698 research outputs found
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
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