Aditi Sen De

Multiqubit W states lead to stronger nonclassicality than Greenberger-Horne-Zeilinger states

The N-qubit states of the W class, for N>10, lead to more robust (against noise admixture) violations of local realism, than the GHZ states. These violations are most pronounced for correlations for a pair of qubits, conditioned on specific measurement results for the remaining (N-2) qubits. The considerations provide us with a qualitative difference between the W state and GHZ state in the situation when they are separately sent via depolarizing channels. For sufficiently high amount of noise in the depolarizing channel, the GHZ states cannot produce a distillable state between two qubits, whereas the W states can still produce a distillable state in a similar situation.

Entanglement Enhances Security in Secret Sharing

In the last few years, the role of entanglement in different branches of physics has been studied extensively, ranging from many-body physics [1, 2] to quantum information processing [3]. In particular, the qualities and thresholds of entanglement for optimal quantum communication performance have been found, e.g. with regard to teleportation [4], dense coding [5], and cryptography [6]. The necessity of entanglement in quantum computation is still under investigation (see e.g. [7]). In a different context, there is an ongoing research on the behavior of entanglement in e.g. quantum phase transitions [2], local cloning [8], and local state distinguishing [9]. In this paper, we will investigate the advantage of entanglement in the security of a quantum communication task, known as secret sharing [10, 11], which is a communication scenario in which a sender Alice (A) wants to provide a (classical) message to two recipients (Bobs – B1, B2), in a way that each of the Bobs individually knows nothing about the message, but they can recover its content once they cooperate. In order to transmit a binary message string {ai}, Alice can then take a sequence of completely random bits {b1,i}, send it to B1, and at the same time send a sequence {b2,i} = {ai ⊕ b1,i} to B2, where ⊕ denotes addition modulo 2. Thus ai = b1,i⊕b2,i, assuring that the Bobs can recover the message if they cooperate, and yet none of them can learn anything on the message of Alice on his own, since the sequences {b1,i}, {b2,i} are completely random. An important issue is of course security, i.e. distributing the message in a way that no third (actually fourth!) party learns about it. This can be achieved using quantum cryptography (e.g. by the BB84 scheme [12]). Alice simply has to establish secret random keys, independently, with both Bobs, and use them as one-time pads to securely send bits in the way required by secret sharing. We call this the BB84 protocol. It has been argued [10] that a more natural way of using quantum states in secret sharing is to send entangled states to the Bobs, and as a result, avoid establishing random keys with each of the Bobs separately, by combining the quantum and classical parts of secret sharing in a single protocol. We call the protocol in [10, 11] as E4 (since it uses four entangled states). In this paper, we consider security thresholds for both E4 and BB84, i.e. the highest quantum bit error rates (QBERs) below which one-way distillation of secret key is possible. There are three main results proven in the paper. First, we provide a criterion for security of secret sharing, for which one-way classical distillation of secret key is possible between the sender and the receivers: the parallel of the Csiszár-Körner criterion in (single-receiver, classical) cryptography [13]. Secondly, we find the optimal quantum eavesdropping attacks on both E4 and BB84, that are individual, without quantum memory, and most importantly, local. Note that an attack which acts by local operations and classical communication (LOCC) on the particles sent through the two channels (A → B1 and A→ B2) is physically more relevant in this distributed receivers case. We show that the threshold QBER for E4 is about 18.2 % higher than that of BB84. This shows, to our knowledge for the first time, that it is more secure to use entangled encoding states in secret sharing. Thirdly, we provide an interesting general method for dealing with local eavesdropping attacks. The protocols. In our setting, a secret sharing protocol can be characterized by {|ψj,0〉, |ψj,1〉, σ 1 ⊗σ 2 }, where j labels the different encoding “bases” used, |ψj,a〉 are two-qubit states send by Alice to the Bobs if she uses basis j and wants to communicate the logical value a, while σ 1 ⊗σ 2 is a set of observables compatible with basis j (so that if the corresponding measurement is performed by the Bobs, it allows them to recover a proper logical bit of Alice). In practice, B1 (B2) randomly measures the observables σ 1 (σ j,k 2 ) on states received from Alice in each round. After the transmission is completed, the Bobs announce the observables they have used in each round to Alice, who, judging on whether this combination of observables is present in σ 1 ⊗σ j,k 2 for the particular j she had used in that round, tells the Bobs whether to keep or reject their measured results for that round – this is called the sifting phase. The BB84 protocol is defined as

Quantum discord length is enhanced while entanglement length is not by introducing disorder in a spin chain

Classical correlations of ground states typically decay exponentially and polynomially, respectively for gapped and gapless short-ranged quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an informationtheoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XY Z spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.Classical correlation functions of ground states typically decay exponentially and polynomially, respectively, for gapped and gapless short-range quantum spin systems. In such systems, entanglement decays exponentially even at the quantum critical points. However, quantum discord, an information-theoretic quantum correlation measure, survives long lattice distances. We investigate the effects of quenched disorder on quantum correlation lengths of quenched averaged entanglement and quantum discord, in the anisotropic XY and XYZ spin glass and random field chains. We find that there is virtually neither reduction nor enhancement in entanglement length while quantum discord length increases significantly with the introduction of the quenched disorder.

Fermion and spin counting in strongly correlated systems

We apply the atom counting theory to strongly correlated Fermi systems and spin models, which can be realized with ultracold atoms. The counting distributions are typically sub-Poissonian and remain smooth at quantum phase transitions, but their moments exhibit critical behavior, and characterize quantum statistical properties of the system. Moreover, more detailed characterizations are obtained with experimentally feasible spatially resolved counting distributions.