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دسته بندی:
محاسبات کوانتومی - Quantum-Computing
سال انتشار:
2022
عنوان انگلیسی مقاله:
Incompressibility of Classical Distributions
ترجمه فارسی عنوان مقاله:
تراکم ناپذیری توزیع های کلاسیک
منبع:
ieee - ieee Transactions on Information Theory;2022;68;3;10:1109/TIT:2021:3130131
نویسنده:
Anurag Anshu; Debbie Leung; Dave Touchette
چکیده انگلیسی:
In blind compression of quantum states, a sender
Alice is given a specimen of a quantum state ρ drawn from
a known ensemble (but without knowing what ρ is), and she
transmits sufficient quantum data to a receiver Bob so that
he can decode a near perfect specimen of ρ. For many such
states drawn iid from the ensemble, the asymptotically achievable
rate is the number of qubits required to be transmitted per
state. The Holevo information is a lower bound for the achievable rate, and is attained for pure state ensembles, or in the
related scenario of entanglement-assisted visible compression of
mixed states wherein Alice knows what state is drawn. In this
paper, we prove a general and robust lower bound on the
achievable rate for ensembles of classical states, which holds
even in the least demanding setting when Alice and Bob share
free entanglement and a constant per-copy error is allowed.
We apply the bound to a specific ensemble of only two states
and prove a near-maximal separation (saturating the dimension
bound in leading order) between the best achievable rate and
the Holevo information for constant error. This also implies
that the ensemble is incompressible – compression does not
reduce the communication cost by much. Since the states are
classical, the observed incompressibility is not fundamentally
quantum mechanical. We lower bound the difference between
the achievable rate and the Holevo information in terms of
quantitative limitations to clone the specimen or to distinguish
the two classical states.
Index Terms— Blind compression | classical distributions | quantum states | free entanglement | Holevo information | constant error | incompressibility
قیمت: رایگان
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