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 of
the B92 quantum key distribution protocol [8]. Even with
no loss on the quantum channel, a CTC-assisted adversary
can learn the identity of every signal that Alice transmits
and then prepare and transmit the same state to Bob. The
adversary gains full information without producing any
disturbance. ...
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 [3].
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 [4]. 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 [5]. 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 [6].
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. [11], 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 [3], 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. [12]). 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 [6] 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 [13]. 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