45 research outputs found
Time-optimal Hamiltonian simulation and gate synthesis using homogeneous local unitaries
Motivated by experimental limitations commonly met in the design of solid
state quantum computers, we study the problems of non-local Hamiltonian
simulation and non-local gate synthesis when only homogeneous local unitaries
are performed in order to tailor the available interaction. Homogeneous (i.e.
identical for all subsystems) local manipulation implies a more refined
classification of interaction Hamiltonians than the inhomogeneous case, as well
as the loss of universality in Hamiltonian simulation. For the case of
symmetric two-qubit interactions, we provide time-optimal protocols for both
Hamiltonian simulation and gate synthesis.Comment: 7 page
Full security of quantum key distribution from no-signaling constraints
We analyze a cryptographic protocol for generating a distributed secret key
from correlations that violate a Bell inequality by a sufficient amount, and
prove its security against eavesdroppers, constrained only by the assumption
that any information accessible to them must be compatible with the
non-signaling principle. The claim holds with respect to the state-of-the-art
security definition used in cryptography, known as universally-composable
security. The non-signaling assumption only refers to the statistics of
measurement outcomes depending on the choices of measurements; hence security
is independent of the internal workings of the devices --- they do not even
need to follow the laws of quantum theory. This is relevant for practice as a
correct and complete modeling of realistic devices is generally impossible. The
techniques developed are general and can be applied to other Bell
inequality-based protocols. In particular, we provide a scheme for estimating
Bell-inequality violations when the samples are not independent and identically
distributed.Comment: 15 pages, 2 figur
Multipartite Bound Information exists and can be activated
We prove the conjectured existence of Bound Information, a classical analog
of bound entanglement, in the multipartite scenario. We give examples of
tripartite probability distributions from which it is impossible to extract any
kind of secret key, even in the asymptotic regime, although they cannot be
created by local operations and public communication. Moreover, we show that
bound information can be activated: three honest parties can distill a common
secret key from different distributions having bound information. Our results
demonstrate that quantum information theory can provide useful insight for
solving open problems in classical information theory.Comment: four page
General properties of Nonsignaling Theories
This article identifies a series of properties common to all theories that do
not allow for superluminal signaling and predict the violation of Bell
inequalities. Intrinsic randomness, uncertainty due to the incompatibility of
two observables, monogamy of correlations, impossibility of perfect cloning,
privacy of correlations, bounds in the shareability of some states; all these
phenomena are solely a consequence of the no-signaling principle and
nonlocality. In particular, it is shown that for any distribution, the
properties of (i) nonlocal, (ii) no arbitrarily shareable and (iii) positive
secrecy content are equivalent.Comment: 10 page
Bipartite entangled stabilizer mutually unbiased bases as maximum cliques of Cayley graphs
We examine the existence and structure of particular sets of mutually
unbiased bases (MUBs) in bipartite qudit systems. In contrast to well-known
power-of-prime MUB constructions, we restrict ourselves to using maximally
entangled stabilizer states as MUB vectors. Consequently, these bipartite
entangled stabilizer MUBs (BES MUBs) provide no local information, but are
sufficient and minimal for decomposing a wide variety of interesting operators
including (mixtures of) Jamiolkowski states, entanglement witnesses and more.
The problem of finding such BES MUBs can be mapped, in a natural way, to that
of finding maximum cliques in a family of Cayley graphs. Some relationships
with known power-of-prime MUB constructions are discussed, and observables for
BES MUBs are given explicitly in terms of Pauli operators.Comment: 8 pages, 1 figur
Secrecy content of two-qubit states
We analyze the set of two-qubit states from which a secret key can be
extracted by single-copy measurements plus classical processing of the
outcomes. We introduce a key distillation protocol and give the corresponding
necessary and sufficient condition for positive key extraction. Our results
imply that the critical error rate derived by Chau, Phys. Rev. A {\bf 66},
060302 (2002), for a secure key distribution using the six-state scheme is
tight. Remarkably, an optimal eavesdropping attack against this protocol does
not require any coherent quantum operation.Comment: 5 pages, RevTe
Multiple copy 2-state discrimination with individual measurements
We address the problem of non-orthogonal two-state discrimination when
multiple copies of the unknown state are available. We give the optimal
strategy when only fixed individual measurements are allowed and show that its
error probability saturates the collective (lower) bound asymptotically. We
also give the optimal strategy when adaptivity of individual von Neumann
measurements is allowed (which requires classical communication), and show that
the corresponding error probability is exactly equal to the collective one for
any number of copies. We show that this strategy can be regarded as Bayesian
updating.Comment: 5 pages, RevTe
Entanglement Capacity of Nonlocal Hamiltonians : A Geometric Approach
We develop a geometric approach to quantify the capability of creating
entanglement for a general physical interaction acting on two qubits. We use
the entanglement measure proposed by us for -qubit pure states (PRA
\textbf{77}, 062334 (2008)). Our procedure reproduces the earlier results (PRL
\textbf{87}, 137901 (2001)). The geometric method has the distinct advantage
that it gives an experimental way to monitor the process of optimizing
entanglement production.Comment: 8 pages, 1 figure