19,597 research outputs found
Identification via Quantum Channels in the Presence of Prior Correlation and Feedback
Continuing our earlier work (quant-ph/0401060), we give two alternative
proofs of the result that a noiseless qubit channel has identification capacity
2: the first is direct by a "maximal code with random extension" argument, the
second is by showing that 1 bit of entanglement (which can be generated by
transmitting 1 qubit) and negligible (quantum) communication has identification
capacity 2.
This generalises a random hashing construction of Ahlswede and Dueck: that 1
shared random bit together with negligible communication has identification
capacity 1.
We then apply these results to prove capacity formulas for various quantum
feedback channels: passive classical feedback for quantum-classical channels, a
feedback model for classical-quantum channels, and "coherent feedback" for
general channels.Comment: 19 pages. Requires Rinton-P9x6.cls. v2 has some minor errors/typoes
corrected and the claims of remark 22 toned down (proofs are not so easy
after all). v3 has references to simultaneous ID coding removed: there were
necessary changes in quant-ph/0401060. v4 (final form) has minor correction
Generic entanglement generation, quantum statistics and complementarity
A general and an arbitrarily efficient scheme for entangling the spins (or
any spin-like degree of freedom) of two independent uncorrelated identical
particles by a combination of two particle interferometry and which way
detection is formulated. It is shown that the same setup could be used to
identify the quantum statistics of the incident particles from either the sign
or the magnitude of measured spin correlations. Our setup also exhibits a
curious complementarity between particle distinguishability and the amount of
generated entanglement.Comment: To appear in Phys. Rev. Let
Quantum and Classical Message Identification via Quantum Channels
We discuss concepts of message identification in the sense of Ahlswede and
Dueck via general quantum channels, extending investigations for classical
channels, initial work for classical-quantum (cq) channels and "quantum
fingerprinting".
We show that the identification capacity of a discrete memoryless quantum
channel for classical information can be larger than that for transmission;
this is in contrast to all previously considered models, where it turns out to
equal the common randomness capacity (equals transmission capacity in our
case): in particular, for a noiseless qubit, we show the identification
capacity to be 2, while transmission and common randomness capacity are 1.
Then we turn to a natural concept of identification of quantum messages (i.e.
a notion of "fingerprint" for quantum states). This is much closer to quantum
information transmission than its classical counterpart (for one thing, the
code length grows only exponentially, compared to double exponentially for
classical identification). Indeed, we show how the problem exhibits a nice
connection to visible quantum coding. Astonishingly, for the noiseless qubit
channel this capacity turns out to be 2: in other words, one can compress two
qubits into one and this is optimal. In general however, we conjecture quantum
identification capacity to be different from classical identification capacity.Comment: 18 pages, requires Rinton-P9x6.cls. On the occasion of Alexander
Holevo's 60th birthday. Version 2 has a few theorems knocked off: Y Steinberg
has pointed out a crucial error in my statements on simultaneous ID codes.
They are all gone and replaced by a speculative remark. The central results
of the paper are all unharmed. In v3: proof of Proposition 17 corrected,
without change of its statemen
Quantum enigma machines and the locking capacity of a quantum channel
The locking effect is a phenomenon which is unique to quantum information
theory and represents one of the strongest separations between the classical
and quantum theories of information. The Fawzi-Hayden-Sen (FHS) locking
protocol harnesses this effect in a cryptographic context, whereby one party
can encode n bits into n qubits while using only a constant-size secret key.
The encoded message is then secure against any measurement that an eavesdropper
could perform in an attempt to recover the message, but the protocol does not
necessarily meet the composability requirements needed in quantum key
distribution applications. In any case, the locking effect represents an
extreme violation of Shannon's classical theorem, which states that
information-theoretic security holds in the classical case if and only if the
secret key is the same size as the message. Given this intriguing phenomenon,
it is of practical interest to study the effect in the presence of noise, which
can occur in the systems of both the legitimate receiver and the eavesdropper.
This paper formally defines the locking capacity of a quantum channel as the
maximum amount of locked information that can be reliably transmitted to a
legitimate receiver by exploiting many independent uses of a quantum channel
and an amount of secret key sublinear in the number of channel uses. We provide
general operational bounds on the locking capacity in terms of other well-known
capacities from quantum Shannon theory. We also study the important case of
bosonic channels, finding limitations on these channels' locking capacity when
coherent-state encodings are employed and particular locking protocols for
these channels that might be physically implementable.Comment: 37 page
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
Optimal superdense coding of entangled states
We present a one-shot method for preparing pure entangled states between a
sender and a receiver at a minimal cost of entanglement and quantum
communication. In the case of preparing unentangled states, an earlier paper
showed that a 2n-qubit quantum state could be communicated to a receiver by
physically transmitting only n+o(n) qubits in addition to consuming n ebits of
entanglement and some shared randomness. When the states to be prepared are
entangled, we find that there is a reduction in the number of qubits that need
to be transmitted, interpolating between no communication at all for maximally
entangled states and the earlier two-for-one result of the unentangled case,
all without the use of any shared randomness. We also present two applications
of our result: a direct proof of the achievability of the optimal superdense
coding protocol for entangled states produced by a memoryless source, and a
demonstration that the quantum identification capacity of an ebit is two
qubits.Comment: Final Version. Several technical issues clarifie
Quantum Security for the Physical Layer
The physical layer describes how communication signals are encoded and
transmitted across a channel. Physical security often requires either
restricting access to the channel or performing periodic manual inspections. In
this tutorial, we describe how the field of quantum communication offers new
techniques for securing the physical layer. We describe the use of quantum
seals as a unique way to test the integrity and authenticity of a communication
channel and to provide security for the physical layer. We present the
theoretical and physical underpinnings of quantum seals including the quantum
optical encoding used at the transmitter and the test for non-locality used at
the receiver. We describe how the envisioned quantum physical sublayer senses
tampering and how coordination with higher protocol layers allow quantum seals
to influence secure routing or tailor data management methods. We conclude by
discussing challenges in the development of quantum seals, the overlap with
existing quantum key distribution cryptographic services, and the relevance of
a quantum physical sublayer to the future of communication security.Comment: 7 pages, 6 figure
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