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Quantum deleting and Signalling

Arun K. Pati, Samuel L. Braunstein

Published Jan 1, 2003• 23 citations
OpenAlex

Abstract

It is known that if we can clone an arbitrary state we can send signal faster than light. Here, we show that deletion of unknown quantum state against a copy can lead to superluminal signalling. But erasure of unknown quantum state does not imply faster than light signalling.

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It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.

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Entanglement, Nonlocality, Superluminal Signaling and Cloning

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The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a machine is incompatible with quantum theory (i.e., the so-called No-Cloning Theorem) has been proved, for the first time, by the author of the present chapter in his referee's report to Herbert's paper. In the final part of the paper some recent (different but similarly not correct) proposals are analyzed and the reasons for which they are basically wrong are presented.

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•Oct 1, 2017•0 citations

Quantum no-deleting principle and some of its implications

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Unmeasureability of a quantum state has important consequences in practical implementation of quantum computers. Like copying, deleting of an unknown state from among several copies is prohibited. This is called no-deletion prinicple. Here, we present a no deleting principle for qudits. We obtain a bound on $N$-to-$M$ deleting and show that the quality of deletion drops exponentially with the number of copies to be deleted. In addition, we investigate conditional, state-dependent and approximate quantum deleting of unknown states. We prove that unitarity does not allow us to delete copies from an alphabet of two non-orthogonal states exactly. Further, we show that no-deleting principle is consistent with no-signalling.

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Limits on quantum deletion from no signaling principle

Aditya Jain, Indranil Chakrabarty

One of the fundamental restrictions that quantum mechanics imposes is the "No deletion Theorem" which tells us that given two identical unknown quantum states, it is impossible to delete one of them. But nevertheless if not perfect, people have tried to delete it approximately. In these approximate deleting processes our basic target is to delete one of the two identical copies as much as possible while preserving the other copy. In this brief report, by using the No communication theorem (NCT) (impossibility of sending signal faster than light using a quantum resource) as a guiding principle, we obtain a bound on the sum of the fidelity of deletion and the fidelity of preservation. Our result not only brings out the complementary relation between these two fidelities but also predicts the optimal value of the fidelity of deletion achievable for a given fidelity of preservation under no signaling constraint. This work eventually saturates the quest for finding out the optimal value of deletion within the NCT framework.

arXiv:1705.07013•May 19, 2017•0 citations
It is known that the stronger no-cloning theorem and the no-deleting theorem taken together provide the permanence property of quantum information. Also, it is known that the violation of the no-deletion theorem would imply signalling. Here, we show that the violation of the stronger no-cloning theorem could lead to signalling. Furthermore, we prove the stronger no-cloning theorem from the conservation of quantum information. These observations imply that the permanence property of quantum information is connected to the no-signalling and the conservation of quantum information.
The paper is a Chapter of a book. In it an exhaustive review of the proposals to send faster than light signals resorting to quantum nonlocality and the reduction process is presented, together with a critical analysis and rebuttal of all proposals. The most interesting part of the Chapter is the one in which the problem of quantum cloning is discussed. Actually, a proposal of superluminal signaling based on an hypothetical cloning machine has been presented by N. Herbert. The proposal does not work just because of the assumption that one can clone nonorthogonal states. The fact that such a machine is incompatible with quantum theory (i.e., the so-called No-Cloning Theorem) has been proved, for the first time, by the author of the present chapter in his referee's report to Herbert's paper. In the final part of the paper some recent (different but similarly not correct) proposals are analyzed and the reasons for which they are basically wrong are presented.
We show that nonlocality of quantum mechanics cannot lead to superluminal transmission of information, even if most general local operations are allowed, as long as they are linear and trace preserving. In particular, any quantum-mechanical approximate cloning transformation does not allow signaling. On the other hand, the no-signaling constraint on its own is not sufficient to prevent a transformation from surpassing the known cloning bounds. We illustrate these concepts on the basis of some examples.
What is proposed here is a simple modication in the quantum protocol [1] for achieving instantaneous teleportation of arbitrary quantum state from Alice to Bob even when Bob is several light years away. This modied quantum protocol is constructed by adding a step the in the celebrated quantum teleportation protocol [1]. It consists of the action of a unitary operator to be performed by Alice on the qubits in her possession before she does the Bell basis measurement. It is important to note that the existing quantum teleportation protocol [1] requires certain classical communication between the participants, Alice and Bob, and we are going to eliminate this classical communication through our modification. In the existing protocol [1] Alice requires sending the classical bits generated during her Bell basis measurement over a classical channel to Bob for Bob to use these classical bits to determine the exact recovery operation to be performed on the qubit(s) in his possession for creating the exactly identical copy of unknown quantum state that was with Alice and got destroyed during her Bell basis measurement. Alice cannot send the classical bits she obtained to Bob with the speed faster than that of light since it is the well known experimentally veried universal upper limit on the speed. We show that by incorporating suitable unitary operation to be performed by Alice on her qubits before the Bell basis measurement the requirement of the transmission of classical bits by Alice to Bob for the creation of the unknown quantum state by Bob at his place can be completely eliminated. Our modification in the teleportation protocols [1], [2] thus clearly demonstrates the enormous advantage of remaining in the quantum regime and avoiding the requirement of any classical communication for the teleportation of the quantum states.
Unmeasureability of a quantum state has important consequences in practical implementation of quantum computers. Like copying, deleting of an unknown state from among several copies is prohibited. This is called no-deletion prinicple. Here, we present a no deleting principle for qudits. We obtain a bound on NNN-to-MMM deleting and show that the quality of deletion drops exponentially with the number of copies to be deleted. In addition, we investigate conditional, state-dependent and approximate quantum deleting of unknown states. We prove that unitarity does not allow us to delete copies from an alphabet of two non-orthogonal states exactly. Further, we show that no-deleting principle is consistent with no-signalling.
One of the fundamental restrictions that quantum mechanics imposes is the "No deletion Theorem" which tells us that given two identical unknown quantum states, it is impossible to delete one of them. But nevertheless if not perfect, people have tried to delete it approximately. In these approximate deleting processes our basic target is to delete one of the two identical copies as much as possible while preserving the other copy. In this brief report, by using the No communication theorem (NCT) (impossibility of sending signal faster than light using a quantum resource) as a guiding principle, we obtain a bound on the sum of the fidelity of deletion and the fidelity of preservation. Our result not only brings out the complementary relation between these two fidelities but also predicts the optimal value of the fidelity of deletion achievable for a given fidelity of preservation under no signaling constraint. This work eventually saturates the quest for finding out the optimal value of deletion within the NCT framework.