The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measurements yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two bipartite quantum states, employing positive operator-valued measures (POVMs) with positive partial transpose (PPT) to achieve optimal success probability through general entangled measurements. We first introduce two quantities called the spectral PPT-distance and relative spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show these quantities are related to the entanglement cost of optimal discrimination by PPT POVMs. Following this, we establish bounds and develop SDP hierarchies to estimate the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging these results, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.
The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measurements yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two bipartite quantum states, employing positive operator-valued measures (POVMs) with positive partial transpose (PPT) to achieve optimal success probability through general entangled measurements. We first introduce two quantities called the spectral PPT-distance and relative spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show these quantities are related to the entanglement cost of optimal discrimination by PPT POVMs. Following this, we establish bounds and develop SDP hierarchies to estimate the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging these results, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.
The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measurements yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two bipartite quantum states, employing positive operator-valued measures (POVMs) with positive partial transpose (PPT) to achieve optimal success probability through general entangled measurements. First, we introduce an efficiently computable quantity called the spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show that it can be a lower bound for the entanglement cost of optimal discrimination by PPT POVMs. Second, we establish an upper bound on the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging this result, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.
Quantum channel discrimination is a fundamental task in quantum information processing. In the one-shot regime, discrimination between two candidate channels is characterized by the diamond norm. Beyond this basic setting, however, many scenarios in distributed quantum information processing remain unresolved, motivating notions of distinguishability that capture the power of the available resources. In this work, we formulate a theory of testers for bipartite channel discrimination, leading to the concept of the entanglement cost of bipartite channel discrimination: the minimum Schmidt rank k of a shared maximally entangled state required for local protocols to achieve the globally optimal success probability. We introduce k-injectable testers as a tester-based description of entanglement-assisted local discrimination and, in particular, study the class of k-injectable positive-partial-transpose (PPT) testers, which constitutes a numerically tractable relaxation of the practically relevant class of LOCC testers.
For every k, we derive a semidefinite program (SDP) for the optimal success probability, which in turn yields an efficiently computable one-shot PPT entanglement cost. To render these optimization problems numerically feasible, we prove a symmetry-reduction principle for covariant channel pairs, thereby reducing the effective dimension of the associated SDPs. Finally, by dualizing the SDP, we derive bounds on the composite channel-discrimination problem and illustrate our framework with proof-of-principle examples based on the depolarizing channel, the depolarized SWAP channel, and the Werner--Holevo channels.
The unique features of entanglement and non-locality in quantum systems, where there are pairs of bipartite states perfectly distinguishable by general entangled measure-ments yet indistinguishable by local operations and classical communication, hold significant importance in quantum entanglement theory, distributed quantum information processing, and quantum data hiding. This paper delves into the entanglement cost for discriminating two quantum states, employing positive operator-valued measures (POVMs) with positive partial trans-pose (PPT) to achieve optimal success probability through general entangled measurements. First, we introduce an efficiently com-putable quantity called the spectral PPT-distance of a POVM to quantify the localness of a general measurement. We show that it can be a lower bound for the entanglement cost of optimal discrimination by PPT POVMs. Second, we establish an upper bound on the entanglement cost of optimal discrimination by PPT POVMs for any pair of states. Leveraging this result, we show that a pure state can be optimally discriminated against any other state with the assistance of a single Bell state. This study advances our understanding of the pivotal role played by entanglement in quantum state discrimination, serving as a crucial element in unlocking quantum data hiding against locally constrained measurements.
Any two orthogonal quantum states can be perfectly distinguished via local operations and classical communication (LOCC), yet whether all orthogonal multipartite pairs incur an identical operational cost remains an open question. Here, we address the resource consumption required for local state discrimination across multipartite pair of states. We demonstrate that distinct pairs of orthogonal multipartite maximally entangled states require unequal amounts of quantum resources to achieve local distinguishability. Extending our framework beyond individual pairs, we analyze larger sets of both locally distinguishable and indistinguishable multipartite orthogonal states, revealing a nontrivial hierarchy in their entanglement consumption. These results show that the resource cost of LOCC discrimination is state-dependent, providing insight into the fine-grained structure of multipartite nonlocality.
We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability, thus establishing the associated Chernoff exponent. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite asymptotic separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB.
Quantum data hiding is the existence of pairs of bipartite quantum states that are (almost) perfectly distinguishable with global measurements, yet close to indistinguishable when only measurements implementable with local operations and classical communication are allowed. Remarkably, data hiding states can also be chosen to be separable, meaning that secrets can be hidden using no entanglement that are almost irretrievable without entanglement -- this is sometimes called `nonlocality without entanglement'. Essentially two families of data hiding states were known prior to this work: Werner states and random states. Hiding Werner states can be made either separable or globally perfectly orthogonal, but not both -- separability comes at the price of orthogonality being only approximate. Random states can hide many more bits, but they are typically entangled and again only approximately orthogonal. In this paper, we present an explicit construction of novel group-symmetric data hiding states that are simultaneously separable, perfectly orthogonal, and even invariant under partial transpose, thus exhibiting the phenomenon of nonlocality without entanglement to the utmost extent. Our analysis leverages novel applications of numerical analysis tools to study convex optimisation problems in quantum information theory, potentially offering technical insights that extend beyond this work.