An ensemble of product states is said to exhibit "quantum nonlocality without entanglement" if the states cannot be optimally discriminated by local operations and classical communication (LOCC). We show that this property can depend on the measure of state discrimination. We present a family of ensembles, each consisting of six linearly independent, equally probable product states for which LOCC fails to achieve optimal minimum-error discrimination but succeeds in achieving optimal unambiguous discrimination.

Quantum state exclusion is the task of identifying at least one state from a known set that was not used in the preparation of a quantum system. In particular, a given set of quantum states is said to admit state exclusion if there exists a measurement such that, for each state in the set, some measurement outcome rules it out with certainty. However, state exclusion is not always possible in the single-copy setting. In this paper, we investigate whether access to multiple identical copies enables state exclusion. We prove that for any set of three or more pure states, state exclusion becomes possible with a finite number of copies. We further show that the required number of copies may be arbitrarily large – in particular, for every natural number N, we construct sets of states for which exclusion remains impossible with N or fewer copies.

We consider the problem of distinguishing between the elements of a bipartite maximally entangled orthonormal basis using local operations and classical communication (LOCC) and a partially entangled state acting as a resource. We derive an exact formula for the optimum success probability and find that it corresponds to the fully entangled fraction of the resource state. The derivation consists of two steps. First, we consider a relaxation of the problem by replacing LOCC with positive-partial-transpose (PPT) measurements and establish an upper bound on the success probability as the solution of a semidefinite program, and then show that this upper bound is achieved by a teleportation-based LOCC protocol. This further implies that separable and PPT measurements provide no advantage over LOCC for this task. We also present lower and upper bounds on the success probability for distinguishing the elements of an incomplete orthonormal maximally entangled basis in the same setup.

In a quantum change point problem, a source emitting particles in a fixed quantum state (default) switches to a different state at some stage, and the objective is to identify when the change happened by measuring a sequence of particles emitted from such a source. Motivated by entanglement-sharing protocols in quantum information, we study this problem within the paradigm of local operations and classical communication (LOCC). Here, we consider a source that emits entangled pairs in a default state, but starts producing another entangled state (mutation) at a later stage. Then, a sequence of entangled pairs prepared from such a source and shared between distant observers cannot be used for quantum information processing tasks as the identity of each entangled pair remains unknown. We show that identifying the change point using LOCC leads to the distillation of free entangled pairs. In particular, if the default and the mutation are mutually orthogonal, there exists an efficient LOCC protocol that identifies the change point without fail and distills a sufficiently large number of pairs. However, if they are nonorthogonal, there is a probability of failure. In this case, we compute the number of entangled pairs that may be obtained on average. We also consider a relaxation of the two-state problem where the mutation is not known a priori, but instead belongs to a known set. Here we show that local distinguishability plays a crucial role: if the default and the possible mutations are locally distinguishable, the problem reduces to the two-state problem with orthogonal states, but if not, one may still identify the mutation, the change point, and distill entanglement, as we illustrate with a concrete example.

A key concept of quantum information theory is that accessing information encoded in a quantum system requires us to discriminate between several possible states the system could be in. A natural generalization of this problem, namely, quantum sequence discrimination, appears in various quantum information processing tasks, the objective being to determine the state of a finite sequence of quantum states. Since such a sequence is a composite quantum system, the fundamental question is whether an optimal measurement is local, i.e., comprising measurements on the individual members, or collective, i.e. requiring joint measurement(s). In some known instances of this problem, the optimal measurement is local, whereas in others, it is collective. But, so far, a definite prescription based solely on the problem description has been lacking. In this paper, we prove that if the members of a given sequence are drawn secretly and independently from an ensemble or even from different ensembles, the optimum success probability is achievable by fixed local measurements on the individual members of the sequence, and no collective measurement is necessary. This holds for both minimum-error and unambiguous state discrimination paradigms.

Signal propagation in biochemical networks is characterized by the inherent randomness in gene expression and fluctuations of the environmental components, commonly known as intrinsic and extrinsic noise, respectively. We present a theoretical framework for noise propagation in a generic two-step cascade (S→X→Y) regarding intrinsic and extrinsic noise. We identify different channels of noise transmission that regulate the individual and the overall noise properties of each component. Our analysis shows that the intrinsic noise of S alleviates the general noise and information transmission capacity along the cascade. On the other hand, the intrinsic noise of X and Y acts as a bottleneck of information transmission. We also show a hierarchical relationship among the intrinsic noise levels of S, X, and Y, with S exhibiting the highest level of intrinsic noise, followed by X and then Y. This hierarchy is preserved within the two-step cascade, facilitating the highest information transmission from S to Y via X.

Recently, it was shown that two distant test masses, each prepared in a spatially superposed quantum state, become entangled through their mutual gravitational interaction. This entanglement, it was argued, is a signature of the quantum nature of gravity. We extend this treatment to a many-body system in a general setup and study the entanglement properties of the time-evolved state. We exactly compute the time-dependent I-concurrence for every bipartition and obtain the necessary and sufficient condition for the creation of genuine many-body entanglement. We further show that this entanglement is of generalised GHZ type when certain conditions are met. We also evaluate the amount of multipartite entanglement in the system using a set of generalised Meyer-Wallach measures.

We consider the problem of determining the state of an unknown quantum sequence without error. The elements of the given sequence are drawn with equal probability from a known set of linearly independent pure quantum states with the property that their mutual inner products are all real and equal. This problem can be posed as an instance of unambiguous state discrimination where the states correspond to that of all possible sequences having the same length as the given one. We calculate the optimum probability by solving the optimality conditions of a semidefinite program. The optimum value is achievable by measuring individual members of the sequence, and no collective measurement is necessary.

The quantum switch describes a quantum operation in which two or more quantum channels act on a quantum system with the order of application determined by the state of an order quantum system. And by suitably choosing the state of the order system, one can create a quantum superposition of the different orders of application, which can perform communication tasks impossible within the framework of the standard quantum Shannon theory. In this paper, we consider the scenario of one-shot heralded qubit communication and ask whether there exist protocols using a given quantum switch or switches that could outperform the given ones. We answer this question in the affirmative. We define a higher-order quantum switch composed of two quantum switches, with their order of application controlled by another order quantum system. We then show that the quantum switches placed in a quantum superposition of their alternative orders can transmit a qubit, without any error, with a probability higher than that achievable with the quantum switches individually. We demonstrate this communication advantage over quantum switches useful as a resource and those that are useless. We also show that there are situations where there is no communication advantage over the individual quantum switches.

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.

Quantum nonlocality has different manifestations that, in general, are revealed by local measurements of the parts of a composite system. In this paper, we study nonlocality arising from a set of orthogonal states that cannot be perfectly distinguished by local operations and classical communication (LOCC). Such a set is deemed nonlocal, for a joint measurement on the whole system is necessary for perfect discrimination of the states with certainty. On the other hand, a set of orthogonal states that can be perfectly distinguished by LOCC is believed to be devoid of nonlocal properties. Here, we show that there exist orthogonal sets that are locally distinguishable but without local redundancy (i.e., they become nonorthogonal on discarding one or more subsystems) whose nonlocality can be activated by local measurements. In particular, a state chosen from such a set can be locally converted, with certainty, into another state, the identity of which can now only be ascertained by global measurement and no longer by LOCC. In other words, a locally distinguishable set without local redundancy may be locally converted into a locally indistinguishable set with certainty. We also suggest an application, namely, local hiding of information, that allows us to locally hide locally available information without losing any part. Once hidden, the information in its entirety can only be retrieved using entanglement.

Entangled states are useful resources for the task of quantum state discrimination by local operations and classical communication (LOCC). For example, a Bell state is necessary (and sufficient) to perfectly discriminate a set of either three or four Bell states by LOCC. In this paper it is proved that a Bell state is also required for optimal discrimination of a family of sets of noisy Bell states by LOCC. Notably, such sets, in general, do not contain any maximally entangled state, and in specific instances, do not even contain any entangled state.

Entangled states can help in quantum state discrimination by local operations and classical communication (LOCC). For example, a Bell state is necessary (and sufficient) to perfectly discriminate a set of either three or four Bell states by LOCC. In this paper, we consider the task of LOCC discrimination of the states of noisy Bell ensembles, where a given ensemble consists of the states obtained by mixing the Bell states with an arbitrary two-qubit state with nonzero probabilities. It is proved that a Bell state is required for optimal discrimination by LOCC, even though the ensembles do not contain, in general, any maximally entangled state, and in specific instances, any entangled state.

We study information-disturbance trade-off in generalized entanglement swapping protocols wherein starting from Bell pairs (1, 2) and (3, 4), one performs an arbitrary joint measurement on (2, 3), so that (1, 4) now becomes correlated. We obtain trade-off inequalities between information gain in correlations of (1, 4) and residual information in correlations of (1, 2) and (3, 4), respectively, and we argue that information contained in correlations (information) is conserved if each inequality is an equality. We show that information is conserved for a maximally entangled measurement but is not conserved for any other complete orthogonal measurement and Bell measurement mixed with white noise. However, rather surprisingly, we find that information is conserved for rank-2 Bell diagonal measurements, although such measurements do not conserve entanglement. We also show that a separable measurement on (2, 3) can conserve information, even if, as in our example, the post-measurement states of all three pairs (1, 2), (3, 4), and (1, 4) become separable. This implies that correlations from an entangled pair can be transferred to separable pairs in nontrivial ways so that no information is lost in the process.

Quantum teleportation with a two-qubit state can be suitably characterized in terms of maximal fidelity and fidelity deviation, where the former is the maximal value of the average fidelity achievable within the standard protocol and local unitary operations and the latter is the standard deviation of fidelity over all input states. In this paper, we consider the problem of characterizing two-qubit states that are optimal for quantum teleportation for a given value of some state property. The optimal states are defined as those states that, for a given value of the state property under consideration, achieve the largest maximal fidelity and also exhibit zero fidelity deviation. We provide a complete characterization of optimal states for a given linear entropy, maximum mean value of the Bell-CHSH observable, and concurrence, respectively. We find that for a given linear entropy or Bell-CHSH violation, the largest maximal fidelity states are optimal, but for a given concurrence, the optimal states form a strict subset of the largest maximal fidelity states.

The superposition principle is fundamental to quantum theory. Yet a recent no-go theorem has proved that quantum theory forbids superposition of unknown quantum states, even with nonzero probability. The implications of this result, however, remain poorly understood so far. In this paper we show that the existence of a protocol that superposes two unknown pure states with nonzero probability (allowed to vary over input states) leads to violation of other no-go theorems. In particular, such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden not only in quantum theory but in no-signaling theories as well.

The superposition principle is fundamental to quantum theory. Yet a recent no-go theorem has proved that quantum theory forbids superposition of unknown quantum states, even with nonzero probability. The implications of this result, however, remain poorly understood so far. In this paper we show that the existence of a protocol that superposes two unknown pure states with nonzero probability (allowed to vary over input states) leads to violation of other no-go theorems. In particular, such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden not only in quantum theory but in no-signaling theories as well.

Quantum teleportation with an arbitrary two-qubit state can be appropriately characterized in terms of maximal fidelity and fidelity deviation. The former quantifies optimality of the process and is defined as the maximal average fidelity achievable within the standard protocol and local unitary strategies, whereas the latter, defined as the standard deviation of fidelity over all input states, is a measure of fidelity fluctuations. The maximal fidelity for a two-qubit state is known and is given by a simple formula that can be exactly computed, but no such formula is known for the fidelity deviation. In this paper, we derive an exact computable formula for the fidelity deviation in optimal quantum teleportation with an arbitrary state of two qubits. From this formula, we obtain the dispersion-free condition, also known as the universality condition: the condition that all input states are teleported equally well and provide a necessary and sufficient condition for a state to be both useful (maximal fidelity larger than the classical bound) and universal (zero fidelity deviation). We also show that for any given maximal fidelity, larger than the classical bound, there always exist dispersion-free or universal states and argue that such states are the most desirable ones within the set of useful states. We illustrate these results with well-known families of two-qubit states: pure entangled states, Bell-diagonal states, and subsets of X states.

Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit "quantum nonlocality without entanglement" if the states are locally indistinguishable; i.e., it is not possible to optimally distinguish the states by any sequence of local operations and classical communication. Here, we present a stronger manifestation of this kind of nonlocality in multiparty systems through the notion of local irreducibility. A set of multiparty orthogonal quantum states is defined to be locally irreducible if it is not possible to locally eliminate one or more states from the set while preserving orthogonality of the postmeasurement states. Such a set, by definition, is locally indistinguishable, but we show that the converse does not always hold. We provide the first examples of orthogonal product bases on C^{d}⊗C^{d}⊗C^{d} for d=3, 4 that are locally irreducible in all bipartitions, where the construction for d=3 achieves the minimum dimension necessary for such product states to exist. The existence of such product bases implies that local implementation of a multiparty separable measurement may require entangled resources across all bipartitions.

We characterise non-selective global projective measurements capable of increasing quantum entanglement between two particles. We show that non-selective global projective measurements are capable of increasing entanglement between two particles, in particular, entanglement of any pure non-maximally entangled state can be improved in this way (but not of any mixed state) and we provide detailed analysis for two qubits. It is then shown that Markovian open system dynamics can only approximate such measurements, but this approximation converges exponentially fast as illustrated using Araki-Zurek model. We conclude with numerical evidence that macroscopic bodies in a random pure state do not gain entanglement in a random non-selective global measurement.