44,810 research outputs found
Entangled Mixed States and Local Purification
Linden, Massar and Popescu have recently given an optimization argument to
show that a single two-qubit Werner state, or any other mixture of the
maximally entangled Bell states, cannot be purified by local operations and
classical communications. We generalise their result and give a simple
explanation. In particular, we show that no purification scheme using local
operations and classical communications can produce a pure singlet from any
mixed state of two spin-1/2 particles. More generally, no such scheme can
produce a maximally entangled state of any pair of finite-dimensional systems
from a generic mixed state. We also show that the Werner states belong to a
large class of states whose fidelity cannot be increased by such a scheme.Comment: 3 pages, Latex with Revtex. Small clarifications and reference adde
On entanglement-assisted classical capacity
This paper is essentially a lecture from the author's course on quantum
information theory, which is devoted to the result of C. H. Bennett, P. W.
Shor, J. A. Smolin and A. V. Thapliyal (quant-ph/0106052) concerning
entanglement-assisted classical capacity of a quantum channel. A modified proof
of this result is given and relation between entanglement-assisted and
unassisted classical capacities is discussed.Comment: 10 pages, LATE
The Parity Bit in Quantum Cryptography
An -bit string is encoded as a sequence of non-orthogonal quantum states.
The parity bit of that -bit string is described by one of two density
matrices, and , both in a Hilbert space of
dimension . In order to derive the parity bit the receiver must
distinguish between the two density matrices, e.g., in terms of optimal mutual
information. In this paper we find the measurement which provides the optimal
mutual information about the parity bit and calculate that information. We
prove that this information decreases exponentially with the length of the
string in the case where the single bit states are almost fully overlapping. We
believe this result will be useful in proving the ultimate security of quantum
crytography in the presence of noise.Comment: 19 pages, RevTe
Negative entropy and information in quantum mechanics
A framework for a quantum mechanical information theory is introduced that is
based entirely on density operators, and gives rise to a unified description of
classical correlation and quantum entanglement. Unlike in classical (Shannon)
information theory, quantum (von Neumann) conditional entropies can be negative
when considering quantum entangled systems, a fact related to quantum
non-separability. The possibility that negative (virtual) information can be
carried by entangled particles suggests a consistent interpretation of quantum
informational processes.Comment: 4 pages RevTeX, 2 figures. Expanded discussion of quantum
teleportation and superdense coding, and minor corrections. To appear in
Phys. Rev. Let
Simple Proof of Security of the BB84 Quantum Key Distribution Protocol
We prove the security of the 1984 protocol of Bennett and Brassard (BB84) for
quantum key distribution. We first give a key distribution protocol based on
entanglement purification, which can be proven secure using methods from Lo and
Chau's proof of security for a similar protocol. We then show that the security
of this protocol implies the security of BB84. The entanglement-purification
based protocol uses Calderbank-Shor-Steane (CSS) codes, and properties of these
codes are used to remove the use of quantum computation from the Lo-Chau
protocol.Comment: 5 pages, Latex, minor changes to improve clarity and fix typo
A Universal Two--Bit Gate for Quantum Computation
We prove the existence of a class of two--input, two--output gates any one of
which is universal for quantum computation. This is done by explicitly
constructing the three--bit gate introduced by Deutsch [Proc.~R.~Soc.~London.~A
{\bf 425}, 73 (1989)] as a network consisting of replicas of a single two--bit
gate.Comment: 3 pages, RevTeX, two figures in a uuencoded fil
Quantum cryptography protocols robust against photon number splitting attacks for weak laser pulses implementations
We introduce a new class of quantum quantum key distribution protocols,
tailored to be robust against photon number splitting (PNS) attacks. We study
one of these protocols, which differs from the BB84 only in the classical
sifting procedure. This protocol is provably better than BB84 against PNS
attacks at zero error.Comment: 4 pages, 2 figure
Shadow Tomography of Quantum States
We introduce the problem of *shadow tomography*: given an unknown
-dimensional quantum mixed state , as well as known two-outcome
measurements , estimate the probability that
accepts , to within additive error , for each of the
measurements. How many copies of are needed to achieve this, with high
probability? Surprisingly, we give a procedure that solves the problem by
measuring only copies. This means, for example, that we can learn the behavior of an
arbitrary -qubit state, on all accepting/rejecting circuits of some fixed
polynomial size, by measuring only copies of the state.
This resolves an open problem of the author, which arose from his work on
private-key quantum money schemes, but which also has applications to quantum
copy-protected software, quantum advice, and quantum one-way communication.
Recently, building on this work, Brand\~ao et al. have given a different
approach to shadow tomography using semidefinite programming, which achieves a
savings in computation time.Comment: 29 pages, extended abstract appeared in Proceedings of STOC'2018,
revised to give slightly better upper bound (1/eps^4 rather than 1/eps^5) and
lower bounds with explicit dependence on the dimension
The trumping relation and the structure of the bipartite entangled states
The majorization relation has been shown to be useful in classifying which
transformations of jointly held quantum states are possible using local
operations and classical communication. In some cases, a direct transformation
between two states is not possible, but it becomes possible in the presence of
another state (known as a catalyst); this situation is described mathematically
by the trumping relation, an extension of majorization. The structure of the
trumping relation is not nearly as well understood as that of majorization. We
give an introduction to this subject and derive some new results. Most notably,
we show that the dimension of the required catalyst is in general unbounded;
there is no integer such that it suffices to consider catalysts of
dimension or less in determining which states can be catalyzed into a given
state. We also show that almost all bipartite entangled states are potentially
useful as catalysts.Comment: 7 pages, RevTe
Quantum privacy amplification and the security of quantum cryptography over noisy channels
Existing quantum cryptographic schemes are not, as they stand, operable in
the presence of noise on the quantum communication channel. Although they
become operable if they are supplemented by classical privacy-amplification
techniques, the resulting schemes are difficult to analyse and have not been
proved secure. We introduce the concept of quantum privacy amplification and a
cryptographic scheme incorporating it which is provably secure over a noisy
channel. The scheme uses an `entanglement purification' procedure which,
because it requires only a few quantum Controlled-Not and single-qubit
operations, could be implemented using technology that is currently being
developed. The scheme allows an arbitrarily small bound to be placed on the
information that any eavesdropper may extract from the encrypted message.Comment: 13 pages, Latex including 2 postcript files included using psfig
macro
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