4,054 research outputs found
Local distinguishability of orthogonal 2\otimes3 pure states
We present a complete characterization for the local distinguishability of
orthogonal pure states except for some special cases of three
states. Interestingly, we find there is a large class of four or three states
that are indistinguishable by local projective measurements and classical
communication (LPCC) can be perfectly distinguishable by LOCC. That indicates
the ability of LOCC for discriminating states is strictly more
powerful than that of LPCC, which is strikingly different from the case of
multi-qubit states. We also show that classical communication plays a crucial
role for local distinguishability by constructing a class of
states which require at least rounds of classical
communication in order to achieve a perfect local discrimination.Comment: 10 pages (revtex4), no figures. This is only a draft. It will be
replaced with a revised version soon. Comments are welcom
Semidefinite programming converse bounds for quantum communication
We derive several efficiently computable converse bounds for quantum
communication over quantum channels in both the one-shot and asymptotic regime.
First, we derive one-shot semidefinite programming (SDP) converse bounds on the
amount of quantum information that can be transmitted over a single use of a
quantum channel, which improve the previous bound from [Tomamichel/Berta/Renes,
Nat. Commun. 7, 2016]. As applications, we study quantum communication over
depolarizing channels and amplitude damping channels with finite resources.
Second, we find an SDP strong converse bound for the quantum capacity of an
arbitrary quantum channel, which means the fidelity of any sequence of codes
with a rate exceeding this bound will vanish exponentially fast as the number
of channel uses increases. Furthermore, we prove that the SDP strong converse
bound improves the partial transposition bound introduced by Holevo and Werner.
Third, we prove that this SDP strong converse bound is equal to the so-called
max-Rains information, which is an analog to the Rains information introduced
in [Tomamichel/Wilde/Winter, IEEE Trans. Inf. Theory 63:715, 2017]. Our SDP
strong converse bound is weaker than the Rains information, but it is
efficiently computable for general quantum channels.Comment: 17 pages, extended version of arXiv:1601.06888. v3 is closed to the
published version, IEEE Transactions on Information Theory, 201
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