Quantum nonlocality without entanglement

Bennett, Charles H.; DiVincenzo, David P.; Fuchs, Christopher A.; Mor, Tal; Rains, Eric M.; Shor, Peter W.; Smolin, John A.; Wootters, William K.

doi:10.1103/physreva.59.1070

Cited by 1,050 publications

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“…An entanglement is known to be very fragile to a local noisy channel. Furthermore, it was shown that a quantum state without entanglement contains non-locality [3]. L. Henderson and V. Vedral [4] suggested a method to obtain a classical correlation between parties.…”

Section: Introductionmentioning

confidence: 99%

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

et al. 2015

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Section: Introductionmentioning

confidence: 99%

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

et al. 2015

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“…For example, [1,2,3,4] discuss whether entanglement is necessary for quantum computation, [5] shows nonlocality without entanglement, and [6,7] discuss how much of the information carried by various quantum states is actually classical. We extend this discussion into another domain: quantum cryptography.…”

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confidence: 99%

Quantum Key Distribution with Classical Bob

2007

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Secure key distribution among two remote parties is impossible when both are classical, unless some unproven (and arguably unrealistic) computation-complexity assumptions are made, such as the difficulty of factorizing large numbers. On the other hand, a secure key distribution is possible when both parties are quantum. What is possible when only one party (Alice) is quantum, yet the other (Bob) has only classical capabilities? We present a protocol with this constraint, and prove its robustness against attacks: we prove that any attempt of an adversary to obtain information (and even a tiny amount of information) necessarily induces some errors that the legitimate users could notice.Introduction. Processing information using quantum twolevel systems (qubits), instead of classical two-state systems (bits), has lead to many striking results such as the teleportation of unknown quantum states and quantum algorithms that are exponentially faster than their known classical counterpart. Given a quantum computer, Shor's factoring algorithm would render many of the currently used encryption protocols completely insecure, but as a countermeasure, quantum information processing has also given quantum cryptography. Quantum key distribution was invented by Bennett and Brassard (BB84), to provide a new type of solution to one of the most important cryptographic problems: the transmission of secret messages. A key distributed via quantum cryptography techniques can be secure even against an eavesdropper with unlimited computing power, and the security is guaranteed forever.The conventional setting is as follows: Alice and Bob have labs that are perfectly secure, they use qubits for their quantum communication, and they have access to a classical communication channel which can be heard, but cannot be jammed (i.e. cannot be tampered with) by the eavesdropper. The last assumption can easily be justified if Alice and Bob can broadcast messages, or if they already share some small number of secret bits in advance, to authenticate the classical channel.In the well-known BB84 protocol as well as in all other suggested protocols, both Alice and Bob perform quantum operations on their qubits (or on their quantum systems). Here we present, for the first time, a protocol in which one party (Bob) is classical. For our purposes, any two orthogonal states of the quantum two-level system can be chosen to be the computational basis |0 and |1 . For reasons that will soon become clear, we shall now call the computational basis "classical" and we shall use the classical notations {0, 1} to describe the two quantum states {|0 , |1 } defining this basis. In the protocol we present, a quantum channel travels from Alice's lab to the outside world and back to her lab. Bob can access a segment of the channel, and whenever a qubit passes through that segment Bob can either let it go undisturbed or (1).-measure the qubit in the classical {0, 1} basis, and (2).-prepare a (fresh) qubit in the classical basis, and send it. If all parties were limited to...

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“…Nevertheless, the characterization of MES can be achieved as follows. The fact that LOCC protocols are strictly included in SEP [21] implies that if a state is not reachable (or convertible) deterministically via SEP it is also not reachable (or convertible) deterministically via LOCC. Hence, a state that is not reachable via SEP has to be in the MES.…”

Section: Theoremmentioning

confidence: 99%

“…They consist of enlarging the set of allowed operations such that one obtains classes of operations that are easier to deal with mathematically as for example PPT preserving maps [19] or separable transformations (SEP) (see [20] and references therein). As it will be important for our discussion we will focus here on SEP. LOCC is strictly included in SEP [21], i.e. any LOCC transformation corresponds to a completely positive trace-preserving map Λ whose action on any density matrix ρ can be written as Λ(ρ) = i X i ρX † i where…”

Section: Preliminariesmentioning

confidence: 99%

Few-Body Entanglement Manipulation

Spee

Vicente

Kraus

2016

Quantum [Un]Speakables II

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In order to cope with the fact that there exists no single maximally entangled state (up to local unitaries) in the multipartite setting, we introduced in [1] the maximally entangled set of n-partite quantum states. This set consists of the states that are most useful under conversion of pure states via Local Operations assisted by Classical Communication (LOCC). We will review our results here on the maximally entangled set of three-and generic four-qubit states. Moreover, we will discuss the preparation of arbitrary (pure or mixed) states via deterministic LOCC transformations. In particular, we will consider the deterministic preparation of arbitrary three-qubit (four-qubit) states via LOCC using as a resource a six-qubit (23-qubit) state respectively.

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Quantum nonlocality without entanglement

Cited by 1,050 publications

References 38 publications

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

Revisiting Quantum Discord for Two-Qubit X States: The Error Bound to an Analytical Formula

Quantum Key Distribution with Classical Bob

Few-Body Entanglement Manipulation

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