Résultats de recherche pour « Separable Operations »

In this paper, we study the distinguishability of multipartite quantum states by separable operations. We first present a necessary and sufficient condition for a finite set of orthogonal quantum states to be distinguishable by separable operations. An analytical version of this condition is derived for the case of(D-1) pure states, whereDis the total dimension of the state space under consideration. A number of interesting consequences of this result are then carefully investigated. Remarkably, we show there exists a large class of 2 otimes 2 separable operations not being realizable by local operations and classical communication. Before our work, only a class of 3 otimes 3 nonlocal separable operations was known [Bennett , Phys. Rev. A 59, 1070 (1999)]. We also show that any basis of the orthogonal complement of a multipartite pure state is indistinguishable by separable operations if and only if this state cannot be a superposition of one or two orthogonal product states, i.e., has an orthogonal Schmidt number not less than three, thus generalize the recent work about indistinguishable bipartite subspaces [Watrous, Phys. Rev. Lett. 95, 080505 (2005)]. Notably, we obtain an explicit construction of indistinguishable subspaces of dimension 7 (or 6) by considering a composite quantum system consisting of two qutrits (resp., three qubits), which is slightly better than the previously known indistinguishable bipartite subspace with dimension 8.

We show that the possible ensembles produced when a separable operation acts on a single pure bipartite entangled state are completely characterized by a majorization condition, a collection of inequalities for Schmidt coefficients, which is identical to that already known for the particular case of local operations and classical communication (LOCC). As a consequence, various known results for LOCC, including some involving monotonicity of entanglement, can be extended to the class of all separable operations.

The weird phenomenon of "quantum nonlocality without entanglement" means that local quantum operations assisted by classical communication constitute a proper subset of the class of separable quantum operations. Despite considerable recent advances, little is known to what extent the class of separable operations differs from local quantum operations and classical communication. In this Letter we show that separable operations are generally stronger than local quantum operations and classical communication when distilling a mixed state into a pure entangled state and thus confirm the existence of entanglement monotones that can increase under separable operations. Our finding can also be interpreted as confirming the ability of separable operations to enhance the entanglement of mixed states relative to certain measures, a sensible but important fact that has never been rigorously proven before.

We study conditions for the deterministic transformation $\ensuremath{\mid}\ensuremath{\psi}⟩\ensuremath{\rightarrow}\ensuremath{\mid}\ensuremath{\phi}⟩$ of a bipartite entangled state by a separable operation. If the separable operation is a local operation with classical communication (LOCC), Nielsen's majorization theorem provides necessary and sufficient conditions. For the general case, we derive a necessary condition in terms of products of Schmidt coefficients, which is equivalent to the Nielsen condition when either of the two factor spaces is of dimension 2, but is otherwise weaker. One implication is that no separable operation can reverse a deterministic map produced by another separable operation, if one excludes the case where the Schmidt coefficients of $\ensuremath{\mid}\ensuremath{\psi}⟩$ are the same as those of $\ensuremath{\mid}\ensuremath{\phi}⟩$. The question of sufficient conditions in the general separable case remains open. When the Schmidt coefficients of $\ensuremath{\mid}\ensuremath{\psi}⟩$ are the same as those of $\ensuremath{\mid}\ensuremath{\phi}⟩$, we show that the Kraus operators of the separable transformation restricted to the supports of $\ensuremath{\mid}\ensuremath{\psi}⟩$ on the factor spaces are proportional to unitaries. When that proportionality holds and the factor spaces have equal dimension, we find conditions for the deterministic transformation of a collection of several full Schmidt rank pure states $\ensuremath{\mid}{\ensuremath{\psi}}_{j}⟩$ to pure states $\ensuremath{\mid}{\ensuremath{\phi}}_{j}⟩$.

We study how multipartite entanglement evolves under the paradigm of separable operations, which include the local operations and classical communication as a special case. We prove that the average ``decay'' of entanglement induced by a separable operation is measure independent (among SL-invariant ones) and state independent: The ratio between the average output entanglement and the initial entanglement is solely a function of the separable operation, regardless of the input state and of the SL-invariant entanglement measure being used. We discuss the ``disentangling power'' of a quantum channel and show that it exhibits a similar state invariance as the average entanglement decay ratio. Our Rapid Communication significantly extends the bipartite results of Horodecki and Horodecki, Quantum Inf. Comput. 10, 901 (2010), Konrad et al., Nat. Phys. 4, 99 (2008), and Tiersch et al., Phys. Rev. Lett. 101, 170502 (2008) as well as the multipartite one of Gour, Phys. Rev. Lett. 105, 190504 (2010), all of the previous work being restricted to one-sided or particular noise models.

In the first part of this Dissertation, I study the differences between LOCC (local operations and classical communication) and the more general class of separable operations. I show that the two classes coincide for the case of pure bipartite state input, and derive a set of important consequences. Using similar techniques I also generalize the no-cloning theorem when restricted to separable operations and show that cloning becomes much more restrictive, by providing necessary (and sometimes sufficient) conditions. In the second part I investigate graph states and graph codes with carrier qudits of arbitrary dimensionality, and extend the notion of stabilizer to any dimension, not necessarily prime. I further study how and where information is located in the various subsets of the qudit carriers of arbitrary additive graph codes, and provide efficient techniques that can be used in deciding what types of information a subset contains.

Bit commitment is a fundamental cryptographic primitive and a cornerstone for numerous two-party cryptographic protocols, including zero-knowledge proofs. However, it has been proven that unconditionally secure bit commitment, both classical and quantum, is impossible. In this work, we demonstrate that imposing a restriction on the committing party to perform only separable operations enables secure quantum bit-commitment schemes. Specifically, we prove that in any perfectly hiding bit-commitment protocol, an honestly committing party limited to separable operations will be detected with high probability if they attempt to alter their commitment. To illustrate our findings, we present an example protocol.

We give a conceptually simple necessary condition such that a separable quantum operation can be implemented by local operations on subsystems and classical communication between parties (LOCC), a condition which follows from a novel approach to understanding LOCC. This necessary condition applies to all LOCC protocols involving any number of parties and any finite number of rounds of communication. Furthermore, it demonstrates an extremely strong difference between separable operations and LOCC, in that there exist examples of the former for which the condition is extensively violated. More precisely, the violation by separable operations of our necessary condition for LOCC grows without limit as the number of parties increases.

In the pursuit of efficient vision architectures, substantial efforts have been devoted to optimizing operator efficiency. Depth-wise separable operators, such as DWConv, are found cheap in both FLOPs and parameters. As a result, they are increasingly incorporated into efficient backbones, trading for deeper and wider architectures to enhance performance. However, separable operators are not really fast on devices due to the discontinuous memory access requirements. In this paper, we propose FreeNets, a family of simple and efficient backbones that free the separable operation to further accelerate the running speed. We introduce sparse sampling mixers (S2-Mixer) to supersede existing separable token mixers. The S2-Mixer samples multiple segments of partially continuous signals across spatial and channel dimensions for convolutional processing, achieving extremely fast on-device speed. The sparse sampling also enables S2-Mixer to capture long-range pixel relationships from dynamic receptive fields. Furthermore, we introduce a Shift Feed-Forward Network (ShiftFFN) as a faster alternative to existing channel mixers. It utilizes a shift neck architecture that aggregates global information to shift features, enabling faster channel mixing while incorporating global pixel information. Extensive experiments demonstrate that FreeNet offers a superior accuracy-efficiency tradeoff compared to the latest efficient models. On ImageNet-1k, FreeNet-S2 outperforms the StarNet-S4 by 0.4% in top-1 accuracy, while running around 40% faster on desktop GPU and 15% faster on Mobile GPU.