This paper discusses energy-time entanglement experiments and their relation to Einstein-Podolsky-Rosen (EPR) elements of reality. The interferometric experiment proposed by J. D. Franson in 1989 provides the background, and the main issue here is a detailed discussion on whether a Local Realist model can give the Quantum-Mechanical predictions for this setup. The Franson interferometer gives the same interference pattern as the usual Bell experiment (modulo postselection). Even so, depending on the precise requirements made on the Local Realist model, this can imply a) no violation, b) smaller violation than usual, or c) full violation of the appropriate statistical bound. This paper discusses what requirements are necessary on the model to reach a violation, and the motivation for making these requirements. The alternatives include using a) only the measurement outcomes as EPR elements of reality, b) the emission time as EPR element of reality, and c) path realism. The subtleties of this discussion needs to be taken into account when designing and setting up future experiments of this kind, intended to test Local Realism.

A postselection step in quantum cryptography based on energy-time entanglement makes the system insecure.

The digital currency Bitcoin has had remarkable growth since it was first proposed in 2008. Its distributed nature allows currency transactions without a central authority by using cryptographic methods and a data structure called the blockchain. In this paper we use the no-cloning theorem of quantum mechanics to introduce Quantum Bitcoin, a Bitcoinlike currency that runs on a quantum computer. We show that our construction of quantum shards and two blockchains allows untrusted peers to mint quantum money without risking the integrity of the currency. The Quantum Bitcoin protocol has several advantages over classical Bitcoin, including immediate local verification of transactions. This is a major improvement since we no longer need the computationally intensive and time-consuming method Bitcoin uses to record all transactions in the blockchain. Instead, Quantum Bitcoin only records newly minted currency which drastically reduces the footprint and increases efficiency. We present formal security proofs for counterfeiting resistance and show that a quantum bitcoin can be re-used a large number of times before wearing out -just like ordinary coins and banknotes. Quantum Bitcoin is the first distributed quantum money system and we show that the lack of a paper trail implies full anonymity for the users. In addition, there are no transaction fees and the system can scale to any transaction volume. * Electronic address: jonathan.jogenfors@liu.se IntroductionModern society relies on money to function. Trade and commerce is performed using physical tokens (coins, banknotes) or electronically (credit cards, bank transfers, securities). Recently, cryptographic currencies such as Bitcoin have emerged as a new method to facilitate trade in a purely digital environment without the need for a backing financial institution. Common to all functioning currencies is demand together with a controlled supply. Traditional, governmentbacked currencies mint currency according to rules decided by politics while Bitcoin works according to pre-defined rules. The currencies are then protected from counterfeiting, either by physical copy-protection in the case of coins, banknotes and cashier's checks, or in Bitcoin by applying cryptography. A detailed description of Bitcoin is given in Section 2.The laws of quantum mechanics have given rise to interesting applications in computer science, from the quadratic speedup of unstructured database search due to Grover [1] to the polynomial-time algorithm for integer factorization by Shor [2]. These "quantum" algorithms are faster than their classical counterparts, showing that some computing problems can be solved more efficiently if a classical computer is replaced by a quantum one. In addition, quantum states are disturbed when measured, which has given rise to to quantum cryptography protocols such as BB84 [3] and E91 [4], where the latter uses the quantum phenomena of entanglement. See Broadbent and Schaffner [5] for a recent survey of quantum cryptography.This begs the question: can quantum m...

The violation of Bell's inequality requires a well-designed experiment to validate the result. In experiments using energy-time and time-bin entanglement, initially proposed by Franson in 1989, there is an intrinsic loophole due to the high postselection. To obtain a violation in this type of experiment, a chained Bell inequality must be used. However, the local realism bound requires a high visibility in excess of 94.63% in the time-bin entangled state. In this work, we show how such a high visibility can be reached in order to violate a chained Bell inequality with six, eight, and ten terms.

In [1], Balygin and his coworkers consider a faked-state attack with detector blinding on Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol. They propose a countermeasure to this attack in a phase-coded system that watches for an abnormally low number of detections in the outer time slots 1 and 3. If the eavesdropper does not pay attention to the outer time slots, the countermeasure will reveal that the attack is being performed (see sections 6, 7 and figure 1(b) in [1]). This approach is conceptually similar to earlier work on non-blinding attacks [2].However, in the faked-state attack [3] the eavesdropper Eve uses a replica of Bob's setup to detect all quantum states emitted by Alice, then induces her exact detection results in Bob's apparatus. Since Eve is using a replica of Bob's setup, she would register detections in the outer time slots, then induce the same detection results in Bob's apparatus by resending additional bright light pulses centered in the time slots 1 and/ or 3. Note that Eve will occasionally register a double click, i.e. simultaneous detection events in both her detectors caused by dark counts or multiphoton pulses from Alice. She may