One-shot rates for entanglement manipulation under non-entangling maps

We obtain expressions for the optimal rates of one- shot entanglement manipulation under operations which generate a negligible amount of entanglement. As the optimal rates for entanglement distillation and dilution in this paradigm, we obtain the max- and min-relative entropies of entanglement, the two logarithmic robustnesses of entanglement, and smoothed versions thereof. This gives a new operational meaning to these entanglement measures. Moreover, by considering the limit of many identical copies of the shared entangled state, we partially recover the recently found reversibility of entanglement manipu- lation under the class of operations which asymptotically do not generate entanglement.Comment: 7 pages; no figure

Distillable entanglement under dually non-entangling operations

Computing the exact rate at which entanglement can be distilled from noisy quantum states is one of the longest-standing questions in quantum information. We give an exact solution for entanglement distillation under the set of dually non-entangling (DNE) operations -- a relaxation of the typically considered local operations and classical communication, comprising all channels which preserve the sets of separable states and measurements. We show that the DNE distillable entanglement coincides with a modified version of the regularised relative entropy of entanglement in which the arguments are measured with a separable measurement. Ours is only the second known regularised formula for the distillable entanglement under any class of free operations in entanglement theory, after that given by Devetak and Winter for one-way LOCCs. An immediate consequence of our finding is that, under DNE, entanglement can be distilled from any entangled state. As our second main result, we construct a general upper bound on the DNE distillable entanglement, using which we prove that the separably measured relative entropy of entanglement can be strictly smaller than the regularisation of the standard relative entropy of entanglement. This solves an open problem in [Li/Winter, CMP 326, 63 (2014)].Comment: 7+26 page

Reversibility of quantum resources through probabilistic protocols

Among the most fundamental questions in the manipulation of quantum resources such as entanglement is the possibility of reversibly transforming all resource states. The most important consequence of this would be the identification of a unique entropic resource measure that exactly quantifies the limits of achievable transformation rates. Remarkably, previous results claimed that such asymptotic reversibility holds true in very general settings; however, recently those findings have been found to be incomplete, casting doubt on the conjecture. Here we show that it is indeed possible to reversibly interconvert all states in general quantum resource theories, as long as one allows protocols that may only succeed probabilistically. Although such transformations have some chance of failure, we show that their success probability can be ensured to be bounded away from zero, even in the asymptotic limit of infinitely many manipulated copies. As in previously conjectured approaches, the achievability here is realised through operations that are asymptotically resource non-generating. Our methods are based on connecting the transformation rates under probabilistic protocols with strong converse rates for deterministic transformations. We strengthen this connection into an exact equivalence in the case of entanglement distillation.Comment: 6+10 page

No second law of entanglement manipulation after all

We prove that the theory of entanglement manipulation is asymptotically irreversible under all non-entangling operations, showing from first principles that reversible entanglement transformations require the generation of entanglement in the process. Entanglement is thus shown to be the first example of a quantum resource that does not become reversible under the maximal set of free operations, that is, under all resource non-generating maps. Our result stands in stark contrast with the reversibility of quantum and classical thermodynamics, and implies that no direct counterpart to the second law of thermodynamics can be established for entanglement -- in other words, there exists no unique measure of entanglement governing all axiomatically possible state-to-state transformations. This completes the solution of a long-standing open problem [Problem 20 in arXiv:quant-ph/0504166]. We strengthen the result further to show that reversible entanglement manipulation requires the creation of exponentially large amounts of entanglement according to monotones such as the negativity. Our findings can also be extended to the setting of point-to-point quantum communication, where we show that there exist channels whose parallel simulation entanglement cost exceeds their quantum capacity, even under the most general quantum processes that preserve entanglement-breaking channels. The main technical tool we introduce is the tempered logarithmic negativity, a single-letter lower bound on the entanglement cost that can be efficiently computed via a semi-definite program.Comment: 16+30 pages, 3 figures. v2: minor clarification

Demonstration of Entanglement of Electrostatically Coupled Singlet-Triplet Qubits

Quantum computers have the potential to solve certain interesting problems significantly faster than classical computers. To exploit the power of a quantum computation it is necessary to perform inter-qubit operations and generate entangled states. Spin qubits are a promising candidate for implementing a quantum processor due to their potential for scalability and miniaturization. However, their weak interactions with the environment, which leads to their long coherence times, makes inter-qubit operations challenging. We perform a controlled two-qubit operation between singlet-triplet qubits using a dynamically decoupled sequence that maintains the two-qubit coupling while decoupling each qubit from its fluctuating environment. Using state tomography we measure the full density matrix of the system and determine the concurrence and the fidelity of the generated state, providing proof of entanglement

General theory of environment-assisted entanglement distillation

We evaluate the one-shot entanglement of assistance for an arbitrary bipartite state. This yields another interesting result, namely a characterization of the one-shot distillable entanglement of a bipartite pure state. This result is shown to be stronger than that obtained by specializing the one-shot hashing bound to pure states. Finally, we show how the one-shot result yields the operational interpretation of the asymptotic entanglement of assistance proved in [Smolin et al., Phys. Rev. A 72, 052317 (2005)].Comment: 23 pages, one column, final published versio