444 research outputs found
LOCC distinguishability of unilaterally transformable quantum states
We consider the question of perfect local distinguishability of mutually
orthogonal bipartite quantum states, with the property that every state can be
specified by a unitary operator acting on the local Hilbert space of Bob. We
show that if the states can be exactly discriminated by one-way LOCC where
Alice goes first, then the unitary operators can also be perfectly
distinguished by an orthogonal measurement on Bob's Hilbert space. We give
examples of sets of N<=d maximally entangled states in for
d=4,5,6 that are not perfectly distinguishable by one-way LOCC. Interestingly
for d=5,6 our examples consist of four and five states respectively. We
conjecture that these states cannot be perfectly discriminated by two-way LOCC.Comment: Revised version, new proofs added; to appear in New Journal of
Physic
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
Relativistic quantum coin tossing
A relativistic quantum information exchange protocol is proposed allowing two
distant users to realize ``coin tossing'' procedure. The protocol is based on
the point that in relativistic quantum theory reliable distinguishing between
the two orthogonal states generally requires a finite time depending on the
structure of these states.Comment: 6 pages, no figure
Limitations on Quantum Key Repeaters
A major application of quantum communication is the distribution of entangled
particles for use in quantum key distribution (QKD). Due to noise in the
communication line, QKD is in practice limited to a distance of a few hundred
kilometres, and can only be extended to longer distances by use of a quantum
repeater, a device which performs entanglement distillation and quantum
teleportation. The existence of noisy entangled states that are undistillable
but nevertheless useful for QKD raises the question of the feasibility of a
quantum key repeater, which would work beyond the limits of entanglement
distillation, hence possibly tolerating higher noise levels than existing
protocols. Here we exhibit fundamental limits on such a device in the form of
bounds on the rate at which it may extract secure key. As a consequence, we
give examples of states suitable for QKD but unsuitable for the most general
quantum key repeater protocol.Comment: 11+38 pages, 4 figures, Statements for exact p-bits weakened as
non-locking bound on measured relative entropy distance contained an erro
Strong and uniform convergence in the teleportation simulation of bosonic Gaussian channels
In the literature on the continuous-variable bosonic teleportation protocol
due to [Braunstein and Kimble, Phys. Rev. Lett., 80(4):869, 1998], it is often
loosely stated that this protocol converges to a perfect teleportation of an
input state in the limit of ideal squeezing and ideal detection, but the exact
form of this convergence is typically not clarified. In this paper, I
explicitly clarify that the convergence is in the strong sense, and not the
uniform sense, and furthermore, that the convergence occurs for any input state
to the protocol, including the infinite-energy Basel states defined and
discussed here. I also prove, in contrast to the above result, that the
teleportation simulations of pure-loss, thermal, pure-amplifier, amplifier, and
additive-noise channels converge both strongly and uniformly to the original
channels, in the limit of ideal squeezing and detection for the simulations.
For these channels, I give explicit uniform bounds on the accuracy of their
teleportation simulations. I then extend these uniform convergence results to
particular multi-mode bosonic Gaussian channels. These convergence statements
have important implications for mathematical proofs that make use of the
teleportation simulation of bosonic Gaussian channels, some of which have to do
with bounding their non-asymptotic secret-key-agreement capacities. As a
byproduct of the discussion given here, I confirm the correctness of the proof
of such bounds from my joint work with Berta and Tomamichel from [Wilde,
Tomamichel, Berta, IEEE Trans. Inf. Theory 63(3):1792, March 2017].
Furthermore, I show that it is not necessary to invoke the energy-constrained
diamond distance in order to confirm the correctness of this proof.Comment: 19 pages, 3 figure
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