No-cloning of quantum steering

Abstract

Einstein-Podolsky-Rosen (EPR) steering allows two parties to verify their entanglement, even if one party's measurements are untrusted. This concept has not only provided new insights into the nature of non-local spatial correlations in quantum mechanics, but also serves as a resource for one-sided device-independent quantum information tasks. Here, we investigate how EPR steering behaves when one-half of a maximally entangled pair of qudits (multidimensional quantum systems) is cloned by a universal cloning machine. We find that EPR steering, as verified by a criterion based on the mutual information between qudits, can only be found in one of the copy subsystems but not both. We prove that this is also true for the single-system analogue of EPR steering. We find that this restriction, which we term 'no-cloning of quantum steering', elucidates the physical reason why steering can be used to secure sources and channels against cloning-based attacks when implementing quantum communication and quantum computation protocols. This has led to a range of conceptually important extensions of the concept of EPR steering and several potential applications for practical quantum information processing. See an in-depth discussion given in the review by Reid et al. 4 As articulated by Wootters and Zurek 5 and Dieks 6 in 1982, it is impossible to perfectly copy an unknown quantum state. This famous no-go theorem of quantum mechanics has significant implications in understanding nonclassical features of quantum systems and profound applications in quantum information science. Although one cannot make perfect copies of an unknown quantum state, it is possible to create imperfect copies. Bužek and Hillery 7 have shown that a universal cloning machine can produce a clone of an unknown state with high fidelity. Such a universal cloning machine has been shown to be optimal and has been extensively studied in the context of possible alternatives, extensions and use as an eavesdropping attack on the protocols of quantum cryptography. 8 Here, inspired by the no-cloning theorem and the concept of quantum steering, we ask a simple question: 'Does quantum mechanics allow quantum steering to be copied by a universal cloning machine?'. To investigate this question, we use the concept of a universal cloning machine to consider how quantum steering is cloned and shared between two copies of a qudit (a multidimensional quantum system), which itself is half of a maximally entangled pair (Figure 1a). In addition, we apply the same method of analysis to the single-system (SS) analogue of EPR

Securing quantum networking tasks with multipartite Einstein-Podolsky-Rosen steering

“…(C11)With Eqs. (C7)-(C11), the upper bound of the mutual information IAsmBsm ≤ 2 log 2 d. (C13)For the simple bipartite case N = 2, the above relation recovers the criterion used by Chiu et al[51] to show no-cloning of EPR steering. For general N ≥ 3, since the measurement operators in the Schmidt bases and those in the locally measurable bases A sm , B sm and C sm commute with each other, we have the relations Eqs.…”

Manipulation and enhancement of asymmetric steering via interference effects induced by closed-loop coupling

“…There has been an increasing interest in EPR steering since it was rigorously defined by mathematical formulation from the perspective of quantum information [7][8][9], i.e., in a network one can verify the entanglement between Alice and Bob without the requirement of trust of Bob's equipment used to perform local measurements at his node by confirming the presence of steering of Alice's system by Bob. This feature makes quantum steering substantial to various quantum information protocols which rely on entanglement by providing extra security [10], such as semi-sided device-independent quantum key distribution [11][12][13] and quantum secret sharing [14][15][16], one-way quantum computing [17], nocloning quantum teleportation [18][19][20], subchannel discrimination [21], and other related protocols.…”

Engineering asymmetric steady-state Einstein-Podolsky-Rosen steering in macroscopic hybrid systems

“…Considering the extraordinarily challenging character of the fully DI experiments, 1sDI protocols based on steering offer a more feasible approach to performing quantum secure tasks on a network where reliability or tampering of devices, dishonest observers, etc. could be an issue, e.g., 1sDI quantum key distribution [13][14][15], quantum secret sharing [16][17][18], and quantum teleportation [19][20][21].…”