21 research outputs found
Disguising quantum channels by mixing and channel distance trade-off
We consider the reverse problem to the distinguishability of two quantum
channels, which we call the disguising problem. Given two quantum channels, the
goal here is to make the two channels identical by mixing with some other
channels with minimal mixing probabilities. This quantifies how much one
channel can disguise as the other. In addition, the possibility to trade off
between the two mixing probabilities allows one channel to be more preserved
(less mixed) at the expense of the other. We derive lower- and upper-bounds of
the trade-off curve and apply them to a few example channels. Optimal trade-off
is obtained in one example. We relate the disguising problem and the
distinguishability problem by showing the the former can lower and upper bound
the diamond norm. We also show that the disguising problem gives an upper bound
on the key generation rate in quantum cryptography.Comment: 27 pages, 8 figures. Added new results for using the disguising
problem to lower and upper bound the diamond norm and to upper bound the key
generation rate in quantum cryptograph
Profitable entanglement for channel discrimination
We investigate the usefulness of side entanglement in discriminating between
two generic qubit channels and determine exact conditions under which it does
enhance (as well as conditions under which it does not) the success
probability. This is done in a constructive way by first analyzing the problem
for channels that are extremal in the set of completely positive and
trace-preserving qubit linear maps and then for channels that are inside such a
set
Coherent Quantum Channel Discrimination
This paper introduces coherent quantum channel discrimination as a coherent
version of conventional quantum channel discrimination. Coherent channel
discrimination is phrased here as a quantum interactive proof system between a
verifier and a prover, wherein the goal of the prover is to distinguish two
channels called in superposition in order to distill a Bell state at the end.
The key measure considered here is the success probability of distilling a Bell
state, and I prove that this success probability does not increase under the
action of a quantum superchannel, thus establishing this measure as a
fundamental measure of channel distinguishability. Also, I establish some
bounds on this success probability in terms of the success probability of
conventional channel discrimination. Finally, I provide an explicit
semi-definite program that can compute the success probability.Comment: 12 pages, 5 figures, submission to ISIT 202
Two-message quantum interactive proofs and the quantum separability problem
Suppose that a polynomial-time mixed-state quantum circuit, described as a
sequence of local unitary interactions followed by a partial trace, generates a
quantum state shared between two parties. One might then wonder, does this
quantum circuit produce a state that is separable or entangled? Here, we give
evidence that it is computationally hard to decide the answer to this question,
even if one has access to the power of quantum computation. We begin by
exhibiting a two-message quantum interactive proof system that can decide the
answer to a promise version of the question. We then prove that the promise
problem is hard for the class of promise problems with "quantum statistical
zero knowledge" (QSZK) proof systems by demonstrating a polynomial-time Karp
reduction from the QSZK-complete promise problem "quantum state
distinguishability" to our quantum separability problem. By exploiting Knill's
efficient encoding of a matrix description of a state into a description of a
circuit to generate the state, we can show that our promise problem is NP-hard
with respect to Cook reductions. Thus, the quantum separability problem (as
phrased above) constitutes the first nontrivial promise problem decidable by a
two-message quantum interactive proof system while being hard for both NP and
QSZK. We also consider a variant of the problem, in which a given
polynomial-time mixed-state quantum circuit accepts a quantum state as input,
and the question is to decide if there is an input to this circuit which makes
its output separable across some bipartite cut. We prove that this problem is a
complete promise problem for the class QIP of problems decidable by quantum
interactive proof systems. Finally, we show that a two-message quantum
interactive proof system can also decide a multipartite generalization of the
quantum separability problem.Comment: 34 pages, 6 figures; v2: technical improvements and new result for
the multipartite quantum separability problem; v3: minor changes to address
referee comments, accepted for presentation at the 2013 IEEE Conference on
Computational Complexity; v4: changed problem names; v5: updated references
and added a paragraph to the conclusion to connect with prior work on
separability testin