Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency

Lloyd, Seth; Maccone, Lorenzo; García−Patrón, Raúl; Giovannetti, Vittorio; Shikano, Yutaka; Pirandola, Stefano; Rozema, Lee A.; Darabi, Ardavan; Soudagar, Yasaman; Shalm, Lynden K.; Steinberg, Aephraim M.

doi:10.1103/physrevlett.106.040403

Cited by 139 publications

(179 citation statements)

References 30 publications

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“…(16), following the model of closed time-like curves considered in Refs. [33][34][35][36]. It is known that such an artificial rescaling of the probability of postselected outcomes has dramatic computational consequences [37].…”

Section: Is Given By S(a ⊗ B)mentioning

confidence: 99%

Quantum computations without definite causal structure

et al. 2013

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We show that quantum theory allows for transformations of black boxes that cannot be realized by inserting the input black boxes within a circuit in a pre-defined causal order. The simplest example of such a transformation is the classical switch of black boxes, where two input black boxes are arranged in two different orders conditionally on the value of a classical bit. The quantum version of this transformation-the quantum switch-produces an output circuit where the order of the connections is controlled by a quantum bit, which becomes entangled with the circuit structure. Simulating these transformations in a circuit with fixed causal structure requires either postselection, or an extra query to the input black boxes.

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Section: Is Given By S(a ⊗ B)mentioning

confidence: 99%

Quantum computations without definite causal structure

et al. 2013

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“…As we will see, this can produce surprising behavior. Bennett and Schumacher [4] and, independently, Svetlichny [5], offered an alternative model of CTCs, which was further developed by Lloyd et al [6][7][8]. This account simulates CTC interactions by quantum teleportation combined with postselection-hence, P-CTCs.…”

Section: Introductionmentioning

confidence: 99%

“…Following Aaronson's proof [15] that the complexity class Post-BQP (post-selected bounded-error quantum polynomial-time) is equivalent to PP, Lloyd et al [7] observed that quantum computers with access to P-CTCs could compute any problem in PP in polynomial time. The complexity class PP is the class of decision problems that a probabilistic Turing machine, running in polynomial time, accepts with probability at least 1/2 if and only if the answer is 'yes.'…”

Section: Introductionmentioning

confidence: 99%

Quantum interactions with closed timelike curves and superluminal signaling

Bub

Stairs

2014

Phys. Rev. A

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There is now a significant body of results on quantum interactions with closed timelike curves (CTCs) in the quantum information literature, for both the Deutsch model of CTC interactions (D-CTCs) and the projective model (P-CTCs). As a consequence, there is a prima facie argument exploiting entanglement that CTC interactions would enable superluminal and, indeed, effectively instantaneous signaling. In cases of spacelike separation between the sender of a signal and the receiver, whether a receiver measures the local part of an entangled state or a disentangled state to access the signal can depend on the reference frame. We propose a consistency condition that gives priority to either an entangled perspective or a disentangled perspective in spacelike separated scenarios. For D-CTC interactions, the consistency condition gives priority to frames of reference in which the state is disentangled, while for P-CTC interactions the condition selects the entangled state. Using the consistency condition, we show that there is a procedure that allows Alice to signal to Bob in the past via relayed superluminal communications between spacelike separated Alice and Clio, and spacelike separated Clio and Bob. This opens the door to time travel paradoxes in the classical domain. Ralph [1] first pointed this out for P-CTCs, but we show that Ralph's procedure for a 'radio to the past' is flawed. Since both D-CTCs and P-CTCs allow classical information to be sent around a spacetime loop, it follows from a result by Aaronson and Watrous [2] for CTC-enhanced classical computation that a quantum computer with access to P-CTCs would have the power of PSPACE, equivalent to a D-CTC-enhanced quantum computer.

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“…For example, it immediately follows that such a theory can also clone unknown quantum states-and thus behaves more like a classical probability theory where different density operators correspond to different points in the state space, and every point is perfectly distinguishable. 6 There already exist models of gravitational decoherence that satisfy these conditions, 21 and it would be exciting to see if this is true for other attempts to reconcile quantum theory with time travel, [22][23][24] or more general non-linear candidate theories of quantum gravity. 25,26 …”

Section: Discussionmentioning

confidence: 99%

Replicating the benefits of Deutschian closed timelike curves without breaking causality

et al. 2015

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In general relativity, closed timelike curves can break causality with remarkable and unsettling consequences. At the classical level, they induce causal paradoxes disturbing enough to motivate conjectures that explicitly prevent their existence. At the quantum level such problems can be resolved through the Deutschian formalism, however this induces radical benefits-from cloning unknown quantum states to solving problems intractable to quantum computers. Instinctively, one expects these benefits to vanish if causality is respected. Here we show that in harnessing entanglement, we can efficiently solve NP-complete problems and clone arbitrary quantum states-even when all time-travelling systems are completely isolated from the past. Thus, the many defining benefits of Deutschian closed timelike curves can still be harnessed, even when causality is preserved. Our results unveil a subtle interplay between entanglement and general relativity, and significantly improve the potential of probing the radical effects that may exist at the interface between relativity and quantum theory. INTRODUCTIONCausality aligns with our natural sense of reality. We expect there to be a natural chronology to our reality-two events should not be simultaneous causes for each other. The breaking of causality defies classical logic, resulting in causal paradoxes with no simple solution-the iconic example being the case where a man travels back in time to kill his own grandfather. Thus, physical predictions that break causality face intense scrutiny-often considered to be theoretical artifacts that are likely suppressed once we gain a more complete understanding of reality-motivating various chronology protection conjectures. 1 Nevertheless, causality breaking theories are consistent with current scientific knowledge. Closed timelike curves (CTCs) are valid solutions of Einstein's equations in general relativity. [2][3][4] Meanwhile, Deutsch put forward a model of CTCs, such that in the quantum regime, the resulting causal paradoxes always have selfconsistent solutions. 5 This resolution, however, has radical operational consequences. Many foundational constraints of quantum theory break. Non-orthogonal quantum states can be perfectly distinguished, the uncertainty principle can be violated, and arbitrary unknown quantum states can be cloned to any fixed fidelity. [6][7][8] In harnessing these effects, many problems thought to be intractable for standard quantum computers now field efficient solutions. 9-12 Though radical, these effects seem somewhat rationalized in the context of requiring broken causality-the sentiment being that they are curiosities that will vanish once causality is imposed.What happens, however, if causality is not strictly broken? In this context, Pienaar et al. considered a special case of Deutschian CTCs known as open timelike curves 13 (OTCs). Consider a particle that travels back in time with respect to a chronology-respecting

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Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency

Cited by 139 publications

References 30 publications

Quantum computations without definite causal structure

Quantum computations without definite causal structure

Quantum interactions with closed timelike curves and superluminal signaling

Replicating the benefits of Deutschian closed timelike curves without breaking causality

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