement are equivalent

Closed timelike curves (CTCs) challenge our conception of causality by allowing information to loop back into its own past. Any consistent description of such scenarios must avoid time-travel paradoxes while respecting the no-new-physics principle, which requires that the set of operations available within any local spacetime region remain unchanged, irrespective of whether CTCs exist elsewhere. Within an information-theoretic framework, this leads to process functions: deterministic classical communication structures that remain logically consistent under arbitrary local operations, yet can exhibit correlations incompatible with any definite causal order - a phenomenon known as non-causality. In this work, we establish a correspondence between process functions and unambiguous complete product bases, i.e. product bases in which every local state belongs to a unique local basis. This equivalence implies that non-causality of process functions is exactly mirrored by quantum nonlocality without entanglement (QNLWE) - the impossibility of perfectly distinguishing separable states using local operations and causal classical communication - for such bases. Our results generalize previous special cases to arbitrary local dimensions and any number of parties, enable systematic constructions of non-causal process functions and unambiguous QNLWE bases, and implies, inter alia, that bipartite unambiguous QNLWE bases do not exist. Finally, this work reveals an unexpected connection between causal and non-signaling inequalities: every process function both maximally violates an associated causal inequality and yields a corresponding Bell inequality that admits no violation.

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arXiv2025

Classifying locally distinguishable sets: No activation across bipartitions

A set of orthogonal quantum states is said to be locally indistinguishable if they cannot be perfectly distinguished by local operations and classical communication (LOCC). Otherwise, the states are locally distinguishable. Interestingly, locally indistinguishable states can have productive applications in quantum information processing protocols. In this sense, locally indistinguishable states are useful. On the other hand, it is usual to consider that locally distinguishable states are useless. Nevertheless, recent works suggest that locally distinguishable states should be given due consideration as in certain situations these states can be converted to locally indistinguishable states under orthogonality-preserving LOCC (OP-LOCC). Such a counterintuitive phenomenon motivates us to ask when the aforesaid conversion is possible and when it is not. In this work, we provide different structures of locally distinguishable product and entangled states which do not allow the aforesaid conversion. We also provide certain structures of locally distinguishable states which allow the aforesaid conversion. In this way, we classify the locally distinguishable sets by introducing hierarchies among them. In a multipartite system, this study becomes more involved as there exist multipartite locally distinguishable sets which cannot be converted to locally indistinguishable sets by OP-LOCC across any bipartition. We say this as ``no activation across bi-partitions".

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arXiv2025

Local unambiguous unidentifiability, entanglement generation, and Hilbert space splitting

We consider collections of mixed states supported on mutually orthogonal subspaces whose rank add up to the total dimension of the underlying Hilbert space. We then ask whether it is possible to find such collections in which no state from the set can be unambiguously identified by local operations and classical communication (LOCC) with non-zero success probability. We show the necessary and sufficient condition for such a property to exist is that the states must be supported in entangled subspaces. In fact, the existence of such a set guarantees the existence of a type of entangling projective measurement other than rank one measurements and vice versa. This projective measurement can create entanglement from any product state picked from the same Hilbert space on which the measurement is applied. Here the form of the product state is not characterized. Ultimately, these sets or the measurements are associated with the splitting of a composite Hilbert space, i.e., the Hilbert space can be written as a direct sum of several entangled subspaces. We then characterize present sets (measurements) in terms of dimensional constraints, maximum-minimum cardinalities (outcomes), etc. The maximum cardinalities of the sets constitute a class of state discrimination tasks where several stronger classes of measurements (like separable measurements, etc.) do not provide any advantage over LOCC. Finally, we discuss genuine local unambiguous unidentifiability and generation of genuine entanglement from completely product states.

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arXiv2024

Unconditionally superposition-robust entangled state in all multiparty quantum systems

We investigate the inseparability of states generated by superposition of a multipartite pure entangled state with a product state. In particular, we identify specific multipartite entangled states that will always produce inseparability after superposition with an arbitrary completely product state. Thus, these entangled states are unconditionally superposition-robust, and we refer to this phenomenon as ``unconditional inseparability of superposition" in multipartite quantum systems. In this way, we complete the picture of unconditional inseparability of superposition which was introduced earlier for bipartite systems. We also characterize the superposition of a multipartite pure entangled state with a pure bi-separable state. However, the present analysis allows us to obtain a more general result, viz., there exists at least one pure entangled state in any multipartite Hilbert space such that its superposition with an arbitrary completely product state always yields an entangled state. On the other hand, for any bipartite pure entangled state, if at least one of the subsystems is a qubit, then it is always possible to find a suitable product state such that the superposition of the entangled state and the product state produces a product state. In this way, we find a feature of multipartite quantum systems which is in sharp contrast with that of bipartite ones. We then show how unconditional inseparability of superposition can be useful in exhibiting an indistinguishability property within the local unambiguous state discrimination problem.

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arXiv2024

Almost device-independent certification of GME states with minimal measurements

Device-independent certification of quantum states enables the characterization of states within a device under minimal physical assumptions. A major problem in this regard is to certify quantum states using minimal resources. Aiming to address this problem, we consider a multipartite quantum steering scenario involving an arbitrary number of parties, of which only one is trusted, meaning that the measurements performed by this party are known. Consequently, the self-testing scheme is almost device-independent. Importantly, all the parties can only perform two measurements each, which is the minimal number of measurements required to observe any form of quantum nonlocality. Then, we propose steering inequalities that are maximally violated by three major classes of genuinely multipartite entangled (GME) states: graph states of arbitrary local dimension, Schmidt states of arbitrary local dimension, and $N$-qubit generalized W states. Using the proposed inequalities, we then provide an almost device-independent certification of the above GME states. Restricting to qubits, we also lift our almost device-independent scheme to device-independent self-testing.

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arXiv2023

Efficient entanglement-assisted discrimination of a class of many-copy indistinguishable sets

We explore entanglement as a resource to distinguish locally indistinguishable orthogonal quantum states. Specifically, we consider sets which contain states from an unextendible product basis along with a pure entangled state. We establish a connection between the aforesaid problem and the entanglement-assisted discrimination of a certain class of many-copy indistinguishable sets. The entanglement-assisted protocols that we construct here are quite efficient, as they render the teleportation-based protocols sub-optimal. In fact, a central aspect of our study is to explore the role of Schmidt rank as a resource to distinguish the states of locally indistinguishable sets. Interestingly, we identify an instance where a set of locally indistinguishable orthogonal states remains locally indistinguishable even with access to any finite number of copies, yet becomes perfectly distinguishable using entangled resources of relatively low cost. This fact makes it possible to compare the degrees of local indistinguishability associated with several locally indistinguishable sets within the same Hilbert space. Consequently, we report a hierarchy of local indistinguishability among the many-copy indistinguishable sets. Thereafter, based on our analysis, we present a theoretical proposal for an information processing protocol exhibiting secure locking of information and its resource-efficient extraction. Furthermore, we also find that the hierarchical difference in local indistinguishability can increase with increasing dimension of the Hilbert space.

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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

Unextendibility, uncompletability, and many-copy indistinguishable ensembles

In this work, we explore the notions unextendible product basis and uncompletability for operators which remain positive under partial transpose. Then, we analyze their connections to the ensembles which are many-copy indistinguishable under local operations and classical communication (LOCC). We show that the orthogonal complement of any bipartite pure entangled state is spanned by product states which form a nonorthogonal unextendible product basis (nUPB) of maximum cardinality. This subspace has one to one correspondence with the maximum dimensional subspace where there is no orthonormal product basis. Due to these, the proof of indistinguishability of a class of ensembles under LOCC in many-copy scenario becomes simpler. Furthermore, it is now clear that there are several many-copy indistinguishable ensembles which are different construction-wise. But if we consider the technique of proving their indistinguishability property under LOCC, then, for many of them it can be done using the general notion of unextendible product basis. Explicit construction of the product states, forming nUPBs is shown. Thereafter, we introduce the notion of positive partial transpose uncompletability to unify different many-copy indistinguishable ensembles. We also report a class of multipartite many-copy indistinguishable ensembles for which local indistinguishability property increases with decreasing number of mixed states.

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arXiv2023

Self-testing composite measurements and bound entangled state in a single quantum network

Within the quantum networks scenario we introduce a single scheme allowing to certify three different types of composite projective measurements acting on a three-qubit Hilbert space: one constructed from genuinely entangled GHZ-like states, one constructed from fully product vectors that exhibit the phenomenon of nonlocality without entanglement (NLWE), and a hybrid measurement obtained from an unextendible product basis (UPB). Noticeably, we certify a basis exhibiting NLWE in the smallest dimension capable of supporting this phenomenon. On the other hand, the possibility of certification of a measurement obtained from a UPB has an interesting implication that one can also self-test a bound entangled state in the considered quantum network. Such a possibility does not seem to exist in the standard Bell scenario. Furthermore, we also analyse the robustness of our scheme towards experimental errors.

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arXiv2023

Information locking and its resource efficient extraction

Locally indistinguishable states are useful to distribute information among spatially separated parties such that the information is locked. This implies that the parties are not able to extract the information completely via local operations and classical communication (LOCC) while it might be possible via LOCC when the parties share entanglement. In this work, we consider an information distribution protocol using orthogonal states for m >= 3 spatially separated parties such that even if any k <= (m-1) parties collaborate still the information cannot be revealed completely. Such a protocol is useful to understand up to what extent the encoded information remains locked. However, if required, the parties can share entanglement and extract the information completely by LOCC. To make the process resource efficient, it should consume less number of entangled states. We show that though the set of states, which are locally indistinguishable across every bipartition, are sufficient for the above protocol, they may consume higher number of entangled states when aiming for complete information extraction. We establish this by constructing a class of locally indistinguishable sets of orthogonal states which can be employed to accomplish the above protocol and these sets consume less number of entangled states, compared to the former sets, for complete information extraction. In fact, this difference in the number of required entangled states for complete information extraction grows linearly with the number of parties. This study sheds light on suitable use of local indistinguishability property of quantum states as resource and thus, we demonstrate an efficient way of information distribution.

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arXiv2022

Identifying the value of a random variable unambiguously: Quantum versus classical approaches

Quantum resources may provide advantage over their classical counterparts. Theoretically, in certain tasks, this advantage can be very high. In this work, we construct such a task based on a game, mediated by Referee and played between Alice and Bob. Referee sends Alice a value of a random variable. At the same time, Referee also sends Bob some partial information regarding that value. Here partial information can be defined in the following way. Bob gets the information of a random set which must contain the value of the variable, that is sent to Alice by the Referee, along with other value(s). Alice is not allowed to know what information is sent to Bob by the Referee. Again, Bob does not know which value of the random variable is sent to Alice. Now, the game can be won if and only if Bob can unambiguously identify the value of the variable, that is sent to Alice, with some nonzero probability, no matter what information Bob receives or which value is sent to Alice. However, to help Bob, Alice sends some limited amount of information to him, based on any strategy which is fixed by Alice and Bob before the game begins. We show that if Alice sends limited amount of classical information then the game cannot be won while the quantum analogue of the `limited amount of classical information' is sufficient for winning the game. Thus, it establishes quantum advantage. We further analyze several variants of the game and provide certain bounds on the success probabilities. Moreover, we establish connections between trine ensemble, mutually unbiased bases, and the encoding-decoding strategies of those variants. We also discuss the role of quantum coherence in the present context.

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arXiv2022

To share and not share a singlet: control qubit and nonclassicality in teleportation

The superposition principle provides us the opportunity to unfold many surprising facts. One such fact leads to the generation of entanglement which may allow one to teleport an unknown quantum state from one location to another. We try to understand the role of superposition in the process of quantum teleportation. We consider, within the scenario of quantum teleportation, a set-up where the sender and the receiver are in a superposed situation of using a maximally entangled state and not using any entangled state in the teleportation protocol, controlled by a qubit. We address two distinct protocols: in the first case, the sender and the receiver do nothing when they do not have the authority to use entanglement, while in the second case, they still use classical communication even if they do not use entanglement. After accomplishing the protocols, we operate a Hadamard gate on the control qubit, measure the control qubit's state, and consider the outcome corresponding to a particular state of the control. We compare the protocol's fidelity with the maximum fidelity achievable through classical resources only. In particular, we provide conditions to achieve nonclassical fidelity in teleportation, in the presence of the control qubit. To explore if there is any quantum advantage (advantage of superposition present in the control qubit), we compare the fidelities of the control qubit-based protocols with the fidelity achieved in a situation where the two parties are in a classical mixture of using and not using the maximally entangled state. We observe that there exists a wide range of parameters defining the initial state of the control qubit for which our protocols provide quantum advantage. To analyse the role of superposition quantitatively, we discuss whether the amount of quantum advantage can be expressed in terms of quantum coherence present in the state of the control qubit.

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arXiv2022

Incompatibility of local measurements provide advantage in local quantum state discrimination

The uncertainty principle may be considered as giving rise to the notion of incompatibility of observables. A pack of quantum measurements that cannot be measured simultaneously is said to form a set of incompatible measurements. Every set of incompatible measurements has an advantage over the compatible ones in a quantum state discrimination task where one prepares a state from an ensemble and sends it to another party, and the latter tries to detect the state using available measurements. Comparison between global and local quantum state discriminations is known to lead to a phenomenon of "nonlocality". In this work, we seal a connection between the domains of local quantum state discrimination and incompatible quantum measurements. We consider the local quantum state discrimination task where a sender prepares a bipartite state and sends the subsystems to two receivers. The receivers try to detect the sent state using locally incompatible measurements. We analyze the ratio of the probability of successfully guessing the state using incompatible measurements and the maximum probability of successfully guessing the state using compatible measurements. We find that this ratio is upper bounded by a simple function of robustnesses of incompatibilities of the local measurements. Interestingly, corresponding to every pair of sets of incompatible measurements, there exists at least one local state discrimination task where this bound can be achieved. We argue that the optimal local quantum state discrimination task does not present any "nonlocality", where the term is used in the sense of a difference between the ratios, of probabilities of successful detection via incompatible and compatible measurements, in global and local state discriminations. The results can be generalized to the regime of multipartite local quantum state distinguishing tasks.

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arXiv2022

Conditions for local transformations between sets of quantum states

We study the problem of transforming a set of pure bipartite states into another using deterministic LOCC (local operations and classical communication). Necessary conditions for the existence of such a transformation are obtained using LOCC constraints on state transformation, entanglement, and distinguishability. These conditions are shown to be independent but not sufficient. We discuss their satisfiability and classify all possible input-output pairs of sets accordingly. We also prove that strict inclusions hold between LOCC, separable, and positive partial transpose operations for set transformation problems.

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