1,417 research outputs found
The information-theoretic costs of simulating quantum measurements
Winters measurement compression theorem stands as one of the most penetrating insights of quantum information theory. In addition to making an original and profound statement about measurement in quantum theory, it also underlies several other general protocols used for entanglement distillation and local purity distillation. The theorem provides for an asymptotic decomposition of any quantum measurement into noise and information. This decomposition leads to an optimal protocol for having a sender simulate many independent instances of a quantum measurement and send the measurement outcomes to a receiver, using as little communication as possible. The protocol assumes that the parties have access to some amount of common randomness, which is a strictly weaker resource than classical communication. In this review, we provide a second look at Winters measurement compression theorem, detailing the information processing task, giving examples for understanding it, reviewing Winters achievability proof, and detailing a new approach to its single-letter converse theorem. We prove an extension of the theorem to the case in which the sender is not required to receive the outcomes of the simulated measurement. The total cost of common randomness and classical communication can be lower for such a non-feedback simulation, and we prove a single-letter converse theorem demonstrating optimality. We then review the Devetak-Winter theorem on classical data compression with quantum side information, providing new proofs of its achievability and converse parts. From there, we outline a new protocol that we call measurement compression with quantum side information, announced previously by two of us in our work on triple trade-offs in quantum Shannon theory. This protocol has several applications, including its part in the classically-assisted state redistribution protocol, which is the most general protocol on the static side of the quantum information theory tree, and its role in reducing the classical communication cost in a task known as local purity distillation. We also outline a connection between measurement compression with quantum side information and recent work on entropic uncertainty relations in the presence of quantum memory. Finally, we prove a single-letter theorem characterizing measurement compression with quantum side information when the sender is not required to obtain the measurement outcome. © 2012 IOP Publishing Ltd
Classical communication cost of quantum steering
Quantum steering is observed when performing appropriate local measurements
on an entangled state. Here we discuss the possibility of simulating
classically this effect, using classical communication instead of entanglement.
We show that infinite communication is necessary for exactly simulating
steering for any pure entangled state, as well as for a class of mixed
entangled states. Moreover, we discuss the communication cost of steering for
general entangled states, as well as approximate simulation. Our findings
reveal striking differences between Bell nonlocality and steering, and provide
a natural way of measuring the strength of the latter.Comment: 7 pages, 1 figure. See also arXiv:1603.xxxxx for related work by S.
Nagy and T. V\'ertes
Identifying the Information Gain of a Quantum Measurement
We show that quantum-to-classical channels, i.e., quantum measurements, can
be asymptotically simulated by an amount of classical communication equal to
the quantum mutual information of the measurement, if sufficient shared
randomness is available. This result generalizes Winter's measurement
compression theorem for fixed independent and identically distributed inputs
[Winter, CMP 244 (157), 2004] to arbitrary inputs, and more importantly, it
identifies the quantum mutual information of a measurement as the information
gained by performing it, independent of the input state on which it is
performed. Our result is a generalization of the classical reverse Shannon
theorem to quantum-to-classical channels. In this sense, it can be seen as a
quantum reverse Shannon theorem for quantum-to-classical channels, but with the
entanglement assistance and quantum communication replaced by shared randomness
and classical communication, respectively. The proof is based on a novel
one-shot state merging protocol for "classically coherent states" as well as
the post-selection technique for quantum channels, and it uses techniques
developed for the quantum reverse Shannon theorem [Berta et al., CMP 306 (579),
2011].Comment: v2: new result about non-feedback measurement simulation, 45 pages, 4
figure
Concrete resource analysis of the quantum linear system algorithm used to compute the electromagnetic scattering cross section of a 2D target
We provide a detailed estimate for the logical resource requirements of the
quantum linear system algorithm (QLSA) [Phys. Rev. Lett. 103, 150502 (2009)]
including the recently described elaborations [Phys. Rev. Lett. 110, 250504
(2013)]. Our resource estimates are based on the standard quantum-circuit model
of quantum computation; they comprise circuit width, circuit depth, the number
of qubits and ancilla qubits employed, and the overall number of elementary
quantum gate operations as well as more specific gate counts for each
elementary fault-tolerant gate from the standard set {X, Y, Z, H, S, T, CNOT}.
To perform these estimates, we used an approach that combines manual analysis
with automated estimates generated via the Quipper quantum programming language
and compiler. Our estimates pertain to the example problem size N=332,020,680
beyond which, according to a crude big-O complexity comparison, QLSA is
expected to run faster than the best known classical linear-system solving
algorithm. For this problem size, a desired calculation accuracy 0.01 requires
an approximate circuit width 340 and circuit depth of order if oracle
costs are excluded, and a circuit width and depth of order and
, respectively, if oracle costs are included, indicating that the
commonly ignored oracle resources are considerable. In addition to providing
detailed logical resource estimates, it is also the purpose of this paper to
demonstrate explicitly how these impressively large numbers arise with an
actual circuit implementation of a quantum algorithm. While our estimates may
prove to be conservative as more efficient advanced quantum-computation
techniques are developed, they nevertheless provide a valid baseline for
research targeting a reduction of the resource requirements, implying that a
reduction by many orders of magnitude is necessary for the algorithm to become
practical.Comment: 37 pages, 40 figure
Strong converse theorems using R\'enyi entropies
We use a R\'enyi entropy method to prove strong converse theorems for certain
information-theoretic tasks which involve local operations and quantum or
classical communication between two parties. These include state
redistribution, coherent state merging, quantum state splitting, measurement
compression with quantum side information, randomness extraction against
quantum side information, and data compression with quantum side information.
The method we employ in proving these results extends ideas developed by Sharma
[arXiv:1404.5940], which he used to give a new proof of the strong converse
theorem for state merging. For state redistribution, we prove the strong
converse property for the boundary of the entire achievable rate region in the
-plane, where and denote the entanglement cost and quantum
communication cost, respectively. In the case of measurement compression with
quantum side information, we prove a strong converse theorem for the classical
communication cost, which is a new result extending the previously known weak
converse. For the remaining tasks, we provide new proofs for strong converse
theorems previously established using smooth entropies. For each task, we
obtain the strong converse theorem from explicit bounds on the figure of merit
of the task in terms of a R\'enyi generalization of the optimal rate. Hence, we
identify candidates for the strong converse exponents for each task discussed
in this paper. To prove our results, we establish various new entropic
inequalities, which might be of independent interest. These involve conditional
entropies and mutual information derived from the sandwiched R\'enyi
divergence. In particular, we obtain novel bounds relating these quantities, as
well as the R\'enyi conditional mutual information, to the fidelity of two
quantum states.Comment: 40 pages, 5 figures; v4: Accepted for publication in Journal of
Mathematical Physic
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