561 research outputs found
Frozen the -norm of coherence under strictly incoherent operations
Quantum coherence as an important physical resource plays the key role in
implementing various quantum tasks, whereas quantum coherence is often
deteriorated due to the system-environment interacting. We analyse under which
dynamical conditions the -norm of coherence is unaffected for an initial
coherent state in a strictly incoherent operation (SIO). Based on this
analysis, we give a complete classification of coherent states from operational
coherence theory. This may provide an insightful physical interpretation for
frozen phenomena of quantum coherence.Comment: 11 pages, 34 reference
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
The coherent measurement cost of coherence distillation
Quantum coherence is an indispensable resource for quantum technological
applications. It is known to be distillable from a noisy form using operations
that cannot create coherence. However, distillation exacts a hidden coherent
measurement cost, whose extent has not previously been estimated. Here we show
that this cost (quantified by an equivalent number of Hadamard measurements) is
related to what we call the irretrievable coherence: the difference between the
coherence of formation and the distillable coherence. We conjecture (and make
partial progress towards proving) that when distilling from many copies of a
given noisy coherent state, the coherent measurement cost scales extensively in
the number of copies, at an asymptotic rate exactly equalling the input's
irretrievable coherence. This cost applies to any application whereof coherence
distillation is an incidental outcome (e.g. incoherent randomness extraction),
but the implications are more dramatic if pure coherence is the only desired
outcome: the measurement cost may often be higher than the distilled yield, in
which case coherence should rather be prepared afresh than distilled from a
noisy input.Comment: 24+5 pages, 1 figur
Tight constraints on probabilistic convertibility of quantum states
We develop two general approaches to characterising the manipulation of
quantum states by means of probabilistic protocols constrained by the
limitations of some quantum resource theory.
First, we give a general necessary condition for the existence of a physical
transformation between quantum states, obtained using a recently introduced
resource monotone based on the Hilbert projective metric. In all affine quantum
resource theories (e.g. coherence, asymmetry, imaginarity) as well as in
entanglement distillation, we show that the monotone provides a necessary and
sufficient condition for one-shot resource convertibility under
resource-non-generating operations, and hence no better restrictions on all
probabilistic protocols are possible. We use the monotone to establish improved
bounds on the performance of both one-shot and many-copy probabilistic resource
distillation protocols.
Complementing this approach, we introduce a general method for bounding
achievable probabilities in resource transformations under
resource-non-generating maps through a family of convex optimisation problems.
We show it to tightly characterise single-shot probabilistic distillation in
broad types of resource theories, allowing an exact analysis of the trade-offs
between the probabilities and errors in distilling maximally resourceful
states. We demonstrate the usefulness of both of our approaches in the study of
quantum entanglement distillation.Comment: 46 pages, 3 figures. Technical companion paper to Phys. Rev. Lett.
128, 110505 (2022) [arXiv:2109.04481]; contains mostly content that was split
off from arXiv:2109.04481v1, plus a lot of clarifications, extensions, and
additional examples. v3: Accepted versio
Exact solution for the quantum and private capacities of bosonic dephasing channels
The capacities of noisy quantum channels capture the ultimate rates of
information transmission across quantum communication lines, and the quantum
capacity plays a key role in determining the overhead of fault-tolerant quantum
computation platforms. In the case of bosonic systems, central to many
applications, no closed formulas for these capacities were known for bosonic
dephasing channels, a key class of non-Gaussian channels modelling, e.g., noise
affecting superconducting circuits or fiber-optic communication channels. Here
we provide the first exact calculation of the quantum, private, two-way
assisted quantum, and secret-key agreement capacities of all bosonic dephasing
channels. We prove that that they are equal to the relative entropy of the
distribution underlying the channel to the uniform distribution. Our result
solves a problem that has been open for over a decade, having been posed
originally by [Jiang & Chen, Quantum and Nonlinear Optics 244, 2010].Comment: 10+20 pages, 6 figures. v2 is close to the published versio
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