415 research outputs found
The squashed entanglement of the noiseless quantum Gaussian attenuator and amplifier
We determine the maximum squashed entanglement achievable between sender and
receiver of the noiseless quantum Gaussian attenuators and amplifiers and we
prove that it is achieved sending half of an infinitely squeezed two-mode
vacuum state. The key ingredient of the proof is a lower bound to the squashed
entanglement of the quantum Gaussian states obtained applying a two-mode
squeezing operation to a quantum thermal Gaussian state tensored with the
vacuum state. This is the first lower bound to the squashed entanglement of a
quantum Gaussian state and opens the way to determine the squashed entanglement
of all quantum Gaussian channels. Moreover, we determine the classical squashed
entanglement of the quantum Gaussian states above and show that it is strictly
larger than their squashed entanglement. This is the first time that the
classical squashed entanglement of a mixed quantum Gaussian state is
determined
Faithful Squashed Entanglement
Squashed entanglement is a measure for the entanglement of bipartite quantum
states. In this paper we present a lower bound for squashed entanglement in
terms of a distance to the set of separable states. This implies that squashed
entanglement is faithful, that is, strictly positive if and only if the state
is entangled. We derive the bound on squashed entanglement from a bound on
quantum conditional mutual information, which is used to define squashed
entanglement and corresponds to the amount by which strong subadditivity of von
Neumann entropy fails to be saturated. Our result therefore sheds light on the
structure of states that almost satisfy strong subadditivity with equality. The
proof is based on two recent results from quantum information theory: the
operational interpretation of the quantum mutual information as the optimal
rate for state redistribution and the interpretation of the regularised
relative entropy of entanglement as an error exponent in hypothesis testing.
The distance to the set of separable states is measured by the one-way LOCC
norm, an operationally-motivated norm giving the optimal probability of
distinguishing two bipartite quantum states, each shared by two parties, using
any protocol formed by local quantum operations and one-directional classical
communication between the parties. A similar result for the Frobenius or
Euclidean norm follows immediately. The result has two applications in
complexity theory. The first is a quasipolynomial-time algorithm solving the
weak membership problem for the set of separable states in one-way LOCC or
Euclidean norm. The second concerns quantum Merlin-Arthur games. Here we show
that multiple provers are not more powerful than a single prover when the
verifier is restricted to one-way LOCC operations thereby providing a new
characterisation of the complexity class QMA.Comment: 24 pages, 1 figure, 1 table. Due to an error in the published
version, claims have been weakened from the LOCC norm to the one-way LOCC
nor
Squashed entanglement and approximate private states
The squashed entanglement is a fundamental entanglement measure in quantum information theory, finding application as an upper bound on the distillable secret key or distillable entanglement of a quantum state or a quantum channel. This paper simplifies proofs that the squashed entanglement is an upper bound on distillable key for finite-dimensional quantum systems and solidifies such proofs for infinite-dimensional quantum systems. More specifically, this paper establishes that the logarithm of the dimension of the key system (call it log 2K) in an ε-approximate private state is bounded from above by the squashed entanglement of that state plus a term that depends only ε and log 2K. Importantly, the extra term does not depend on the dimension of the shield systems of the private state. The result holds for the bipartite squashed entanglement, and an extension of this result is established for two different flavors of the multipartite squashed entanglement
Squashed entanglement for multipartite states and entanglement measures based on the mixed convex roof
New measures of multipartite entanglement are constructed based on two
definitions of multipartite information and different methods of optimizing
over extensions of the states. One is a generalization of the squashed
entanglement where one takes the mutual information of parties conditioned on
the state's extension and takes the infimum over such extensions. Additivity of
the multipartite squashed entanglement is proved for both versions of the
multipartite information which turn out to be related. The second one is based
on taking classical extensions. This scheme is generalized, which enables to
construct measures of entanglement based on the {\it mixed convex roof} of a
quantity, which in contrast to the standard convex roof method involves
optimization over all decompositions of a density matrix rather than just the
decompositions into pure states. As one of the possible applications of these
results we prove that any multipartite monotone is an upper bound on the amount
of multipartite distillable key. The findings are finally related to analogous
results in classical key agreement.Comment: improved version, 13 pages, 1 figur
Bounds on entanglement distillation and secret key agreement for quantum broadcast channels
The squashed entanglement of a quantum channel is an additive function of
quantum channels, which finds application as an upper bound on the rate at
which secret key and entanglement can be generated when using a quantum channel
a large number of times in addition to unlimited classical communication. This
quantity has led to an upper bound of on the capacity
of a pure-loss bosonic channel for such a task, where is the average
fraction of photons that make it from the input to the output of the channel.
The purpose of the present paper is to extend these results beyond the
single-sender single-receiver setting to the more general case of a single
sender and multiple receivers (a quantum broadcast channel). We employ
multipartite generalizations of the squashed entanglement to constrain the
rates at which secret key and entanglement can be generated between any subset
of the users of such a channel, along the way developing several new properties
of these measures. We apply our results to the case of a pure-loss broadcast
channel with one sender and two receivers.Comment: 35 pages, 1 figure, accepted for publication in IEEE Transactions on
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