The problem of sharing quantum correlations is an interesting problem in the study of quantum information theory. Silva et al. proposed the study of sharing quantum nonlocality at first. They studied the fundamental limits on nonlocality, asking whether a single pair of entangled qubits could generate a long sequence of nonlocal correlations. At the same time, the sequential scenario was also introduced first, in which Alice and Bob each have half of a pair of entangled qubit states. The first Bob measures his half and then passes his part to a second Bob who measures again and so on. Obviously, even partial preservation of entanglement in a shared state in spite of a few sequences of local operations performed by the sharing parties can be important for information processing schemes in which entanglement is utilized as a resource. Thus, the problem of sharing quantum entanglement has also been extensively investigated. Recently, Srivastava et al. proved that there exist a class of T-states whose entanglement can be shared by arbitrarily many independent observers in [ Phys. Rev. A 2022 105 062413 ]. Here, we want to find whether there are other entangled states that can be shared entanglement arbitrarily many times. In this paper, we consider the problem of sharing quantum entanglement when the initial shared state is a two-qubit entangled Werner state. The goal is to maximize the number of Bobs that can share entanglement with a single Alice. By suitably choosing the entanglement witness operator and the unsharp measurement settings by the Bobs, we prove that there exist two-qubit entangled initial shared Werner states whose entanglement can be detected by arbitrarily many sequential observers Bobs with a single Alice. Then, we also consider the special case of the Werner state, that is, the maximally entangled state as the initial shared state. In this case, its entanglement can also be witnessed arbitrarily many times, and the number of Bobs increases with the decrease of parameter.The problem of sharing quantum correlations is an interesting problem in the study of quantum information theory. Silva et al. proposed the study of sharing quantum nonlocality at first. They studied the fundamental limits on nonlocality, asking whether a single pair of entangled qubits could generate a long sequence of nonlocal correlations. At the same time, the sequential scenario was also introduced first, in which Alice and Bob each have half of a pair of entangled qubit states. The first Bob measures his half and then passes his part to a second Bob who measures again and so on. Obviously, even partial preservation of entanglement in a shared state in spite of a few sequences of local operations performed by the sharing parties can be important for information processing schemes in which entanglement is utilized as a resource. Thus, the problem of sharing quantum entanglement has also been extensively investigated. Recently, Srivastava et al. proved that there exist a class of T-states whose entanglement can be shared by arbitrarily many independent observers in [ Phys. Rev. A 2022 105 062413 ]. Here, we want to find whether there are other entangled states that can be shared entanglement arbitrarily many times. In this paper, we consider the problem of sharing quantum entanglement when the initial shared state is a two-qubit entangled Werner state. The goal is to maximize the number of Bobs that can share entanglement with a single Alice. By suitably choosing the entanglement witness operator and the unsharp measurement settings by the Bobs, we prove that there exist two-qubit entangled initial shared Werner states whose entanglement can be detected by arbitrarily many sequential observers Bobs with a single Alice. Then, we also consider the special case of the Werner state, that is, the maximally entangled state as the initial shared state. In this case, its entanglement can also be witnessed arbitrarily many times, and the number of Bobs increases with the decrease of parameter.

Acta Physica SinicaJan 1, 20230 citations

Untangling Entanglement

ScienceFeb 5, 20040 citations

Untangling Entanglement

Peter Mark Ainsworth

Foundations of PhysicsJan 5, 20073 citations

Matching upper bounds on symmetric predicates in quantum communication complexity

Daiki Suruga

In this paper, we focus on the quantum communication complexity of functions of the form $f \circ G = f(G(X_1, Y_1), \ldots, G(X_n, Y_n))$ where $f: \Bset^n \to \Bset$ is a symmetric function, $G: \Bset^j \times \Bset^k \to \Bset$ is any function and Alice (resp. Bob) is given $(X_i)_{i \in [n]}$ (resp. $(Y_i)_{i \in [n]}$ ). Recently, Chakraborty et al. [STACS 2022] showed that the quantum communication complexity of $f \circ G$ is $O(Q(f)\QCCEX(G))$ when the parties are allowed to use shared entanglement, where $Q(f)$ is the query complexity of $f$ and $\QCCEX(G)$ is the exact communication complexity of $G$ . }{In this paper, we first show that the same statement holds \emph{without both shared entanglement and shared randomness}, which generalizes their result. Based on the improved result, we next show tight upper bounds on $f \circ \mathrm{AND}_2$ for any symmetric function $f$ (where $\textrm{AND}_2 : \Bset \times \Bset \to \Bset$ denotes the 2-bit AND function) in both models: with shared entanglement and without shared entanglement. This matches the well-known lower bound by Razborov~[Izv. Math. 67(1) 145, 2003] when shared entanglement is allowed and improves Razborov's bound when shared entanglement is not allowed.In this paper, we focus on the quantum communication complexity of functions of the form $f \circ G = f(G(X_1, Y_1), \ldots, G(X_n, Y_n))$ where $f: \Bset^n \to \Bset$ is a symmetric function, $G: \Bset^j \times \Bset^k \to \Bset$ is any function and Alice (resp. Bob) is given $(X_i)_{i \in [n]}$ (resp. $(Y_i)_{i \in [n]}$). Recently, Chakraborty et al. [STACS 2022] showed that the quantum communication complexity of $f \circ G$ is $O(Q(f)\QCCEX(G))$ when the parties are allowed to use shared entanglement, where $Q(f)$ is the query complexity of $f$ and $\QCCEX(G)$ is the exact communication complexity of $G$. }{In this paper, we first show that the same statement holds \emph{without both shared entanglement and shared randomness}, which generalizes their result. Based on the improved result, we next show tight upper bounds on $f \circ \mathrm{AND}_2$ for any symmetric function $f$ (where $\textrm{AND}_2 : \Bset \times \Bset \to \Bset$ denotes the 2-bit AND function) in both models: with shared entanglement and without shared entanglement. This matches the well-known lower bound by Razborov~[Izv. Math. 67(1) 145, 2003] when shared entanglement is allowed and improves Razborov's bound when shared entanglement is not allowed.

arXiv:2301.00370Quantum Information and ComputationOct 1, 20242 citations

ENTANGLEMENT MANIPULATION

WORLD SCIENTIFIC eBooksApr 20, 20200 citations

Sequential sharing of ‘local’ entanglement under robust projective measurements

zhongyue yue zhong, Duanfeng feng Liu, Shao-Ming Fei +1 more

Abstract While previous studies on sequential quantum sharing rely on either sharp measurements for ‘non-local’ entangled states or weak measurements for ‘local’ entangled states, we bridge this gap by investigating ‘local’ entangled states under a robust projective measurement framework. We demonstrate that probabilistic projective measurements with fixed probability can enable entanglement sharing for certain ‘local’ entangled states. Furthermore, we show that by probabilistic combination of certain different projective measurement strategies, the entanglement sharing can be expanded even under strict probability constraints. Subsequently, we prove that under projective measurements with deterministic probabilities, the maximum number of observers capable of sharing entanglement for ‘local’ entangled states is explicitly derived in terms of the entanglement of the initial state. Finally, the relationship among the sharing capacity, the initial state’s entanglement and the measurement strength of projective measurements is analytically presented.Abstract While previous studies on sequential quantum sharing rely on either sharp measurements for ‘non-local’ entangled states or weak measurements for ‘local’ entangled states, we bridge this gap by investigating ‘local’ entangled states under a robust projective measurement framework. We demonstrate that probabilistic projective measurements with fixed probability can enable entanglement sharing for certain ‘local’ entangled states. Furthermore, we show that by probabilistic combination of certain different projective measurement strategies, the entanglement sharing can be expanded even under strict probability constraints. Subsequently, we prove that under projective measurements with deterministic probabilities, the maximum number of observers capable of sharing entanglement for ‘local’ entangled states is explicitly derived in terms of the entanglement of the initial state. Finally, the relationship among the sharing capacity, the initial state’s entanglement and the measurement strength of projective measurements is analytically presented.

Quantum Science and TechnologyJul 28, 20260 citations

In this paper, we focus on the quantum communication complexity of functions of the form

f \circ G = f(G(X_1, Y_1), \ldots, G(X_n, Y_n))

where $f: \Bset^n \to \Bset$ is a symmetric function, $G: \Bset^j \times \Bset^k \to \Bset$ is any function and Alice (resp. Bob) is given

(X_i)_{i \in [n]}

(resp.

(Y_i)_{i \in [n]}

). Recently, Chakraborty et al. [STACS 2022] showed that the quantum communication complexity of

f \circ G

is $O(Q(f)\QCCEX(G))$ when the parties are allowed to use shared entanglement, where

Q(f)

is the query complexity of

f

and $\QCCEX(G)$ is the exact communication complexity of

G

. }{In this paper, we first show that the same statement holds \emph{without both shared entanglement and shared randomness}, which generalizes their result. Based on the improved result, we next show tight upper bounds on

f \circ \mathrm{AND}_2

for any symmetric function

f

(where $\textrm{AND}_2 : \Bset \times \Bset \to \Bset$ denotes the 2-bit AND function) in both models: with shared entanglement and without shared entanglement. This matches the well-known lower bound by Razborov~[Izv. Math. 67(1) 145, 2003] when shared entanglement is allowed and improves Razborov's bound when shared entanglement is not allowed.