My SLAC APS 11-11-11 paper in essence achieves an effective quasi "as-if" CTC.
"Localized Closed Timelike Curves Can Perfectly Distinguish Quantum States Todd A. Brun,1 Jim Harrington,2 and Mark M. Wilde1,3 1Communication Sciences Institute, Department of Electrical Engineering, University of Southern California, Los Angeles, California 90089, USA 2Applied Modern Physics (P-21), MS D454, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA 3Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543 (Received 7 November 2008; published 27 May 2009)
This scheme then breaks the security ofthe B92 quantum key distribution protocol . Even withno loss on the quantum channel, a CTC-assisted adversarycan learn the identity of every signal that Alice transmitsand then prepare and transmit the same state to Bob. Theadversary gains full information without producing anydisturbance. ...
We show that qubits traveling along closed timelike curves are a resource that a party can exploit to distinguish perfectly any set of quantum states. As a result, an adversary with access to closed timelike curves can break any prepare-and-measure quantum key distribution protocol. Our result also implies that a party with access to closed timelike curves can violate the Holevo bound.
Introduction.—The theory of general relativity points to the possible existence of closed timelike curves (CTCs) [1,2]. The grandfather paradox is one criticism raised to their existence, but Deutsch resolved this paradox by presenting a method for finding self-consistent solutions of CTC interactions .
Recently, several quantum information researchers have assumed that CTCs exist and have examined the consequences of this assumption for computation [4–6]. Brun showed that a classical treatment (assuming a lack of contradictions) allows NP-hard problems to be computed with a polynomial number of gates . Bacon followed with a purely quantum treatment that demonstrates the same reduction of NP-hard problems to P, along with a sketch of how to perform this reduction in a fault-tolerant manner . Aaronson and Watrous have recently established that either classical or quantum computers interacting with closed timelike curves can compute any function in PSPACE in polynomial time .
In this Letter, we show how a party with access to CTCs, or a ‘‘CTC-assisted’’ party, can perfectly distinguish nonorthogonal quantum states. The result has implications for fundamental protocols in quantum communication because a simple corollary is that a CTC-assisted party can break any prepare-and-measure quantum key distribution protocol [7–9]. (The security of such a scheme relies on the information-disturbance trade-off for identifying quantum states.) Furthermore, the capacity for quantum systems to carry classical information becomes unbounded. Our work here raises fundamental questions concerning the nature of a physical world in which closed timelike curves exist because it challenges the postulate of quantum mechanics that nonorthogonal states cannot be perfectly distinguished. A full theory of quantum gravity would have to resolve this apparent contradiction between the implication of CTCs and the laws of quantum mechanics. Note that any alternative source of nonlinearity would raise similar questions. ...
Conclusion.—We have shown how to exploit closed timelike curves to distinguish nonorthogonal states. Two direct implications are that one could break any prepare and- measure quantum key distribution protocol as well as violate the Holevo bound. If CTC qubits are treated as a free resource, then the achievable classical communication rate with a single noiseless quantum transmission is unbounded. We conjecture that the addition of any nonlinearity to quantum mechanics, such as that considered in Ref. , could be exploited similarly.
There are at least three ways to consider the implications of the results in this Letter. First, note that even if our Universe contains no stable wormholes, the existence of microscopic, short-lived closed timelike curves can still revolutionize information processing tasks if they persist long enough to engineer specific unitary interactions with qubits traveling their worldlines. Second, while issues such as the grandfather paradox are resolved by Deutsch’s formalism for stochastic and quantum bits traveling along closed timelike curves , the eroding of a finite capacity for classical communication with a qubit is a strong information theoretic argument casting doubt on the allowed existence of CTCs (similar in vein to the quantum communication complexity argument in Ref. ). A third tack is to consider whether Deutsch’s fixed point solution for resolving CTC paradoxes is itself somehow flawed. If the formalism is invalidated, then computational complexity results such as PCTC 1/4 PSPACE  should be reexamined. Any theory of quantum gravity will need to reconcile this intersection of quantum information theory and general relativity.
Finally, it should be interesting to study the effect of noise on the physical processes outlined in this Letter. For instance, how stable are these maps to perturbations in the input states? Recent work utilizing the Heisenberg picture may be a useful approach . We conjecture that a CTC-assisted party can construct a universal cloner with fidelity approaching one, at the cost of increasing the available dimensions in ancillary and CTC resources. One area of future work could be to optimize this fidelity given CTC resources of fixed dimension.
PRL 102, 210402 (2009) PHYSICAL REVIEW LETTERS week ending 29 MAY 2009