149 research outputs found
Private states, quantum data hiding and the swapping of perfect secrecy
We derive a formal connection between quantum data hiding and quantum
privacy, confirming the intuition behind the construction of bound entangled
states from which secret bits can be extracted. We present three main results.
First, we show how to simplify the class of private states and related states
via reversible local operation and one-way communication. Second, we obtain a
bound on the one-way distillable entanglement of private states in terms of
restricted relative entropy measures, which is tight in many cases and shows
that protocols for one-way distillation of key out of states with low
distillable entanglement lead to the distillation of data hiding states. Third,
we consider the problem of extending the distance of quantum key distribution
with help of intermediate stations. In analogy to the quantum repeater, this
paradigm has been called the quantum key repeater. We show that when extending
private states with one-way communication, the resulting rate is bounded by the
one-way distillable entanglement. In order to swap perfect secrecy it is thus
essentially optimal to use entanglement swapping.Comment: v3 published version, some details of the main proofs have been moved
to the appendix, 21 pages. v2 claims changed from LOCC to one-way LOCC in the
process of correcting a mistake found in v1 (in proof of Lemma 3). v1: 15
pages, 9 figure
Entanglement distillation from Greenberger-Horne-Zeilinger shares
We study the problem of converting a product of Greenberger-Horne-Zeilinger
(GHZ) states shared by subsets of several parties in an arbitrary way into GHZ
states shared by every party. Our result is that if SLOCC transformations are
allowed, then the best asymptotic rate is the minimum of bipartite log-ranks of
the initial state. This generalizes a result by Strassen on the asymptotic
subrank of the matrix multiplication tensor.Comment: 8 pages, v2: minor correction
Distillation of Greenberger-Horne-Zeilinger states by combinatorial methods
We prove a lower bound on the rate of Greenberger-Horne-Zeilinger states
distillable from pure multipartite states by local operations and classical
communication (LOCC). Our proof is based on a modification of a combinatorial
argument used in the fast matrix multiplication algorithm of Coppersmith and
Winograd. Previous use of methods from algebraic complexity in quantum
information theory concerned transformations with stochastic local operations
and classical operation (SLOCC), resulting in an asymptotically vanishing
success probability. In contrast, our new protocol works with asymptotically
vanishing error.Comment: 26 pages, 2 figures; v2: updated to match published versio
Uncertainty, Monogamy, and Locking of Quantum Correlations
Squashed entanglement and entanglement of purification are quantum mechanical
correlation measures and defined as certain minimisations of entropic
quantities. We present the first non-trivial calculations of both quantities.
Our results lead to the conclusion that both measures can drop by an arbitrary
amount when only a single qubit of a local system is lost. This property is
known as "locking" and has previously been observed for other correlation
measures, such as the accessible information, entanglement cost and the
logarithmic negativity.
In the case of squashed entanglement, the results are obtained with the help
of an inequality that can be understood as a quantum channel analogue of
well-known entropic uncertainty relations. This inequality may prove a useful
tool in quantum information theory.
The regularised entanglement of purification is known to equal the
entanglement needed to prepare a many copies of quantum state by local
operations and a sublinear amount of communication. Here, monogamy of quantum
entanglement (i.e., the impossibility of a system being maximally entangled
with two others at the same time) leads to an exact calculation for all quantum
states that are supported either on the symmetric or on the antisymmetric
subspace of a dxd-dimensional system.Comment: 7 pages revtex4, no figures. v2 has improved presentation and a
couple of references adde
Quantum Anonymous Transmissions
We consider the problem of hiding sender and receiver of classical and
quantum bits (qubits), even if all physical transmissions can be monitored. We
present a quantum protocol for sending and receiving classical bits
anonymously, which is completely traceless: it successfully prevents later
reconstruction of the sender. We show that this is not possible classically. It
appears that entangled quantum states are uniquely suited for traceless
anonymous transmissions. We then extend this protocol to send and receive
qubits anonymously. In the process we introduce a new primitive called
anonymous entanglement, which may be useful in other contexts as well.Comment: 18 pages, LaTeX. Substantially updated version. To appear at
ASIACRYPT '0
Asymptotic entanglement transformation between W and GHZ states
We investigate entanglement transformations with stochastic local operations
and classical communication (SLOCC) in an asymptotic setting using the concepts
of degeneration and border rank of tensors from algebraic complexity theory.
Results well-known in that field imply that GHZ states can be transformed into
W states at rate 1 for any number of parties. As a generalization, we find that
the asymptotic conversion rate from GHZ states to Dicke states is bounded as
the number of subsystems increase and the number of excitations is fixed. By
generalizing constructions of Coppersmith and Winograd and by using monotones
introduced by Strassen we also compute the conversion rate from W to GHZ
states.Comment: 11 page
Smooth Entropy Bounds on One-Shot Quantum State Redistribution
In quantum state redistribution as introduced in [Luo and Devetak (2009)] and
[Devetak and Yard (2008)], there are four systems of interest: the system
held by Alice, the system held by Bob, the system that is to be
transmitted from Alice to Bob, and the system that holds a purification of
the state in the registers. We give upper and lower bounds on the amount
of quantum communication and entanglement required to perform the task of
quantum state redistribution in a one-shot setting. Our bounds are in terms of
the smooth conditional min- and max-entropy, and the smooth max-information.
The protocol for the upper bound has a clear structure, building on the work
[Oppenheim (2008)]: it decomposes the quantum state redistribution task into
two simpler quantum state merging tasks by introducing a coherent relay. In the
independent and identical (iid) asymptotic limit our bounds for the quantum
communication cost converge to the quantum conditional mutual information
, and our bounds for the total cost converge to the conditional
entropy . This yields an alternative proof of optimality of these rates
for quantum state redistribution in the iid asymptotic limit. In particular, we
obtain a strong converse for quantum state redistribution, which even holds
when allowing for feedback.Comment: v3: 29 pages, 1 figure, extended strong converse discussio
Post-selection technique for quantum channels with applications to quantum cryptography
We propose a general method for studying properties of quantum channels
acting on an n-partite system, whose action is invariant under permutations of
the subsystems. Our main result is that, in order to prove that a certain
property holds for any arbitrary input, it is sufficient to consider the
special case where the input is a particular de Finetti-type state, i.e., a
state which consists of n identical and independent copies of an (unknown)
state on a single subsystem. A similar statement holds for more general
channels which are covariant with respect to the action of an arbitrary finite
or locally compact group.
Our technique can be applied to the analysis of information-theoretic
problems. For example, in quantum cryptography, we get a simple proof for the
fact that security of a discrete-variable quantum key distribution protocol
against collective attacks implies security of the protocol against the most
general attacks. The resulting security bounds are tighter than previously
known bounds obtained by proofs relying on the exponential de Finetti theorem
[Renner, Nature Physics 3,645(2007)].Comment: 3.5 page
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