6,796 research outputs found
Discrimination of quantum states under locality constraints in the many-copy setting
We study the discrimination of a pair of orthogonal quantum states in the
many-copy setting. This is not a problem when arbitrary quantum measurements
are allowed, as then the states can be distinguished perfectly even with one
copy. However, it becomes highly nontrivial when we consider states of a
multipartite system and locality constraints are imposed. We hence focus on the
restricted families of measurements such as local operation and classical
communication (LOCC), separable operations (SEP), and the
positive-partial-transpose operations (PPT) in this paper.
We first study asymptotic discrimination of an arbitrary multipartite
entangled pure state against its orthogonal complement using LOCC/SEP/PPT
measurements. We prove that the incurred optimal average error probability
always decays exponentially in the number of copies, by proving upper and lower
bounds on the exponent. In the special case of discriminating a maximally
entangled state against its orthogonal complement, we determine the explicit
expression for the optimal average error probability and the optimal trade-off
between the type-I and type-II errors, thus establishing the associated
Chernoff, Stein, Hoeffding, and the strong converse exponents. Our technique is
based on the idea of using PPT operations to approximate LOCC.
Then, we show an infinite separation between SEP and PPT operations by
providing a pair of states constructed from an unextendible product basis
(UPB): they can be distinguished perfectly by PPT measurements, while the
optimal error probability using SEP measurements admits an exponential lower
bound. On the technical side, we prove this result by providing a quantitative
version of the well-known statement that the tensor product of UPBs is UPB.Comment: Comments are welcom
Discrimination of quantum states under locality constraints in the many-copy setting
We study the discrimination of a pair of orthogonal quantum states in the many-copy setting. This is not a problem when arbitrary quantum measurements are allowed, as then the states can be distinguished perfectly even with one copy. However, it becomes highly nontrivial when we consider states of a multipartite system and locality constraints are imposed. We hence focus on the restricted families of measurements such as local operation and classical communication (LOCC), separable operations (SEP), and the positive-partial-transpose operations (PPT) in this paper. We first study asymptotic discrimination of an arbitrary multipartite entangled pure state against its orthogonal complement using LOCC/SEP/PPT measurements. We prove that the incurred optimal average error probability always decays exponentially in the number of copies, by proving upper and lower bounds on the exponent. In the special case of discriminating a maximally entangled state against its orthogonal complement, we determine the explicit expression for the optimal average error probability, thus establishing the associated Chernoff exponent. Our technique is based on the idea of using PPT operations to approximate LOCC. Then, we show an infinite asymptotic separation between SEP and PPT operations by providing a pair of states constructed from an unextendible product basis (UPB): they can be distinguished perfectly by PPT measurements, while the optimal error probability using SEP measurements admits an exponential lower bound. On the technical side, we prove this result by providing a quantitative version of the well-known statement that the tensor product of UPBs is UPB
Entanglement as a resource for discrimination of classical environments
We address extended systems interacting with classical fluctuating
environments and analyze the use of quantum probes to discriminate local noise,
described by independent fluctuating fields, from common noise, corresponding
to the interaction with a common one. In particular, we consider a bipartite
system made of two non interacting harmonic oscillators and assess
discrimination strategies based on homodyne detection, comparing their
performances with the ultimate bounds on the error probabilities of
quantum-limited measurements. We analyze in details the use of Gaussian probes,
with emphasis on experimentally friendly signals. Our results show that a joint
measurement of the position-quadrature on the two oscillators outperforms any
other homodyne-based scheme for any input Gaussian state
Tight bounds on the distinguishability of quantum states under separable measurements
One of the many interesting features of quantum nonlocality is that the
states of a multipartite quantum system cannot always be distinguished as well
by local measurements as they can when all quantum measurements are allowed. In
this work, we characterize the distinguishability of sets of multipartite
quantum states when restricted to separable measurements -- those which contain
the class of local measurements but nevertheless are free of entanglement
between the component systems. We consider two quantities: The separable
fidelity -- a truly quantum quantity -- which measures how well we can "clone"
the input state, and the classical probability of success, which simply gives
the optimal probability of identifying the state correctly.
We obtain lower and upper bounds on the separable fidelity and give several
examples in the bipartite and multipartite settings where these bounds are
optimal. Moreover the optimal values in these cases can be attained by local
measurements. We further show that for distinguishing orthogonal states under
separable measurements, a strategy that maximizes the probability of success is
also optimal for separable fidelity. We point out that the equality of fidelity
and success probability does not depend on an using optimal strategy, only on
the orthogonality of the states. To illustrate this, we present an example
where two sets (one consisting of orthogonal states, and the other
non-orthogonal states) are shown to have the same separable fidelity even
though the success probabilities are different.Comment: 19 pages; published versio
A framework for bounding nonlocality of state discrimination
We consider the class of protocols that can be implemented by local quantum
operations and classical communication (LOCC) between two parties. In
particular, we focus on the task of discriminating a known set of quantum
states by LOCC. Building on the work in the paper "Quantum nonlocality without
entanglement" [BDF+99], we provide a framework for bounding the amount of
nonlocality in a given set of bipartite quantum states in terms of a lower
bound on the probability of error in any LOCC discrimination protocol. We apply
our framework to an orthonormal product basis known as the domino states and
obtain an alternative and simplified proof that quantifies its nonlocality. We
generalize this result for similar bases in larger dimensions, as well as the
"rotated" domino states, resolving a long-standing open question [BDF+99].Comment: 33 pages, 7 figures, 1 tabl
Quantum state discrimination bounds for finite sample size
In the problem of quantum state discrimination, one has to determine by
measurements the state of a quantum system, based on the a priori side
information that the true state is one of two given and completely known
states, rho or sigma. In general, it is not possible to decide the identity of
the true state with certainty, and the optimal measurement strategy depends on
whether the two possible errors (mistaking rho for sigma, or the other way
around) are treated as of equal importance or not. Results on the quantum
Chernoff and Hoeffding bounds and the quantum Stein's lemma show that, if
several copies of the system are available then the optimal error probabilities
decay exponentially in the number of copies, and the decay rate is given by a
certain statistical distance between rho and sigma (the Chernoff distance, the
Hoeffding distances, and the relative entropy, respectively). While these
results provide a complete solution to the asymptotic problem, they are not
completely satisfying from a practical point of view. Indeed, in realistic
scenarios one has access only to finitely many copies of a system, and
therefore it is desirable to have bounds on the error probabilities for finite
sample size. In this paper we provide finite-size bounds on the so-called Stein
errors, the Chernoff errors, the Hoeffding errors and the mixed error
probabilities related to the Chernoff and the Hoeffding errors.Comment: 31 pages. v4: A few typos corrected. To appear in J.Math.Phy
Local discrimination of mixed states
We provide rigorous, efficiently computable and tight bounds on the average
error probability of multiple-copy discrimination between qubit mixed states by
Local Operations assisted with Classical Communication (LOCC). In contrast to
the pure-state case, these experimentally feasible protocols perform strictly
worse than the general collective ones. Our numerical results indicate that the
gap between LOCC and collective error rates persists in the asymptotic limit.
In order for LOCC and collective protocols to achieve the same accuracy, the
former requires up to twice the number of copies of the latter. Our techniques
can be used to bound the power of LOCC strategies in other similar settings,
which is still one of the most elusive questions in quantum communication.Comment: 4 pages, 2 figures+ supplementary materia
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