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arXiv:2312.15476 · Journal of Physics A Mathematical and Theoretical

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

Abhay Srivastav, Saronath Halder

Published Sep 15, 2025• 0 citations
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Abstract

Abstract 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.

DOI
10.1088/1751-8121/ae06df

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Abstract 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.
Any set of states which cannot be perfectly distinguished by local operations and classical communication (LOCC) alone can always be locally distinguished using quantum teleportation with a maximally entangled state as resource. However, in quantum information theory, entanglement is a very valuable resource, so it leaves the following problem: How to accomplish this task more efficiently than teleportation, that is, design the local discrimination protocol using less entanglement. In this paper, we first present two protocols to locally distinguish a particular unextendible product bases (UPB) in $5\ensuremath{\bigotimes}5$ by using different entanglement resource. Then, we generalize the distinguishing methods for a class of UPB in $d\ensuremath{\bigotimes}d$, where ddd is odd and $d\ensuremath{\geqslant}3$. Furthermore, for a class of UPB in $d\ensuremath{\bigotimes}d$, where ddd is even and $d\ensuremath{\geqslant}4$, we prove that these states can also be distinguished by LOCC with multiple copies of low-dimensional entanglement resource. These results offer rather general insight into how to use entanglement resource more efficiently and also reveal the phenomenon of less nonlocality with more entanglement.
Entanglement is a central resource in quantum information science, and it is therefore important to design local discrimination protocols that minimize entanglement cost. In this paper, we propose several entanglement-assisted discrimination schemes for the local discrimination of a representative strongly nonlocal unextendible product basis (UPB) in a 3⊗3⊗33\otimes 3\otimes 33⊗3⊗3 system. By exploiting the structure of the UPB and the properties of maximally entangled resources, we generalize the protocols to a family of strongly nonlocal UPBs in d⊗d⊗dd\otimes d\otimes dd⊗d⊗d systems. In particular, we show that these UPBs can be perfectly distinguished using two bipartite maximally entangled states, distributed between different pairs of parties, without employing quantum teleportation. We further compare the total supplied and average consumed entanglement under a clearly specified accounting convention. The results demonstrate that avoiding teleportation can reduce the required entanglement in suitable resource-allocation scenarios and clarify the operational role of low-dimensional maximally entangled resources.
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 $m\ensuremath{\ge}3$ spatially separated parties such that even if any $k\ensuremath{\le}(m\ensuremath{-}1)$ 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 a 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 with 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 a resource, and thus we demonstrate an efficient way of information distribution.
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.
Entanglement-assisted discrimination of orthogonal quantum states exhibiting quantum nonlocality is a frontier topic in quantum information theory. In this paper, we investigate the role of multipartite entanglement and develop resource-efficient LOCC discrimination protocols for nonlocal sets of orthogonal states, including multipartite orthogonal product-state sets and entangled-state sets with different nonlocal features. By incorporating controlled-NOT (CNOT) operations into the discrimination procedure, we construct protocols for genuinely nonlocal GHZ bases in four- and five-qubit systems that require only a single EPR pair. For the same target sets, we compare different entanglement-assisted schemes and identify those with lower entanglement consumption. We further observe that, on average, protocols avoiding teleportation consume fewer resources than teleportation-based approaches. In addition, when higher-partite GHZ-type resources (with n>3n>3n>3) are available among suitable subsystems, they can in some cases reduce the overall entanglement cost. Our results highlight the operational significance of multipartite entanglement and provide practical protocols for the local discrimination of orthogonal state sets exhibiting quantum nonlocality.
We study the problem of locally distinguishing pure quantum states using shared entanglement as a resource. For a given set of locally indistinguishable states, we define a resource state to be useful if it can enhance local distinguishability and optimal if it can distinguish the states as well as global measurements and is also minimal with respect to a partial ordering defined by entanglement and dimension. We present examples of useful resources and show that an entangled state need not be useful for distinguishing a given set of states. We obtain optimal resources with explicit local protocols to distinguish multipartite Greenberger-Horne-Zeilinger and graph states and also show that a maximally entangled state is an optimal resource under one-way local operations and classical communication to distinguish any bipartite orthonormal basis which contains at least one entangled state of full Schmidt rank.