1,004 research outputs found
On the communication cost of entanglement transformations
We study the amount of communication needed for two parties to transform some
given joint pure state into another one, either exactly or with some fidelity.
Specifically, we present a method to lower bound this communication cost even
when the amount of entanglement does not increase. Moreover, the bound applies
even if the initial state is supplemented with unlimited entanglement in the
form of EPR pairs, and the communication is allowed to be quantum mechanical.
We then apply the method to the determination of the communication cost of
asymptotic entanglement concentration and dilution. While concentration is
known to require no communication whatsoever, the best known protocol for
dilution, discovered by Lo and Popescu [Phys. Rev. Lett. 83(7):1459--1462,
1999], requires a number of bits to be exchanged which is of the order of the
square root of the number of EPR pairs. Here we prove a matching lower bound of
the same asymptotic order, demonstrating the optimality of the Lo-Popescu
protocol up to a constant factor and establishing the existence of a
fundamental asymmetry between the concentration and dilution tasks.
We also discuss states for which the minimal communication cost is
proportional to their entanglement, such as the states recently introduced in
the context of ``embezzling entanglement'' [W. van Dam and P. Hayden,
quant-ph/0201041].Comment: 9 pages, 1 figure. Added a reference and some further explanations.
In v3 some arguments are given in more detai
Time reversal and exchange symmetries of unitary gate capacities
Unitary gates are an interesting resource for quantum communication in part
because they are always invertible and are intrinsically bidirectional. This
paper explores these two symmetries: time-reversal and exchange of Alice and
Bob. We will present examples of unitary gates that exhibit dramatic
separations between forward and backward capacities (even when the back
communication is assisted by free entanglement) and between
entanglement-assisted and unassisted capacities, among many others. Along the
way, we will give a general time-reversal rule for relating the capacities of a
unitary gate and its inverse that will explain why previous attempts at finding
asymmetric capacities failed. Finally, we will see how the ability to erase
quantum information and destroy entanglement can be a valuable resource for
quantum communication.Comment: 17 pages. v2: improved bounds, clarified proofs. v3: published
version, added section explaining notatio
The entanglement of purification
We introduce a measure of both quantum as well as classical correlations in a
quantum state, the entanglement of purification. We show that the (regularized)
entanglement of purification is equal to the entanglement cost of creating a
state asymptotically from maximally entangled states, with negligible
communication. We prove that the classical mutual information and the quantum
mutual information divided by two are lower bounds for the regularized
entanglement of purification. We present numerical results of the entanglement
of purification for Werner states in .Comment: 12 pages RevTex, 1 figure, to appear in JMP special issue on quantum
information. v3 contains additional references, motivation, and a small
change in the figur
Quantum Reverse Shannon Theorem
Dual to the usual noisy channel coding problem, where a noisy (classical or
quantum) channel is used to simulate a noiseless one, reverse Shannon theorems
concern the use of noiseless channels to simulate noisy ones, and more
generally the use of one noisy channel to simulate another. For channels of
nonzero capacity, this simulation is always possible, but for it to be
efficient, auxiliary resources of the proper kind and amount are generally
required. In the classical case, shared randomness between sender and receiver
is a sufficient auxiliary resource, regardless of the nature of the source, but
in the quantum case the requisite auxiliary resources for efficient simulation
depend on both the channel being simulated, and the source from which the
channel inputs are coming. For tensor power sources (the quantum generalization
of classical IID sources), entanglement in the form of standard ebits
(maximally entangled pairs of qubits) is sufficient, but for general sources,
which may be arbitrarily correlated or entangled across channel inputs,
additional resources, such as entanglement-embezzling states or backward
communication, are generally needed. Combining existing and new results, we
establish the amounts of communication and auxiliary resources needed in both
the classical and quantum cases, the tradeoffs among them, and the loss of
simulation efficiency when auxiliary resources are absent or insufficient. In
particular we find a new single-letter expression for the excess forward
communication cost of coherent feedback simulations of quantum channels (i.e.
simulations in which the sender retains what would escape into the environment
in an ordinary simulation), on non-tensor-power sources in the presence of
unlimited ebits but no other auxiliary resource. Our results on tensor power
sources establish a strong converse to the entanglement-assisted capacity
theorem.Comment: 35 pages, to appear in IEEE-IT. v2 has a fixed proof of the Clueless
Eve result, a new single-letter formula for the "spread deficit", better
error scaling, and an improved strong converse. v3 and v4 each make small
improvements to the presentation and add references. v5 fixes broken
reference
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