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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

Category: MyBlog

Written by Jack Sarfatti

Published on Sunday, 25 December 2011 14:05

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